Search

The variational level set model is widely used in image segmentation tasks due to its sound theoretical basis and reliable performance. However, it often faces limitations when dealing with images that contain intensity inhomogeneity and noise. To address this challenge, a novel variational level set model based on local-global function approximation (LSM-LGA) is proposed in this paper. In this approach, an approximation function space is first introduced for the input image. This space defines the function as a linear combination of a local approximation image and a global one, weighted by two coefficients and two complementary characteristic functions defined by a level set function. To achieve the optimal representation of the input image within this approximation function space, a hybrid-metric strategy that combines Euclidean distance and Jeffreys divergence is introduced. An alternating direction method of multiplier (ADMM) based on Euclidean distance is developed to solve for the optimal weight coefficients of the local and global approximation images. Additionally, gradient descent based on Jeffreys divergence is utilized to solve for the optimal level set function. Furthermore, the existence and uniqueness of the optimal approximation function are proven using the theory of projection onto convex sets. Extensive numerical experiments on natural and synthetic images with intensity inhomogeneity, textures, and noise validate that the LSM-LGA exhibits superior performance compared with several state-of-the-art models in terms of segmentation quality and computational efficiency. [ABSTRACT FROM AUTHOR]

There has been a continued need for technology to prevent the illegal use of music in online transactions and protect the rights of copyright holders. Recently, the types of attacks have become very diverse due to various online environments and content production methods. Therefore, an adaptive protection method aware of content and attacks is needed. This paper proposes a robust watermarking algorithm of a blind method to protect audio copyright in online streaming services. After detecting the transient points of the audio and processing the signals, they are used as reference triggers for frequency conversion. Transient triggers should be determined to be detected even after an attack. Audio samples are converted into the fast Fourier transform (FFT) frequency coefficients, and a watermark is embedded using the quantization index modulation (QIM) method. Various user-defined parameters can be adjusted during the watermark embedding process. Such parameters may be determined through experiments or an optimization process by targeting both the quality of the watermarked audio and the bit error rate (BER) of the watermark extracted after the attack. A watermark can be extracted using a similar process using parameters used in watermark embedding. If there is no information about the parameters used in embedding, the watermark can be extracted by tracking the minimum BER of the extracted watermark. Compared to the existing methods, the proposed watermarking technique showed excellent performance against most attacks and superior performance for filtering, shifting, and moving picture expert group (MPEG)-2 audio layer 3 (MP3) compression attacks. Therefore, the proposed method is likely a good solution for protecting audio copyright in an online streaming environment. [ABSTRACT FROM AUTHOR]

Sound event detection (SED) is a widely studied field that has achieved considerable success. The dynamic routing mechanism of capsule networks has been used for SED, but its performance in capturing global information of audio is still limited. In this paper, we propose a method for SED that by combining the capsule network with transformer leverages the strength of transformer in capturing global features with that of capsule network in capturing local features. The proposed method was evaluated on the DCASE 2017 Task 4 weakly labeled dataset. The obtained F-score and Equal Error Rate are 60.6% and 0.75, respectively. Compared to other baseline systems, our method achieves significantly improved performance. Keywords : Sound event detection, audio tagging, gated convolution, transformer, capsule network. [ABSTRACT FROM AUTHOR]

Due to the intricate underwater environment, underwater images frequently exhibit issues such as low contrast, detail loss, and color distortion, which significantly affect underwater operations. To alleviate these concerns and improve image quality, multi-scale cross-layer feature interaction GAN for underwater image enhancement model (MCFIGAN) is proposed in this paper. In the proposed model, we have designed a cross-layer feature interaction module (CLFIM) that fosters the fusion and transmission of features at various levels. This approach aims to extract more comprehensive feature information and enhance the robustness of the network model. Additionally, we have constructed a multi-scale feature module (MSFEM) to extract features at different levels and scales, enabling the model to gain a more comprehensive understanding of the object. By utilizing CLFIM and MSFEM, the generator is capable of producing a generated image that contains a wealth of feature information. Then, an enhanced discriminator module (EDM) is designed to improve the model's ability to identify generated images, thereby encouraging the generator network to generate more realistic underwater images. Finally, several training sessions utilizing multiple joint losses yield underwater images with characteristics of high contrast and rich detail. Through simulation experiments conducted on EUVP dataset and UIEB dataset, our proposed model is found to be superior to related models in terms of visual effect and quantitative index, particularly in contrast enhancement, detail recovery, and color restoration. [ABSTRACT FROM AUTHOR]

Due to the capability of supporting high-speed data communication with low energy cost, visible light communication has emerged as a promising supplement to radio frequency communications. However, the inherent nonlinearity caused by the light emitting diode could distort the signal, and thus posing a challenging problem for the system performance. In order to mitigate the nonlinear effect, reproducing kernel Hilbert spaces based schemes are recently investigated, where the minimum symbol error rate (MSER) criterion is proposed as a more suitable criterion compared to the commonly used minimum mean square error (MMSE), since MSER directly optimizes the symbol error rate. In this paper, we present a new post-distortion scheme by exploiting the MSER criterion based kernel affine projection algorithm to combat the signal distortion. In addition, to avoid the linearly increased computational complexity, the surprise criterion is introduced for sparsification. Simulations are carried out to validate the performance, and the numerical results show that the proposed method can obtain remarkable performance improvement over the available algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study the application of frequency response masking (FRM) technology in polyphase discrete Fourier transform (DFT) filter bank (FB). Due to the inability of FRM methods with conventional structure to simultaneously meet the needs of sharp transition band polyphase DFT FB to improve the signal-to-interference ratio of channelized signals and reduce the complexity of FBs, an improved conjugate frequency modulation frequency response masking (CFM-FRM) method is proposed. The proposed CFM-FRM method solves the problem by frequency modulation, and consumes less multipliers by taking advantage of the orthogonality between sub-filters in CFM-FRM FB. The efficient realization of CFM-FRM based polyphase DFT FB is derived and the multi-size configuration method is illustrated via coefficient decimation. We analyze the adaptability of related FRM works to polyphase DFT FB. The simulation and analysis show that the CFM-FRM method is applicable to polyphase DFT FB, the CFM-FRM based polyphase DFT FB has less multipliers than related methods in other works, and the performances of multi-size FBs meet the requirements. [ABSTRACT FROM AUTHOR]

Convolution theorems for the free metaplectic transformation (FMT) have great significance in the fields of fractional domain non-stationary signal processing theory and method. The existing results have found many applications in high-dimensional non-stationary signal sampling and filtering. However, a widely accepted closed-form expression has not yet been established. In this paper, we introduce the definitions of generalized convolution and product operators in the FMT domain, and use them to formulate the generalized convolution and product theorems for the FMT. The derived results include particular cases the existing convolution and product theorems for the FMT and also the convolution and product theorems for the Fourier transform, the fractional Fourier transform, and the linear canonical transform. We employ the generalized convolution theorem for the FMT in designing an optimal filter in the FMT domain. We also validate the correctness and effectiveness of the theoretical analysis through numerical experiments, demonstrating the superiority of the proposed optimal filtering method over the conventional ones. • We derive the generalized convolution and product theorems for the FMT, which have widely accepted closed-form expressions. The derived results can degenerate into convolution and product theorems in other transformation domains, such as the FT, FRFT and LCT. • We design the optimal filter for the FMT based on the proposed generalized convolution theory, which can be implemented in the time domain. The proposed method overcomes the defects of the multiplicative filters and is easy to implement. • We validate the correctness and effectiveness of the theoretical analysis through numerical simulations, demonstrating the superiority of the proposed optimal filtering method over the conventional ones. [ABSTRACT FROM AUTHOR]

Currently, weapon detection through video surveillance has been extensively studied using deep learning techniques by researchers. However, limited attention has been given to the detection of weapons in night time or dark scenarios. This paper aims to address this gap by proposing a novel approach for weapon detection specifically modified for low-light conditions. The authors demonstrate accurate and robust detection of weapons in challenging nighttime environments by modifying the deep learning model YOLOv7. The YOLOv7-DarkVision model has been developed by combining a brightening algorithm with the advanced image processing techniques and architecture of YOLOv7. A dataset of 15,367 images were collected for training of the model, along with five dark videos from various sources for performance evaluation. The derived detection model, which has a precision score of 95.50% and an F1-Score of 93.41%, performs absolutely well as a weapon detector. [ABSTRACT FROM AUTHOR]

Integrated sensing and communication (ISAC), millimeter wave (mmWave) massive multiple-input multiple-output (MIMO), and cell-free networks are emerged as some of the most potential physical layer enablers for the future wireless communication networks. In this paper, we consider a cell-free ISAC mmWave massive MIMO system with hybrid analog and digital precoders while accounting for the impacts of capacity-constrained fronthaul links. In the system, the digital baseband processing is dictated at a geographical scale while the analog precoders are carried out at each transmit access point (AP). Based on the characteristics of the considered model, we formulate the optimization problem as a function of power allocation and fronthaul compression strategies. To address this problem, two block coordinate descend (BCD)-based methods are proposed to alternatively solve the three decomposed subproblems corresponding to the power allocation, the downlink and backward fronthaul compression strategies. Simulation results indicate that the proposed schemes can achieve 90% performance of the optimal full-search (FS) method with much lower computational complexity. In addition, there exists an optimal configuration of APs, UEs, and antennas for a cell-free ISAC system with capacity-constrained fronthaul links. [ABSTRACT FROM AUTHOR]

At present, there are fewer studies on the polarization-sensitive mirrored array (PS-MA). Meantime, the estimation accuracy will decrease when the array element spacing is lower than half wavelength. This paper focuses on the aperture expansion of the PS-MA to improve the estimation accuracy. To this end, we establish the received signal model of the 2-D PS-MA with two perpendicular reflectors. Unlike the existing virtual array without polarization information, a novel model of the polarization-sensitive virtual array (PS-VA) is suggested based on the hybrid coarray technique. Additionally, the spatial smoothing (SS) technique is used to recover the rank of the covariance matrix, and the modulus value boundedness (MVB) of the polarization vector is used to reduce the dimension of the polarization-spatial spectrum. Then, the MVB-MA-SS algorithm is proposed for polarization-DOA estimation, which is much more efficient than the standard group-lasso algorithm used in the 1-D PS-MA. Numerical experiments show that the proposed algorithm can provide satisfactory estimation accuracy with significantly reduced computational complexity. [ABSTRACT FROM AUTHOR]

Most learned image compression methods focus on reducing the average code length of the image, which is unreasonable for the human visual system. Thus, appropriate bit allocation gains significance. This paper presents a novel end-to-end method for perceptual image compression, emphasizing content prioritization and a region-based hierarchical strategy. Firstly, our modified class activation mapping (CAM) can serve as the visual perception network for simulating human visual perception. On this basis, we develop an efficient compression system that leverages a discretized hybrid entropy model to allocate bits automatically according to the perceptual prioritization of image content. In our compression system, an image is compressed jointly and hierarchically with different standards, guided by the importance map extracted by the visual perception network. We introduce content-weighted perceptual metrics to evaluate visual quality more reasonably and objectively. Experiments on publicly available datasets demonstrate that our method outperforms traditional codecs and recent content-oriented learned methods in overall performance. Compared with other methods, the proposed method reconstructs images that are more friendly to the human visual system. [ABSTRACT FROM AUTHOR]

Neighborhood preserving embedding (NPE) is a classical method for dimensionality reduction (DR), and it is a linear version of the locally linear embedding method. However, NPE and all its variants only consider the one-way mapping from high-dimensional space to low-dimensional space. The projected low-dimensional data may not accurately and effectively "represent" the original samples. To address this problem, we improve NPE based on linear autoencoder. The conventional projection of NPE is considered as the encoding stage, and the decoder stage is a reconstruction from the low-dimensional space to the original high-dimensional space, which is the key to maintaining more significant information. Based on this, we propose a new NPE method called NPEAE (neighborhood preserving embedding with autoencoder) in this paper. NPEAE performs excellently in face recognition, handwritten character categorization, object classification, etc. The experiments on MNIST, COIL-20, the Extended Yale B, Olivetti Research Laboratory (ORL), and FERET show that NPEAE has a higher recognition accuracy than other comparative methods. [ABSTRACT FROM AUTHOR]

The placenta is an important organ that connects the fetus with the mother during pregnancy. Many pregnancies fail because of the placental abnormality. Nowadays, placental segmentation techniques based on magnetic resonance (MR) images are increasingly used to assist in the diagnosis of placental abnormalities. However, manual segmentation of the placenta is unreliable and time-consuming. In comparison to manually segmentation methods, the CNN-based methods perform better. However, due to the limitations of the fixed geometric structures in the traditional convolution, the features of the edge are not completely obtained. That is the challenge in placenta segmentation. By incorporating offsets into the regular grid sampling locations of standard convolution, deformable convolution allows for the utilization of spatial information to its full potential. Therefore, in this paper, we proposed a fully automatic placental segmentation method based on deformable convolution, termed as Deformable Convolution O-shape Network (DCO-Net). Specifically, we adopt the U-shaped architecture and employed a bi-directional O-shaped route by adding backward skip connections. The bi-directional O-shaped route recurrently reused the building blocks without introducing any extra parameters. To evaluate the performance of the proposed DCO-Net, a total of 871 MR images from 20 pregnant women were used for the experiments. The dice and average symmetric surface distance (ASSD) obtained by DCO-Net were 0.8488 and 3.0976, respectively. The experimental results demonstrate that the proposed DCO-Net is more efficient for automatic placental segmentation compared with the other competitive approaches. [ABSTRACT FROM AUTHOR]

Target detection is pivotal for modern urban computing applications. While image-based techniques are widely adopted, they falter under challenging environmental conditions such as adverse weather, poor lighting, and occlusion. To improve the target detection performance under complex real-world scenarios, this paper proposes an intelligent integrated optical camera and millimeter-wave (mmWave) radar system. Utilizing both physical knowledge and data-driven methods, a long-term robust radar-camera fusion algorithm is proposed to solve the heterogeneous data fusion problem for detection improvement. For the occlusion scenarios, the proposed algorithm can effectively detect occluded targets with the help of memory through performing long-term detection. For dark scenarios with low-light conditions, the proposed algorithm can effectively mark the target in the dark picture as well as provide rough stickman imaging. The above two innovative functions of the hybrid optical camera and mmWave radar system are tested in real-world scenarios. The results demonstrate the robustness and significant enhancement in the target detection performance of our integrated system. [ABSTRACT FROM AUTHOR]

Array antenna with reconfigurable elements can further suppress the peak sidelobe level (PSLL) by selecting reconfigurable element pattern (REP) combination according to the variation of the beam directions. However, the pattern selection for N array elements from K possible REPs is a typical non-deterministic polynomial-hard problem, resulting in the REP selection being intractable even with small N and K. To solve this REP selection problem effectively, this paper proposes an improved genetic algorithm to shrink the REP combinations that contain the suboptimal one. As a result, the proposed algorithm can adaptively select the best REP combination for different scanning beams by searching a relatively minor solution space. The alternating direction multiplier method is used to accelerate the computational speed of optimizing the array excitation. Array antennas with two-type REPs and three-type REPs, respectively, are simulated with high-frequency simulation software (HFSS) to validate the superiority of the proposed algorithm. Comparisons with the existing algorithms show that the proposed algorithm can select a superior REP combination to obtain 1 dB to 3 dB lower PSLL for different scanning beams. [ABSTRACT FROM AUTHOR]

The issue of adaptive detection for double subspace (DOS) signals under the Gaussian noise background is investigated in this paper. The DOS signal has the special structure where the rows and columns of the matrix-valued signal lie in known subspaces with unknown coordinates. To deal with the DOS signal detection problem, two kinds of Gradient tests are proposed in homogeneous environments and partially homogeneous environments. Remarkably, the Durbin test, as well as its two-step version, is also used for the detector design, which is consistent with the existing methods. To evaluate the performance of the proposed methods, both simulated data and real data collected by IPIX radar are used. The results indicate that the Gradient tests ensure the constant false alarm rate property. Furthermore, the proposed detectors obtain relatively robust characteristics and achieve superior performance to existing competitors in some scenarios. [ABSTRACT FROM AUTHOR]

Electroencephalogram (EEG) signals contains a major role in examining the behavior of brain activity. Moreover, these signals are contaminated with artifacts, which may affect the EEG signal analysis. The EEG performs as the low spatial resolution in the unimodal analysis. Owing to the highly time-consumption procedure, the removal of artifact techniques cannot be applied in practical applications. In existing works, automatic artifact removal techniques are ineffective for eliminating the artifacts in the EEG signals. Thus, the core of this concept is to design a low complexity aware, intelligent artifacts removal model using deep learning. This paper attempts to introduce a 1-Dimensional-Convolutional Neural Network with a Weighted Deep Feature (1D-CNN-WDF), which acts as a filter to remove the unnecessary noise in EEG signals. The WDF extraction in 1D-CNN-WDF is developed by combining the Coyote Optimization Algorithm (COA), and Bird Swarm Algorithm (BSA) named Hybrid Bird-COA (HB-COA). The same hybrid algorithm is used for the tuning of model parameters in 1D-CNN-WDF. The analysis results confirm that the recommended method is more enriched than recently introduced methods when considering the improved Signal to Noise Ratio (SNR), less Mean Squared Error (MSE), and reduced computational complexity, which shows that the suggested method is attained the superior reconstruction quality. [ABSTRACT FROM AUTHOR]

This paper proposes two methods for multi-wide null steering in the beampattern of preconfigured partially adaptive planar array antennas using convex optimization and sparse recovery theory. The array elements are split into two categories. One of which is nonadjustable or has fixed excitations, and the other is adjustable. The weights of the adjustable part are perturbed to form wide nulls at the interference directions. In the first proposed method, all the adaptive array elements are used to steer the nulls. Here, convex optimization is used to obtain the required weight perturbations of all the adaptive elements. In addition to the constraints that are needed to impose the nulls, constraints were added to mitigate the pointing error and the lower peak-to-sidelobe ratio (PSLR) problems. In the second proposed method, the optimization problem is cast as a sparse recovery problem to reduce the number of elements to be perturbed from the set of adjustable elements only. The optimization problem is then relaxed to achieve a convex optimization problem and solved iteratively to cut down the number of radiating elements which needs to be perturbed from the set of adjustable elements. Simulations were conducted for different sizes of planar arrays up to a few hundred antennas and different configurations of adjustable elements. The results showed that changing the excitations of only 20-35% of the adjustable array elements is sufficient to steer the nulls without any pointing error or decrease in the PSLR. Also, the interference rejection ratio (IRR) achieved by the proposed methods is better than the minimum mean square error (MMSE) analytical solution. [ABSTRACT FROM AUTHOR]

The Elo algorithm, renowned for its simplicity, is widely used for rating in sports tournaments and other applications. However, despite its widespread use, a detailed understanding of the convergence characteristics of the Elo algorithm is still lacking. Aiming to fill this gap, this paper presents a comprehensive (stochastic) analysis of the Elo algorithm, considering round-robin tournaments. Specifically, analytical expressions are derived describing the evolution of the skills and performance metrics. Then, taking into account the relationship between the behavior of the algorithm and the step-size value, which is a hyperparameter that can be controlled, design guidelines and discussions about the performance of the algorithm are provided. Experimental results are shown confirming the accuracy of the analysis and illustrating the applicability of the theoretical findings using real-world data obtained from SuperLega, the Italian volleyball league. [ABSTRACT FROM AUTHOR]

Glaucoma is a prevalent eye disease that is responsible for causing blindness worldwide. To diagnose glaucoma, the cup-to-disc ratio (CDR) is an important factor. We introduce MRSNet, a novel segmentation network that incorporates encoding and decoding structures. The key innovation of this network is the application of convolutional block with large kernel convolutional attention to the task of medical image segmentation for optic cup and disc. By combining the benefits of residual and self-attention, our network achieves improved performance. The coding region of the network utilizes convolutional block with large kernel convolutional attention, enabling the extraction of multi-scale features with lower computational resources while also enhancing spatial attention. The self-attention layer acts as a transition between the encoding and decoding regions, capturing long connection information and providing additional image details. To further enhance segmentation performance, we employ a multi-resolution image combination approach and adaptively extract the input form using the compression and excitation module. Additionally, we propose a novel approach that combines the principle of consistency of deep supervision mechanisms with cross-entropy and Dice loss to guide the network towards accurate segmentation. In this study, we utilized a five-fold cross-validation method to train our network model. We then performed experimental validation and evaluation on three widely-used datasets, namely REFUGE, DRISHTI-GS, and RIM-ONE-r3. Our model achieved impressive results in the cup-to-disc ratio metric, which accurately reflects the segmentation effect. Specifically, we achieved scores of 0.0242, 0.0941, and 0.0158 for the aforementioned datasets, respectively. These scores outperformed some current classical algorithms. The experimental results demonstrate that the method proposed in this paper has the capability to extract more comprehensive information about the optic cup and disc, with the ability to generalize across different datasets. Furthermore, it shows that the convolutional block with large kernel convolutional attention module can be effectively utilized for the segmentation task of optic cup and disc. These findings provide a valuable research foundation for future researchers. [ABSTRACT FROM AUTHOR]

The existing methodologies for hybrid narrow-band active noise control (HNANC) systems utilises variants of the FXLMS algorithm, which typically resulted in degraded convergence and steady-state performance. In this paper, a class of variable step size (VSS) adaptive algorithms are explicitly developed for a HNANC system analyses and the convergence as well as the steady-state performance of the proposed framework are evaluated in comparison to the existing state-of-the-art. For an HNANC system designed to operate in a multiple noise environment, the VSS filtered-x LMS (VSSFXLMS) and momentum VSS filtered- x weight accumulated least mean square (MVSS-FXWALMS) algorithms are proposed. The proposed algorithm employs a variable step size that is inspired by the variable momentum factor, and combines these two parameters to drive the FXWALMS algorithm for an HNANC system in order to accomplish maximum noise reduction. In a multiple noise environment setup for an HNANC system, the proposed algorithm surpasses the state-of-the-art in nearly all conventional operating conditions. A detailed performance analysis of the proposed algorithm has been carried out using mean noise reduction ratio, steady-state power spectra at different conditions. The results demonstrate a significant improvement in noise reduction performance compared to the counterparts. [ABSTRACT FROM AUTHOR]

Dual-function radar communication (DFRC) system exploits a hardware platform to achieve both radar and communication functions. Compared to utilizing separate radar and communication systems, DFRC has better performance in spectrum utilization. In this paper, assisted by orthogonal frequency division multiplexing-multiple input multiple output (OFDM-MIMO) radar, we propose a DFRC system architecture combining generalized space shift keying (GSSK) modulation and subcarrier index modulation (SIM) techniques. In this scheme, linear frequency modulation (LFM) signal is explored as the transmission waveform of OFDM-MIMO radar to complete the radar function. Furthermore, the proposed scheme combines GSSK and SIM to carry the communication information to the antenna index and subcarrier index to complete the communication function. Based on this architecture, a novel low complexity frequency detection communication demodulation algorithm is proposed, and the achievable rate communication performance of the system is analyzed. Numerical and simulation results verify the feasibility and effectiveness of the proposed system. [ABSTRACT FROM AUTHOR]

This paper studies a robust moving target detection problem for frequency diverse array multiple-input multiple-output (FDA-MIMO) radar with a target embedded in Gaussian clutter with an unknown covariance matrix. We focus on the case of signal mismatch where the errors exist in the transmit-receive vector and Doppler steering vector. To solve the above detection problem, we adopt the subspace approach, where the true and nominal transmit-receive and Doppler steering vectors are assumed to lie in four-dimensional and two-dimensional subspaces, respectively, for the special framework for FDA-MIMO radar. At the detector design stage, we propose three robust adaptive detectors based on the one-step generalized likelihood ratio test (GLRT), two-step GLRT, and Wald test, respectively, with the training data free. The proposed detectors own the constant false alarm rate (CFAR) property against the clutter covariance matrix. The numerical examples validate the effectiveness of the proposed detectors. [ABSTRACT FROM AUTHOR]

Orthogonal polyphase sequence sets with desirable properties have numerous applications in sensing fields, e.g., a monostatic radar transmitting such waveforms can effectively counter the coherent repeater jamming (CRJ). However, due to imperfections in practical systems, the delicately designed sequences may suffer significant distortion and reduction in performance when transmitted as radar waveforms. In this paper, we focus on the problem of designing polyphase sequence sets with good correlation properties under spectral distortion. To address this issue, we first introduce a new metric called distortion correlation properties (DCorr), which quantifies the quality of such sequence sets. Subsequently, a majorization-minimization (MM)-based iterative algorithm is developed to solve the problem of minimizing DCorr. A number of numerical examples are provided to demonstrate the effectiveness of the proposed method in improving the correlation properties of polyphase sequence sets under spectral distortion. The results also validate that our proposed algorithms can effectively mitigate the performance reduction caused by the imperfections in practical radar systems simply. [ABSTRACT FROM AUTHOR]

Multi-modal fusion can exploit complementary information from various modalities and improve the accuracy of prediction or classification tasks. In this paper, we propose a semi-tensor product-based multi-modal factorized multilinear (STP-MFM) pooling method for information fusion in sentiment analysis. Initially, we extend the bilinear pooling to multilinear pooling for multi-modal fusion. Next, we propose a multi-modal factorized multilinear pooling (MFM) method, which parametrizes the fusion weight tensor with the Tucker decomposition. Furthermore, we propose to use Semi-Tensor Product (STP) in MFM to obtain more flexible and compact tensor decompositions with smaller factor sizes, this process permits the connection of two factors with different dimensionality by using the semi-tensor mode product. The proposed method removes the limitation of dimension consistency in matrix multiplication and expresses the information in a more compact structure with less memory. Most importantly, the STP leverages temporal and spatial information from video, audio, and text, producing a better representation of intra-modality correlations. We verified the proposed STP-MFM for sentiment analysis on the CMU-MOSI and the IEMOCAP datasets. The experimental results indicate that the proposed method outperforms the baselines by a significant margin. Moreover, it also gains a superior training speed and lowers model complexity. • We extend the idea of bilinear pooling to multilinear pooling, which can fuse the information from more than two modalities and enhance the representation capacity of fused features. Moreover, it avoids the parameter of exponential growth when more than two modalities are fused simultaneously. • We propose a multi-modal factorized multilinear pooling method (MFM) based on Tucker tensor decomposition, which can decrease the data redundancy and parameter complexity while can promote fast and rich interactions between modalities in modeling sparse. • We present a semi-tensor product-based multi-modal factorized multilinear pooling (STP-MFM) method. The STP-MFM eliminates the limitation of dimension consistency in matrix multiplication and expresses the information in a more compact structure with less memory. • The effectiveness of the proposed method is evaluated using experiments on two different multi-modal datasets. [ABSTRACT FROM AUTHOR]

This paper proposes a new robust cost function, which combines the inverse hyperbolic sine cost function and the generalized maximum correlation entropy. Based on this cost function, a robust diffusion generalized correntropy-based inverse hyperbolic sine (DGCIHS) algorithm is proposed. The mean-square performance and convergence analysis are performed to theoretically prove the reliability of the algorithm. Simulation experimental results confirm the theoretical analysis, demonstrating the algorithm's robustness. Compared with similar algorithms, the robust diffusion generalized maximum correlation entropy inverse hyperbolic sinusoidal algorithm demonstrates superior performance. [ABSTRACT FROM AUTHOR]

Non-contact heart rate measurement based on face video is rapidly developed due to its comfort and wide application. However, it is difficult to extract the pulse signals for non-contact heart rate measurement due to the various interference factors, such as illumination variation, head motion and face expression. In this paper, we propose group sparse representation to reconstruct the pulse signals, then estimate the heart rate based on the fact that the real heart rate is consistent at the same time from different sub-regions. Specifically, we formulate the reconstruction of pulse signals as group sparse representation problem and require the raw signals of all the sub-regions to be similar sparse representation. Firstly, we use the face detection algorithm to obtain the region of interest (ROI) and divide it into sub-regions, followed by the distortion compensation of color signals from different sub-regions. Then we extract the sub-region chrominance signals and select the high-quality chrominance signals to construct the raw pulse signals matrix. After that, we construct a mixed pulse dictionary containing discrete cosine bases and wavelet bases considering the periodicity and pulsatility of the pulse signals. Finally, we conduct group sparse representation to reconstruct the pulse signals and estimate the heart rate via spectral analysis based on the reconstructed pulse signals. Experimental results on three public datasets show that this method outperforms most existing heart rate measurement methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach to improve the accuracy of human pose estimation, which is a technique to predict the coordinates of human body keypoints in an input image. Existing methods often focus on keypoint localization without considering their positional relationships. We introduce two regularization terms based on SimCC coordinates: Bone loss and Sum loss of visible keypoints. They constrain the spatial relationship and visible number of keypoints respectively. To better leverage these loss functions, we enhance the deconvolution module with a combination of convolution and bilinear interpolation, which effectively recovers image resolution and preserves more feature map details. We conduct a comprehensive evaluation of our approach on the COCO dataset. Our approach enhances the accuracy of the top-down method by incorporating HRNet-W48. We achieve 77.7AP on the COCO validation set, which is competitive with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

An integrated navigation/communication signal is proposed in our previous work. It considered Cyclic Code Shift Keying (CCSK) as a communication signal combined with traditional Global Navigation Satellite System (GNSS) signal, further the optimized cyclic shift set for communication signal was designed. Based on the previous research, a fuzzy judging algorithm is proposed to acquire the integrated signal in this paper. This algorithm adopts segmenting correlation domain to improve the integrated signal transmission robustness. Moreover, in order to solve incompatibility problem between the integrated signal and binary communication system, a strategy for optimizing cyclic shift set basing on dual-thresholds is proposed, in which interleaving coding is used to resist interference. The fault-tolerant rate of proposed algorithm is improved by about 87% compared with traditional algorithms. Based on the compatibility, the Bit Error Rate (BER) of the integrated signal decreases obviously, and the reliability of the communication system is improved greatly, benefiting from that interleaving technology and error correction coding is applied. [ABSTRACT FROM AUTHOR]

Few-shot segmentation is a task that aims to generalize well to segment novel categories in images leveraging only a few annotated samples. Most existing methods adopt the prototype learning architecture, where support prototype vectors are expanded and concatenated with query features to perform conditional segmentation. However, such framework may potentially focus more on query features and neglect the similarity between support and query features. Moreover, it is valuable to mine information and latent categories in the background region to improve method generalization. To address these issues, this paper proposes a contrastive enhancement approach that can mine latent prototypes from background regions and leverage latent classes to raise the utilization of similarity information between prototype and query features. Specifically, a latent prototype sampling module is proposed to generate pseudo-mask and novel prototypes from the region with same category. It is based on feature similarity in high-level features, which is cost-effective for conducting end-to-end learning. This module does not require prior knowledge of object categories and has no strong dependence on clustering numbers like cluster-based method. Besides, a contrastive enhancement module is developed to drive models to provide different predictions with the same query features. It introduces the latent prototypes to regularize the decoder to concentrate more on similarity between support and query features. The proposed modules can be used as auxiliary modules to flexibly integrate into other baselines for better segmentation performance. Extensive experiments show our approach remarkably improves the performance of state-of-the-art methods for 1-shot and 5-shot segmentation, especially outperforming baseline by 5.9% and 7.3% for 5-shot task on Pascal- 5 i and COCO- 20 i. [ABSTRACT FROM AUTHOR]

The design of integrated radar-communication (IRC) systems is seen as a promising solution to alleviate the congestion of spectrum resource in recent years. Additionally, with the deployment of large-scaled arrays in base stations, sparse array design via antenna selection has become prominent to reduce system overheads and alleviate mutual coupling effect. In this paper, we propose a joint design of antenna selection and transmit beamformer for IRC systems to realize the dual operations of radar and communications. Specifically, we propose a joint model that achieves a trade-off between minimizing the total number of antennas for IRC and suppressing the peak sidelobe level (PSL) of overall transmit beampattern with well-controlled mainlobe ripples. Unlike the existing schemes that focus on individual beamformer design with varying sparse array configurations, we impose a group sparsity on the beamforming matrix and jointly optimize multiple beamformers to obtain a common sparse array for the constellation of all communication symbols. To solve the resulting non-convex problem, we employ the alternating direction method of multipliers to split the original problem into parallel subproblems which are then solved iteratively. Simulation results illustrate the superiority of the proposed method over the conventional approaches in obtaining a lower PSL using fewer antennas with dual functions. [ABSTRACT FROM AUTHOR]

In this paper, we develop an orthogonal time frequency space (OTFS) modulation based integrated (radar) sensing and communication (ISAC) technique, namely OTFS-ISAC, for the high mobility multiuser system. In particular, at the transmitter, it can alternate the modes between sensing and communication using time division multiplexing so that it takes advantage of radar assistance to design the OTFS frame structure for reducing the overhead of guard symbols. At the receiver, based on the embedded pilot-aided channel estimation, it employs zero-forcing (ZF) equalization. For performance analysis, we derive the error probability of channel estimation based on radar sensing, and find the outage probability of downlink communication. Then, we introduce an adaptive power allocation scheme at the transmitter to optimize the outage probability of the communication link. Our simulations show that, by properly selecting N , M , and the pilot symbol strength, the proposed OTFS-ISAC scheme can reduce the overhead of guard symbols while achieving promising reliability performance of the downlink transmission with relative low channel estimation error. [ABSTRACT FROM AUTHOR]

This paper presents a novel Poisson multi-Bernoulli mixture (PMBM) filter for tracking multiple resolvable group targets (MRGT) based on graph theory. Firstly, the number of groups and the relationships between members within the group are modelled by the adjacency matrix. Then, considering that a single dynamic evolution model is insufficient to guarantee stable tracking performance for group targets, the virtual leader-follower model (VLFM) is introduced to predict the evolution trend of unknown and potentially detected targets, respectively. Furthermore, we prove the conjugation of the proposed algorithm with the probability generating functionals (PGF) and give a detailed implementation of the Gaussian mixture (GM). Based on the coexistence scenario of splitting, merging and non-linear motion of the group targets, the simulation results show the effectiveness of the proposed algorithm in comparison with the existing methods. [ABSTRACT FROM AUTHOR]

In practical FIR digital filter applications it is often necessary to represent the filter coefficients with a finite number of bits. The finite wordlength coefficient restriction reduces the filter quality and increases the filter deviation. This increase can be reduced substantially if the optimal finite wordlength coefficients are used. Computing these coefficients is more difficult and can be slow. It was shown before that the computation time can be significantly reduced with the help of a lower bound on the deviation increase. Derivation of a new algorithm that uses a much better lower bound is the purpose of this paper. We consider the general case of a length N filter with a discrete set of allowable real coefficients and demonstrate the effectiveness of the new algorithm on a set of filter design cases. The results show that this algorithm reduces the computation times up to 3 times when compared with the previously best results. • Practical FIR filter implementations often require low bit filter coefficients. • Quantization of FIR filter coefficients reduces the filter quality. • Optimal finite wordlength FIR filter coefficients are much better. • Computing the optimal low bit coefficients can be computationally demanding. • A new faster algorithm for optimal finite wordlength FIR design is a solution. [ABSTRACT FROM AUTHOR]

Near-field multiple-input multiple-output (MIMO) radar imaging systems have recently gained significant attention. These systems generally reconstruct the three-dimensional (3D) complex-valued reflectivity distribution of the scene using sparse measurements. Consequently, imaging quality highly relies on the image reconstruction approach. Existing analytical reconstruction approaches suffer from either high computational cost or low image quality. In this paper, we develop novel non-iterative deep learning-based reconstruction methods for real-time near-field MIMO imaging. The goal is to achieve high image quality with low computational cost at compressive settings. The developed approaches have two stages. In the first approach, physics-based initial stage performs adjoint operation to back-project the measurements to the image-space, and deep neural network (DNN)-based second stage converts the 3D backprojected measurements to a magnitude-only reflectivity image. Since scene reflectivities often have random phase, DNN processes directly the magnitude of the adjoint result. As DNN, 3D U-Net is used to jointly exploit range and cross-range correlations. To comparatively evaluate the significance of exploiting physics in a learning-based approach, two additional approaches that replace the physics-based first stage with fully connected layers are also developed as purely learning-based methods. The performance is also analyzed by changing the DNN architecture for the second stage to include complex-valued processing (instead of magnitude-only processing), 2D convolution kernels (instead of 3D), and ResNet architecture (instead of U-Net). Moreover, we develop a synthesizer to generate large-scale dataset for training the neural networks with 3D extended targets. We illustrate the performance through experimental data and extensive simulations. The results show the effectiveness of the developed physics-based learned reconstruction approach compared to commonly used approaches in terms of both runtime and image quality at highly compressive settings. Our source codes and dataset are made available at https://github.com/METU-SPACE-Lab/Efficient-Learned-3D-Near-Field-MIMO-Imaging upon publication to advance research in this field. • 3D image reconstruction methods are developed for near-field MIMO radar imaging using deep learning-based direct inversion and 3D CNNs. • A synthesizer to generate 3D scenes with extended targets is developed to obtain large data for training the neural networks. • Resolution analysis is performed for compressive imaging settings with sparse arrays. • Performance is comprehensively evaluated with simulated and experimental data, using both magnitude-only and complex-valued processing. • The results show the effectiveness of the developed physics-based learned reconstruction method in terms of image quality and runtime. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to audio-visual consistency judgment (AVCJ), in which vowel-like regions exhibiting significant changes in lip shape are used as key pronunciations. Unlike conventional methods that typically apply speech information to the whole utterance and corresponding visual features, the proposed technique involves key pronunciation analysis and frontal lip reconstruction for non-frontal lip frames corresponding to these key pronunciations. This is done to eliminate the influence of variations in video viewing angle on consistency judgment and address the limitations of whole-sentence analysis in a process consisting of four steps. First, key pronunciations are detected in speech utterance. Second, view angle classification is performed on lip frames corresponding to the key pronunciations and then frontal reconstruction is performed by a proposed SL-CycleGAN. Third, deep correlation analysis is applied to the covariance of the deep features obtained from both audio and visual features. Fourth, time-delay and correlation differences are combined to estimate the joint score of each key pronunciation. The results of AVCJ are then acquired by calculating a sentence level score from each joint score. Experimental results from the OuluVS2 bimodal multi-view database showed that the proposed method outperformed several state-of-the-art algorithms, including quadratic mutual information (QMI), space-time canonical correspondence analysis, and multiple variations of SyncNet. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach for the optimal identification of correlated segments in noisy correlation matrices. The proposed model is known as CoSeNet (Correlation Segmentation Network) and is based on a four-layer algorithmic architecture that includes several processing layers: input, formatting, re-scaling, and segmentation layer. The proposed model can effectively identify correlated segments in such matrices, better than previous approaches for similar problems. Internally, the proposed model utilizes an overlapping technique and uses pre-trained Machine Learning (ML) algorithms, which makes it robust and generalizable. CoSeNet approach also includes a method that optimizes the parameters of the re-scaling layer using a heuristic algorithm and fitness based on a Window Difference-based metric. The output of the model is a binary noise-free matrix representing optimal segmentation as well as its segmentation points and can be used in a variety of applications, obtaining compromise solutions between efficiency, memory, and speed of the proposed deployment model. • A novel multi-algorithm architecture for correlation matrices segmentation is proposed. • The proposed approach efficiently solves the matrix segmentation with high performance. • The proposed method can simplify a classification task enormously if the data are spatially sorted. • Transferability experiments show that noisy data can be excellent candidates for training the models. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of polarimetric detection for targets with energy spillover in non-Gaussian clutter. The polarization diversity and spillover of target energy to consecutive range bins are jointly exploited to enhance the performance of target detection. Two adaptive detectors are designed according to the Rao test, as well as its two-step implementation, i.e., 2S-Rao test. It is shown that the 2S-Rao test detector coincides with the existing generalized likelihood ratio test (GLRT) detector, whereas the Rao test detector is new, and outperforms the existing detectors in probability of detection. Experiments based on both simulated and real data illustrate the superiority of the proposed detector. [ABSTRACT FROM AUTHOR]

In some communication systems, the transmitted signal is contaminated by impulsive noise with a non-Gaussian distribution, which usually causes significant performance degradation to communication receivers. To deal with the impulsive noise, this paper proposes an efficient equalizer based on new fractional lower-order statistic (FLOS). Firstly, a nonlinear function-based new FLOS associated with the linear equalizer is designed to decrease the influence of impulsive noise. Secondly, referring to minimum mean square error (MMSE) criterion, an unconstrained optimization problem is formulated, and it is solved by the gradient descent method. Thirdly, to further improve the robustness of the proposed algorithm, the gradient is normalized by the l ∞ -norm of the equalizer input vector. Finally, simulation results demonstrate that the proposed algorithm achieves superior performance under Gaussian noise, even in the case of strong impulsive noise. Also, the simulation results prove the rationality of the new statistics under impulsive noise environments. [ABSTRACT FROM AUTHOR]

The linear frequency modulation-binary phase shift keying (LFM-BPSK) hybrid modulated signal combines the advantages of linear frequency modulation (LFM) and binary phase shift keying (BPSK). It has been extensively applied in the field of integrated radar communication. For the parameters estimation problem of LFM-BPSK signal, the traditional technologies based on the Nyquist theorem will bring a huge quantities of sample data with heavy data handling burden. This paper has presented a dual-channel cooperative sub-Nyquist sampling system for LFM-BPSK hybrid modulated signal. In the main channel, a time-interleaved sub-Nyquist sampling structure is proposed to resolve the frequency ambiguity problem caused by low sampling rate. In the other channel, a time-interleaved sub-Nyquist sampling structure based on self-mixing is proposed to estimate the phases of binary symbols and the positions of discontinuities from the low-rate samples. Simulation results have demonstrated the effectiveness and anti-noise performance of the proposed system. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surfaces (RISs) are considered a key paradigm to improve the coverage of beyond-fifth-generation (B5G) networks as signal reflectors. Moreover, device-to-device (D2D) communications and non-orthogonal multiple-access (NOMA) schemes will enable networks with a large number of devices for the Internet of Things. This paper analyzes the performance of the downlink of B5G network, where both a NOMA-empowered BS and a RIS support cellular communications co-existing with inband D2D transmissions. We derive approximate expressions of the outage probability, the cumulative distribution function (CDF), and the probability density function (PDF) of the signal-to-noise-plus-interference ratio (SINR) of the NOMA-connected users and the D2D receivers. We further derive similar expressions under orthogonal multiple access (OMA) transmission for comparison purpose. Then, we numerically compute the ergodic rate of each user for a given power allocation. The derived expressions are validated by extensive simulations. • Outage probability for RIS-Assisted NOMA-empowered system with D2D transmissions. • CDF and PDF of the SINR of downlink users and D2D receivers. • Achieved ergodic rate for the downlink users and D2D receivers. [ABSTRACT FROM AUTHOR]

This paper proposes a Degradation-Aware Deep Retinex Network (DA-DRN) for enhancing low-light images. DA-DRN is composed of a decomposition U-Net and an enhancement U-Net, and can tackle various degradation issues commonly found in real-world low-light environments, such as low brightness, color distortion, unknown noise, invisible detail, and halo artifacts. To achieve noise removal while preserving details, we introduce a Degradation-Aware Module (DA Module) that guides the decomposer's training process and enables it to be a restorer during training without additional computational cost in the test phase. The DA Module also addresses color distortion and halo artifacts. To train the enhancement network, we use Perceptual Loss to generate brightness-improved illumination maps that are more consistent with human visual perception. Our proposed model is trained and evaluated on the popular LOL real-world and synthetic datasets, as well as several other frequently used datasets without Ground-Truth (LIME, DICM, MEF, and NPE datasets). The results demonstrate that our method achieves promising performance with good robustness and generalization, outperforming many other state-of-the-art methods both qualitatively and quantitatively. Additionally, our method only takes 7 ms to process an image with 600 × 400 resolution on a TITAN Xp GPU. [ABSTRACT FROM AUTHOR]

Aiming the extract micro-motion features of rotor targets when the flashes are in the echo, this paper proposes a method based on the GS-IRadon algorithm. At first, we analyze the time-frequency characteristics of rotor targets through a scattering point signal model. Then, we analyze and study the usage conditions of the algorithm and use the Moving Target Indication (MTI) algorithm to remove the direct-current (DC) frequency component in signal's time-frequency results. Finally, we utilize the Inverse Radon transform algorithm based on the golden section method (GS-IRadon) to extract the target micro-motion features. The estimation of speed, length, and number of blades in the presence of flashes phenomenon in rotor targets was achieved. Simulation results showed that the algorithm can significantly reduce computational complexity while maintaining high estimation accuracy and has a more stable performance than regular algorithms. [ABSTRACT FROM AUTHOR]

The development of network technology and its use have led society into the internet world and communication through digital data. The ease of access to digital resources and the possibility of unauthorized copies and distribution of them have gave rise to the significant challenge of protecting the ownership of these data. In this context, steganography is cited as a possible solution to some of these problems. Steganography can be understood as the practice of hiding secret information within another object, as for instance a text, image or video, such that the presence of this hidden information is not evident and it can be extracted if necessary. In this paper we provide an image steganography algorithm in order to insert a grayscale secret image into a RGB color cover image. This algorithm is based on a general hybrid chaos map and a 3D shift function applied to the pixels of a color image. In order to select suitable hiding places in the host image, we develop a genetic algorithm with permutation encoding aiming to optimize this task. We demonstrate empirically the effectiveness of the proposed method from various perspectives, including transparency, security, and resistance. [ABSTRACT FROM AUTHOR]

The adoption of three-dimensional (3D) measurement technology for parts surface defect detection can improve inspection reliability. For online inspection purposes, 3D measurement technologies must possess the characteristics of high speed and high efficiency. The photometric stereo method is a potential 3D measurement method with high speed and low cost. However, the traditional photometric stereo method is unsuitable for dynamic scenes due to its initial design for static scenes. In this paper, we propose a novel dynamic photometric stereo method based on an image registration method. To achieve fast speed and high efficiency, we reduce the computational cost by automatically generating regions of interest (ROI). Additionally, we innovatively map the depth information (the surface normal vectors) to a mean curvature map of the surface and use it to detect defects, which combines the robustness of 3D methods and the fast speed of 2D methods. We designed experiments and the results showed that our method can detect defects on the surfaces of aluminum alloy castings accurately and robustly in an online manner. This paper also aims to reveal the importance of utilizing multidimensional information in high-speed online inspections. [ABSTRACT FROM AUTHOR]

An online dictionary learning algorithm for kernel sparse representation is developed in the current paper. In this framework, the input signal nonlinearly mapped into the feature space is sparsely represented based on a virtual dictionary in the same space. At any instant, the dictionary is updated in two steps. In the first step, the input signal samples are sparsely represented in the feature space, using the dictionary that has been updated based on the previous data. In the second step, the dictionary is updated. In this paper, a novel recursive dictionary update algorithm is derived, based on the recursive least squares (RLS) approach. This algorithm gradually updates the dictionary, upon receiving one or a mini-batch of training samples. An efficient implementation of the algorithm is also formulated. Experimental results over four datasets in different fields show the superior performance of the proposed algorithm in comparison with its counterparts. In particular, the classification accuracy obtained by the dictionaries trained using the proposed algorithm gradually approaches that of the dictionaries trained in batch mode. Moreover, in spite of lower computational complexity, the proposed algorithm overdoes all existing online kernel dictionary learning algorithms. [ABSTRACT FROM AUTHOR]

Synthetic Aperture Radar (SAR) imaging is generally characterized by a large amount of data and a high sampling rate. The traditional one-bit compressed sensing will generate virtual targets when recovering images at a low SNR, resulting in low reconstruction accuracy and obvious noise impact of the algorithm. In this paper, a one-bit SAR imaging algorithm based on the Minimax Concave (MC) penalty function and the Total Variation (TV) norm is proposed, which can potentially improve the reconstruction accuracy. At the same time, to solve the problem of speckle noise generated in the imaging process, this paper proposes a Fast Low-rank Sparse Decomposition (FLRSD) algorithm based on the one-bit contaminated image, which potentially improves the anti-noise performance and reconstruction efficiency. The results of simulation and measured data show that the proposed algorithms have better reconstruction accuracy and focusing performance than other algorithms. Even at low SNR, they also have good reconstruction effect. [ABSTRACT FROM AUTHOR]

Doignon and Falmagne (1985) introduced a surmise system, which generalized the precedence relation, allowing multiple possible learning paths for an item. Heller (2021) took into account precedence relations on an extended set of (virtual) items and further generalized quasi-ordinal knowledge spaces to polytomous items. Wang et al. (2022) proposed CD-polytomous knowledge space and provided its corresponding polytomous surmise system. Following these developments and drawing upon the so-called extended polytomous knowledge structure, this paper presents two concepts: weak polytomous structure and extended surmise system. Via setting up a Galois connection, a one-to-one correspondence is established between the collection of all extended surmise functions and the collection of certain weak polytomous structures. This paper also comprehensively discusses the relationships among the precedence relations, the polytomous surmise systems, and the extended surmise systems. • A new type of polytomous surmise system is proposed. • The concept of weak polytomous knowledge structure is provided. • The Galois connection is established. • The concepts associated with the extended surmise system are discussed. [ABSTRACT FROM AUTHOR]

Self-determination theory is a well-established theory of motivation. This theory provides for fundamental concepts related to human motivation, including self-determination. The mathematization of this theory has been envisaged in a series of two papers by the author. The first paper entitled "Mathematical self-determination theory I: Real representation" addressed the representation of the theory in reals. This second paper is in continuation of it. The representation of the first part allows to abstract the results in more general mathematical structures, namely, affine spaces. The simpler real representation is reobtained as a special instance. We take convexity as the pivotal starting point to generalize the whole exposition and represent self-determination theory in abstract affine spaces. This includes the affine space analogs of the notions of internal locus, external locus, and impersonal locus, of regulated and graded motivation, and self-determination. We also introduce polar coordinates in Euclidean affine motivation spaces to study self-determination on radial and angular line segments. We prove the distributivity of the lattice of general self-determination in the affine space formulation. The representation in an affine space is free in the choice of primitives. However, the different representations, in reals or affine, are shown to be unique up to canonical isomorphism. The aim of this paper is to extend on the results obtained in the first paper, thereby to further lay the mathematical foundations of self-determination motivation theory. • Mathematization of self-determination theory. • Combinatorial definitions and characterizations of self-determination. • Algebraic self-determination. • Self-determination theory in reals. • Self-determination theory in affine space. [ABSTRACT FROM AUTHOR]

In two parts, MSDT1 this paper and MSDT2 the follow-up paper, we treat the topic of mathematical self-determination theory. MSDT1 considers the real representation, MSDT2 the affine space representation. The aim of the two papers is to lay the mathematical foundations of self-determination motivation theory. Self-determination theory was proposed by Deci and Ryan, which is a popular theory of motivation. The fundamental concepts are extrinsic and intrinsic motivation, amotivation, their type of regulation, locus of causality, and especially, self-determination. First, we give a geometric description of its concepts for the regulated case (no amotivation), as the unit 1-simplex. Thereby, we derive a symmetric definition of self-determination. Second, we extend the geometric description to the regulated and unregulated case, based on a more general ternary model, in internal motivation, external motivation, and amotivation. We define gradations of amotivation (and motivation), as 1-simplexes parallel to the unit 1-simplex. The ternary representation implies the types of strong, weak, and general self-determination, as partial orders on the motivation space. Third, we study the order, lattice, and algebraic properties of self-determination. In a version of polar coordinates, strong self-determination turns out to be a complete lattice on angular line segments, weak self-determination is a complete lattice on radial line segments, and general self-determination entails a complete lattice on the entire motivation space. In addition, the modified polar coordinates are employed to obtain necessary and sufficient conditions for strong, weak, and general self-determination. We propose measures for the strength of an ordinal dependency in self-determination, which are partial metrics on the motivation space. [ABSTRACT FROM AUTHOR]