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Learning a graph from data is the key to taking advantage of graph signal processing tools. Most of the conventional algorithms for graph learning require complete data statistics, which might not be available in some scenarios. In this work, we aim to learn a graph from incomplete time-series observations. From another viewpoint, we consider the problem of semi-blind recovery of time-varying graph signals where the underlying graph model is unknown. We propose an algorithm based on the method of block successive upperbound minimization (BSUM), for simultaneous inference of the signal and the graph from incomplete data. Simulation results on synthetic and real time-series demonstrate the performance of the proposed method for graph learning and signal recovery.

Distributed algorithms, particularly Diffusion Least Mean Square, are widely favored for their reliability, robustness, and fast convergence in various industries. However, limited observability of the target can compromise the integrity of the algorithm. To address this issue, this paper proposes a framework for analyzing combination strategies by drawing inspiration from signal flow analysis. A thresholding-based algorithm is also presented to identify and utilize the support vector in scenarios with missing information about the target vector's support. The proposed approach is demonstrated in two combination scenarios, showcasing the effectiveness of the algorithm in situations characterized by sparse observations in the time and transform domains.

This paper presents an innovative approach leveraging Spectrally Efficient Frequency Division Multiplexing (SEFDM) with enhancements, including Frequency Domain Cyclic Prefix (FDCP) and Modified Non-Linear (MNL) acceleration, to address challenges arising from delay and Doppler shift in mobile communication channels. Our methodology demonstrates superior performance and enhanced spectral efficiency while incurring minimal computational overhead. We conduct a rigorous evaluation of the SEFDM system model, examining the impact of the MNL acceleration on SEFDM detection, and assessing the effectiveness of FDCP in mitigating Doppler shift effects. Bit Error Rate (BER) results obtained through Regularized Sphere Decoding in diverse simulation scenarios affirm the capability of our proposed solution to effectively manage challenges, ensuring robust and high-quality connectivity in mobile communication networks.

This paper proposes a Time-Frequency Space Transformation (TFST) to derive non-orthogonal bases for modulation techniques over the delay-doppler plane. A family of Overloaded Delay-Doppler Modulation (ODDM) techniques is proposed based on the TFST, which enhances flexibility and efficiency by expressing modulated signals as a linear combination of basis signals. A Non-Orthogonal Time-Frequency Space (NOTFS) digital modulation is derived for the proposed ODDM techniques, and simulations show that they offer high-mobility communication systems with improved spectral efficiency and low latency, particularly in challenging scenarios such as high overloading factors and Additive White Gaussian Noise (AWGN) channels. A modified sphere decoding algorithm is also presented to efficiently decode the received signal. The proposed modulation and decoding techniques contribute to the advancement of non-orthogonal approaches in the next-generation of mobile communication systems, delivering superior spectral efficiency and low latency, and offering a promising solution towards the development of efficient high-mobility communication systems.

Price movement prediction has always been one of the traders' concerns in financial market trading. In order to increase their profit, they can analyze the historical data and predict the price movement. The large size of the data and complex relations between them lead us to use algorithmic trading and artificial intelligence. This paper aims to offer an approach using Twin-Delayed DDPG (TD3) and the daily close price in order to achieve a trading strategy in the stock and cryptocurrency markets. Unlike previous studies using a discrete action space reinforcement learning algorithm, the TD3 is continuous, offering both position and the number of trading shares. Both the stock (Amazon) and cryptocurrency (Bitcoin) markets are addressed in this research to evaluate the performance of the proposed algorithm. The achieved strategy using the TD3 is compared with some algorithms using technical analysis, reinforcement learning, stochastic, and deterministic strategies through two standard metrics, Return and Sharpe ratio. The results indicate that employing both position and the number of trading shares can improve the performance of a trading system based on the mentioned metrics.

This paper proposes a robust adaptive algorithm for smooth graph signal recovery which is based on generalized correntropy. A proper cost function is defined for this purpose. The proposed algorithm is derived and a kernel width learning-based version of the algorithm is suggested which the simulation results show the superiority of it to the fixed correntropy kernel version of the algorithm. Moreover, some theoretical analysis of the proposed algorithm are provided. In this regard, firstly, the convexity analysis of the cost function is discussed. Secondly, the uniform stability of the algorithm is investigated. Thirdly, the mean convergence analysis is also added. Finally, the complexity analysis of the algorithm is incorporated. In addition, some synthetic and real-world experiments show the advantage of the proposed algorithm in comparison to some other adaptive algorithms in the literature of adaptive graph signal recovery.

Implicit Neural Representation (INR) has recently attracted considerable attention for storing various types of signals in continuous forms. The existing INR networks require lengthy training processes and high-performance computational resources. In this paper, we propose a novel sub-optimal ensemble architecture for INR that resolves the aforementioned problems. In this architecture, the representation task is divided into several sub-tasks done by independent sub-networks. We show that the performance of the proposed ensemble INR architecture may decrease if the dimensions of sub-networks increase. Hence, it is vital to suggest an optimization algorithm to find the sub-optimal structure of the ensemble network, which is done in this paper. According to the simulation results, the proposed architecture not only has significantly fewer floating-point operations (FLOPs) and less training time, but it also has better performance in terms of Peak Signal to Noise Ratio (PSNR) compared to those of its counterparts., Comment: IEEE Signal Processing Letters submitted, 5 pages, 6 figures, 2 tables

The brain, as the source of inspiration for Artificial Neural Networks (ANN), is based on a sparse structure. This sparse structure helps the brain to consume less energy, learn easier and generalize patterns better than any other ANN. In this paper, two evolutionary methods for adopting sparsity to ANNs are proposed. In the proposed methods, the sparse structure of a network as well as the values of its parameters are trained and updated during the learning process. The simulation results show that these two methods have better accuracy and faster convergence while they need fewer training samples compared to their sparse and non-sparse counterparts. Furthermore, the proposed methods significantly improve the generalization power and reduce the number of parameters. For example, the sparsification of the ResNet47 network by exploiting our proposed methods for the image classification of ImageNet dataset uses 40 % fewer parameters while the top-1 accuracy of the model improves by 12% and 5% compared to the dense network and their sparse counterpart, respectively. As another example, the proposed methods for the CIFAR10 dataset converge to their final structure 7 times faster than its sparse counterpart, while the final accuracy increases by 6%., Comment: Submitted in IEEE Transactions on Neural Networks and Learning Systems

PPG based heart rate (HR) monitoring has recently attracted much attention with the advent of wearable devices such as smart watches and smart bands. However, due to severe motion artifacts (MA) caused by wristband stumbles, PPG based HR monitoring is a challenging problem in scenarios where the subject performs intensive physical exercises. This work proposes a novel approach to the problem based on supervised learning by Neural Network (NN). By simulations on the benchmark datasets [1], we achieve acceptable estimation accuracy and improved run time in comparison with the literature. A major contribution of this work is that it alleviates the need to use simultaneous acceleration signals. The simulation results show that although the proposed method does not process the simultaneous acceleration signals, it still achieves the acceptable Mean Absolute Error (MAE) of 1.39 Beats Per Minute (BPM) on the benchmark data set.

This paper considers the problem of detecting impaired and noisy nodes over network. In a distributed algorithm, lots of processing units are incorporating and communicating with each other to reach a global goal. Due to each one's state in the shared environment, they can help the other nodes or mislead them (due to noise or a deliberate attempt). Previous works mainly focused on proper locating agents and weight assignment based on initial environment state to minimize malfunctioning of noisy nodes. We propose an algorithm to be able to adapt sharing weights according to behavior of the agents. Applying the introduced algorithm to a multi-agent RL scenario and the well-known diffusion LMS demonstrates its capability and generality.

Iterative methods have led to better understanding and solving problems such as missing sampling, deconvolution, inverse systems, impulsive and Salt and Pepper noise removal problems. However, the challenges such as the speed of convergence and or the accuracy of the answer still remain. In order to improve the existing iterative algorithms, a non-linear method is discussed in this paper. The mentioned method is analyzed from different aspects, including its convergence and its ability to accelerate recursive algorithms. We show that this method is capable of improving Iterative Method (IM) as a non-uniform sampling reconstruction algorithm and some iterative sparse recovery algorithms such as Iterative Reweighted Least Squares (IRLS), Iterative Method with Adaptive Thresholding (IMAT), Smoothed l0 (SL0) and Alternating Direction Method of Multipliers (ADMM) for solving LASSO problems family (including Lasso itself, Lasso-LSQR and group-Lasso). It is also capable of both accelerating and stabilizing the well-known Chebyshev Acceleration (CA) method. Furthermore, the proposed algorithm can extend the stability range by reducing the sensitivity of iterative algorithms to the changes of adaptation rate.

In this paper, we propose the family of Iterative Methods with Adaptive Thresholding (IMAT) for sparsity promoting reconstruction of Delta Modulated (DM) voice signals. We suggest a novel missing sampling approach to delta modulation that facilitates sparsity promoting reconstruction of the original signal from a subset of DM samples with less quantization noise. Utilizing our proposed missing sampling approach to delta modulation, we provide an analytical discussion on the convergence of IMAT for DM coding technique. We also modify the basic IMAT algorithm and propose the Iterative Method with Adaptive Thresholding for Delta Modulation (IMATDM) algorithm for improved reconstruction performance for DM coded signals. Experimental results show that in terms of the reconstruction SNR, this novel method outperforms the conventional DM reconstruction techniques based on lowpass filtering. It is observed that by migrating from the conventional low pass reconstruction technique to the sparsity promoting reconstruction technique of IMATDM, the reconstruction performance is improved by an average of 7.6 dBs. This is due to the fact that the proposed IMATDM makes simultaneous use of both the sparse signal assumption and the quantization noise suppression effects by smoothing. The proposed IMATDM algorithm also outperforms some other sparsity promoting reconstruction methods.

In this paper, we propose a new method to reconstruct a signal corrupted by noise where both signal and noise are sparse but in different domains. The problem investigated in this paper arises in different applications such as impulsive noise removal from images, audios and videos, decomposition of low-rank and sparse components of matrices, and separation of texts from images. First, we provide a cost function for our problem and then present an iterative method to find its local minimum. The analysis of the algorithm is also provided. As an application of this problem, we apply our algorithm for impulsive noise Salt-and-Pepper noise (SPN) and Random-Valued Impulsive Noise (RVIN)) removal from images and compare our results with other notable algorithms in the literature. Furthermore, we apply our algorithm for removing clicks from audio signals. Simulation results show that our algorithms is simple and fast, and it outperforms other state-of-the-art methods in terms of reconstruction quality and/or complexity.

Sparse Inverse Covariance Estimation (SICE) is useful in many practical data analyses. Recovering the connectivity, non-connectivity graph of covariates is classified amongst the most important data mining and learning problems. In this paper, we introduce a novel SICE approach using adaptive thresholding. Our method is based on updates in a transformed domain of the desired matrix and exponentially decaying adaptive thresholding in the main domain (Inverse Covariance matrix domain). In addition to the proposed algorithm, the convergence analysis is also provided. In the Numerical Experiments Section, we show that the proposed method outperforms state-of-the-art methods in terms of accuracy.

Compressive sensing is a new technology for modern computational imaging systems. In comparison to widespread conventional image sensing, the compressive imaging paradigm requires specific forensic analysis techniques and tools. In this regards, one of basic scenarios in image forensics is to distinguish traditionally sensed images from sophisticated compressively sensed ones. To do this, we first mathematically and systematically model the imaging system based on compressive sensing technology. Afterwards, a simplified version of the whole model is presented, which is appropriate for forensic investigation applications. We estimate the nonlinear system of compressive sensing with a linear model. Then, we model the imaging pipeline as an inverse problem and demonstrate that different imagers have discriminative degradation kernels. Hence, blur kernels of various imaging systems have utilized as footprints for discriminating image acquisition sources. In order to accomplish the identification cycle, we have utilized the state-of-the-art Convolutional Neural Network (CNN) and Support Vector Machine (SVM) approaches to learn a classification system from estimated blur kernels. Numerical experiments show promising identification results. Simulation codes are available for research and development purposes.

In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to control the violation from quantization bounds due to two properties: 1- It is differentiable, 2- It is less sensitive to outliers than the quadratic loss. A Smooth Rank Approximation is utilized to endorse lower rank on the genuine data matrix. Thus, an unconstrained optimization problem with differentiable objective function is obtained allowing us to advantage from Gradient Descent (GD) technique. Novel and firm theoretical analysis on problem model and convergence of our algorithm to the global solution are provided. Another contribution of our work is that our method does not require projections or initial rank estimation unlike the state- of-the-art. In the Numerical Experiments Section, the noticeable outperformance of our proposed method in learning accuracy and computational complexity compared to those of the state-of- the-art literature methods is illustrated as the main contribution.

In this paper, we propose a novel approach in order to recover a quantized matrix with missing information. We propose a regularized convex cost function composed of a log-likelihood term and a Trace norm term. The Bi-factorization approach and the Augmented Lagrangian Method (ALM) are applied to find the global minimizer of the cost function in order to recover the genuine data. We provide mathematical convergence analysis for our proposed algorithm. In the Numerical Experiments Section, we show the superiority of our method in accuracy and also its robustness in computational complexity compared to the state-of-the-art literature methods.

In this paper, we propose two new algorithms for transduction with Matrix Completion (MC) problem. The joint MC and prediction tasks are addressed simultaneously to enhance the accuracy, i.e., the label matrix is concatenated to the data matrix forming a stacked matrix. Assuming the data matrix is of low rank, we propose new recommendation methods by posing the problem as a constrained minimization of the Smoothed Rank Function (SRF). We provide convergence analysis for the proposed algorithms. The simulations are conducted on real datasets in two different scenarios of randomly missing pattern with and without block loss. The results confirm that the accuracy of our proposed methods outperforms those of state-of-the-art methods even up to 10% in low observation rates for the scenario without block loss. Our accuracy in the latter scenario, is comparable to state-of-the-art methods while the complexity of the proposed algorithms are reduced up to 4 times.

Well-known methods are employed to localize mobile station (MS) using line of sight (LOS) measurements. These methods may result in large error if they are fed with non LOS (NLOS) measurements. Our proposed algorithm, referred to as Sparse Recovery of NLOS using IMAT (SRNI), considers NLOS as unknown variables and solves the resultant underdetermined system emphasizing on its sparsity feature based on IMAT methods. Simulations are conducted to investigate the performance of SRNI in comparison of other conventional algorithms. Results demonstrate that SRNI is fast enough to deal with large combination of BSs and also accurate in lower number of BSs, Comment: 6 pages, 7 figures

In this letter, we propose a sparsity promoting feedback acquisition and reconstruction scheme for sensing, encoding and subsequent reconstruction of spectrally sparse signals. In the proposed scheme, the spectral components are estimated utilizing a sparsity-promoting, sliding-window algorithm in a feedback loop. Utilizing the estimated spectral components, a level signal is predicted and sign measurements of the prediction error are acquired. The sparsity promoting algorithm can then estimate the spectral components iteratively from the sign measurements. Unlike many batch-based Compressive Sensing (CS) algorithms, our proposed algorithm gradually estimates and follows slow changes in the sparse components utilizing a sliding-window technique. We also consider the scenario in which possible flipping errors in the sign bits propagate along iterations (due to the feedback loop) during reconstruction. We propose an iterative error correction algorithm to cope with this error propagation phenomenon considering a binary-sparse occurrence model on the error sequence. Simulation results show effective performance of the proposed scheme in comparison with the literature.

In this letter, the problem of sparse signal reconstruction from one bit compressed sensing measurements is investigated. To solve the problem, a variational Bayes framework with a new statistical multivariate model is used. The dependency of the wavelet decomposition coefficients is modeled with a multivariate Gaussian copula. This model can separate marginal structure of coefficients from their intra scale dependency. In particular, the drawable Gaussian vine copula multivariate double Lomax model is suggested. The reconstructed signal is derived by variational Bayes algorithm which can calculate closed forms for posterior of all unknown parameters and sparse signal. Numerical results illustrate the effectiveness of the proposed model and algorithm compared with the competing approaches in the literature.

This paper proposes some bounds on the maximum of magnitude of a random mask in Fourier domain. The random mask is used in random sampling scheme. Having a bound on the maximum value of a random mask in Fourier domain is very useful for some iterative recovery methods that use thresholding operator. In this paper, we propose some different bounds and compare them with the empirical examples.

This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion on the convergence of our method called Simultaneous Iterative Method with Adaptive Thresholding (SIMAT). Additionally, we compare our method with other group-sparse reconstruction techniques, i.e., Simultaneous Orthogonal Matching Pursuit (SOMP), and Block Iterative Method with Adaptive Thresholding (BIMAT) through numerical experiments. The simulation results demonstrate that SIMAT outperforms these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIMAT is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.

In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image processing and for this purpose, we suggest an iterative sparse recovery algorithm based on constrained $l_1$-norm minimization with a new fidelity metric. The proposed metric called Convex SIMilarity (CSIM) index, is a simplified version of the Structural SIMilarity (SSIM) index, which is convex and error-sensitive. The optimization problem incorporating this criterion, is then solved via Alternating Direction Method of Multipliers (ADMM). Simulation results show the efficiency of the proposed method for missing sample recovery of 1D patch vectors and inpainting of 2D image signals.

This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient information content of image patches. By leveraging texture in space, sparsity locations in DCT domain, and directional decomposition of gradients, the sampler structure consists of a combination of uniform, random, and nonuniform sampling strategies. For reconstruction, we model the recovery problem as a two-state cellular automaton to iteratively restore image with scalable windows from generation to generation. We demonstrate the recovery algorithm quickly converges after a few generations for an image with arbitrary degree of texture. For a given number of measurements, extensive experiments on standard image-sets, infra-red, and mega-pixel range imaging devices show that the proposed measurement matrix considerably increases the overall recovery performance, or equivalently decreases the number of sampled pixels for a specific recovery quality compared to random sampling matrix and Gaussian linear combinations employed by the state-of-the-art compressive sensing methods. In practice, the proposed measurement-adaptive sampling/recovery framework includes various applications from intelligent compressive imaging-based acquisition devices to computer vision and graphics, and image processing technology. Simulation codes are available online for reproduction purposes.

In this paper, we propose an Adaptive Singular Value Thresholding (ASVT) for low rank recovery under affine constraints. Unlike previous iterative methods that the threshold level is independent of the iteration number, in our proposed method, the threshold in adaptively decreases during iterations. The simulation results reveal that we get better performance with this thresholding strategy.

In this paper, we will provide a comparison between uniform and random sampling for speech and music signals. There are various sampling and recovery methods for audio signals. Here, we only investigate uniform and random schemes for sampling and basic low-pass filtering and iterative method with adaptive thresholding for recovery. The simulation results indicate that uniform sampling with cubic spline interpolation outperforms other sampling and recovery methods.

In this paper, we design a system in order to perform the real-time beat tracking for an audio signal. We use Onset Strength Signal (OSS) to detect the onsets and estimate the tempos. Then, we form Cumulative Beat Strength Signal (CBSS) by taking advantage of OSS and estimated tempos. Next, we perform peak detection by extracting the periodic sequence of beats among all CBSS peaks. In simulations, we can see that our proposed algorithm, Online Beat TrAckINg (OBTAIN), outperforms state-of-art results in terms of prediction accuracy while maintaining comparable and practical computational complexity. The real-time performance is tractable visually as illustrated in the simulations.

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding operator. This algorithm is fast and can be implemented easily. We compare it with one of the most common fast methods in which the rank and sparsity are approximated by $\ell_1$ norm. We also apply it to some real applications where the noise is not so sparse. The simulation results show that it has a suitable performance with low run-time.

This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used as the similarity criterion between the original and the reconstructed images. The proposed criterion called Convex SIMilarity (CSIM) index is a modified version of the Structural SIMilarity (SSIM) index, which despite its predecessor, is convex and uni-modal. We derive mathematical properties for the proposed index and show how to optimally choose the parameters of the proposed criterion, investigating the Restricted Isometry (RIP) and error-sensitivity properties. We also propose an iterative sparse recovery method based on a constrained $l_1$-norm minimization problem, incorporating CSIM as the fidelity criterion. The resulting convex optimization problem is solved via an algorithm based on Alternating Direction Method of Multipliers (ADMM). Taking advantage of the convexity of the CSIM index, we also prove the convergence of the algorithm to the globally optimal solution of the proposed optimization problem, starting from any arbitrary point. Simulation results confirm the performance of the new similarity index as well as the proposed algorithm for missing sample recovery of image patch signals., Comment: 13 pages, 3 figures

In this paper, prediction for linear systems with missing information is investigated. New methods are introduced to improve the Mean Squared Error (MSE) on the test set in comparison to state-of-the-art methods, through appropriate tuning of Bias-Variance trade-off. First, the use of proposed Soft Weighted Prediction (SWP) algorithm and its efficacy are depicted and compared to previous works for non-missing scenarios. The algorithm is then modified and optimized for missing scenarios. It is shown that controlled over-fitting by suggested algorithms will improve prediction accuracy in various cases. Simulation results approve our heuristics in enhancing the prediction accuracy.

This letter considers the problem of sparse signal reconstruction from the timing of its Level Crossings (LC)s. We formulate the sparse Zero Crossing (ZC) reconstruction problem in terms of a single 1-bit Compressive Sensing (CS) model. We also extend the Smoothed L0 (SL0) sparse reconstruction algorithm to the 1-bit CS framework and propose the Binary SL0 (BSL0) algorithm for iterative reconstruction of the sparse signal from ZCs in cases where the number of sparse coefficients is not known to the reconstruction algorithm a priori. Similar to the ZC case, we propose a system of simultaneously constrained signed-CS problems to reconstruct a sparse signal from its Level Crossings (LC)s and modify both the Binary Iterative Hard Thresholding (BIHT) and BSL0 algorithms to solve this problem. Simulation results demonstrate superior performance of the proposed LC reconstruction techniques in comparison with the literature., Comment: Submitted to IEEE Signal Processing Letters

Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired support of the signal and resisting against noisy systems. When sparse models are also suffering from MI, the sparse recovery and inference of the missing models are taken into account simultaneously. In this paper, we will introduce an approach which enjoys sparse regression and covariance matrix estimation to improve matrix completion accuracy, and as a result enhancing feature selection preciseness which leads to reduction in prediction Mean Squared Error (MSE). We will compare the effect of employing covariance matrix in enhancing estimation accuracy to the case it is not used in feature selection. Simulations show the improvement in the performance as compared to the case where the covariance matrix estimation is not used.

Adaptive thresholding methods have proved to yield high SNRs and fast convergence in finding the solution to the Compressed Sensing (CS) problems. Recently, it was observed that the robustness of a class of iterative sparse recovery algorithms such as Iterative Method with Adaptive Thresholding (IMAT) has outperformed the well-known LASSO algorithm in terms of reconstruction quality, convergence speed, and the sensitivity to the noise. In this paper, we introduce a new method towards solving the CS problem. The logic of this method is based on iterative projections of the thresholded signal onto the null-space of the sensing matrix. The thresholding is carried out by recovering the support of the desired signal by projection on thresholding subspaces. The simulations reveal that the proposed method has the capability of yielding noticeable output SNR values with about as many samples as twice the sparsity number, while other methods fail to recover the signals when approaching the algebraic bound for the number of samples required. The computational complexity of our method is also comparable to other methods as observed in the simulations. We have also extended our Algorithm to Matrix Completion (MC) scenarios and compared its efficiency to other well-reputed approaches for MC in the literature.

The common and traditional method for dispersion compensation in optical domain is concatenating the transmit optical fiber by a compensating optical fiber having high-negative dispersion coefficient. In this paper, we take an opposite direction and show how an optical fiber with high-positive dispersion coefficient can also be used for dispersion compensation. Our optical dispersion compensating structure is the optical implementation of an iterative algorithm in signal processing. The proposed dispersion compensating system is constructed by cascading a number of compensating sub-systems and its compensation capability is improved by increasing the number of embedded sub-systems. We also show that the compensation capability is a trade-off between transmission length and bandwidth. We use simulation results to validate the performance of the introduced dispersion compensating module. Photonic crystal fibers with high-positive dispersion coefficient can be used for constructing the proposed optical dispersion compensating module., Comment: 5 pages, 5 figures

This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been lowpass/ band-limitedness of the underlying graph signal. However, inspired by the findings on sparse signal reconstruction, we consider the graph signal to be rather sparse/compressible in the Graph Fourier Transform (GFT) domain and propose the Iterative Method with Adaptive Thresholding for Graph Interpolation (IMATGI) algorithm for sparsity promoting interpolation of the underlying graph signal.We analytically prove convergence of the proposed algorithm. We also demonstrate efficient performance of the proposed IMATGI algorithm in reconstructing randomly generated sparse graph signals. Finally, we consider the widely desirable application of recommendation systems and show by simulations that IMATGI outperforms state-of-the-art algorithms on the benchmark datasets in this application., Comment: 12th International Conference on Sampling Theory and Applications (SAMPTA 2017)

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion on the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To this end, we employ a technique to initially approximate the support of the sparse vector. We further propose to unify the partial matrix completion and sparse vector recovery into an augmented four-step problem. Simulation results reveal that the augmented approach achieves the best performance, while both proposed methods outperform the natural two-step technique with substantially less computational requirements.

Consider a continuous signal that cannot be observed directly. Instead, one has access to multiple corrupted versions of the signal. The available corrupted signals are correlated because they carry information about the common remote signal. The goal is to reconstruct the original signal from the data collected from its corrupted versions. The information theoretic formulation of the remote reconstruction problem assumes that the corrupted signals are uniformly sampled and the focus is on optimal compression of the samples. In this paper we revisit this problem from a sampling perspective. We look at the problem of finding the best sampling locations for each signal to minimize the total reconstruction distortion of the remote signal. In finding the sampling locations, one can take advantage of the correlation among the corrupted signals. Our main contribution is a fundamental lower bound on the reconstruction distortion for any arbitrary nonuniform sampling strategy. This lower bound is valid for any sampling rate. Furthermore, it is tight and matches the optimal reconstruction distortion in low and high sampling rates. Moreover, it is shown that in the low sampling rate region, it is optimal to use a certain nonuniform sampling scheme on all the signals. On the other hand, in the high sampling rate region, it is optimal to uniformly sample all the signals. We also consider the problem of finding the optimal sampling locations to recover the set of corrupted signals, rather than the remote signal. Unlike the information theoretic formulation of the problem in which these two problems were equivalent, we show that they are not equivalent in our setting., Comment: Under review

In this paper, we will investigate the efficacy of IMAT (Iterative Method of Adaptive Thresholding) in recovering the sparse signal (parameters) for linear models with missing data. Sparse recovery rises in compressed sensing and machine learning problems and has various applications necessitating viable reconstruction methods specifically when we work with big data. This paper will focus on comparing the power of IMAT in reconstruction of the desired sparse signal with LASSO. Additionally, we will assume the model has random missing information. Missing data has been recently of interest in big data and machine learning problems since they appear in many cases including but not limited to medical imaging datasets, hospital datasets, and massive MIMO. The dominance of IMAT over the well-known LASSO will be taken into account in different scenarios. Simulations and numerical results are also provided to verify the arguments.

In this paper, the problem of Magnetic Resonance (MR) image reconstruction from partial Fourier samples has been considered. To this aim, we leverage the evidence that MR images are sparser than their zero-filled reconstructed ones from incomplete Fourier samples. This information can be used to define an optimization problem which searches for the sparsest possible image conforming with the available Fourier samples. We solve the resulting problem using the well-known Alternating Direction Method of Multipliers (ADMM). Unlike most existing methods that work with small over-lapping image patches, the proposed algorithm considers the whole image without dividing it into small blocks. Experimental results prominently confirm its promising performance and advantages over the existing methods.

Multiple-input multiple-output (MIMO) radars offer higher resolution, better target detection, and more accurate target parameter estimation. Due to the sparsity of the targets in space-velocity domain, we can exploit Compressive Sensing (CS) to improve the performance of MIMO radars when the sampling rate is much less than the Nyquist rate. In distributed MIMO radars, block CS methods can be used instead of classical CS ones for more performance improvement, because the received signal in this group of MIMO radars is a block sparse signal in a basis. In this paper, two new methods are proposed to improve the performance of the block CS-based distributed MIMO radars. The first one is a new method for optimal energy allocation to the transmitters, and the other one is a new method for optimal design of the measurement matrix. These methods are based on the minimization of an upper bound of the sensing matrix block-coherence. Simulation results show an increase in the accuracy of multiple targets parameters estimation for both proposed methods., Comment: The paper is accepted in Elseveir Aerospace Science and Technology