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Developing an electroencephalogram (EEG)-based motor imagery and motor execution (MI/ME) decoding system that is both highly accurate and calibration-free for cross-subject applications remains challenging due to domain shift problem inherent in such scenario. Recent research has increasingly embraced transfer learning strategies, especially domain adaptation techniques. However, domain adaptation becomes impractical when the target subject data is either difficult to obtain or unknown. To address this issue, we propose a supervised contrastive learning-based domain generalization network (SCLDGN) for cross-subject MI/ME decoding. Firstly, the feature encoder is purposefully designed to learn the EEG discriminative feature representations. Secondly, the domain alignment based on deep correlation alignment constrains the representations distance across various domains to learn domain-invariant features. In addition, the class regularization block is proposed, where the supervised contrastive learning with domain-agnostic mixup is established to learn the class-relevant features and achieve class-level alignment. Finally, in the latent space, clusters of domain-agnostic representations from the same class are mapped closer together. Consequently, SCLDGN is capable of learning domain-invariant and class-relevant discriminative representations, which are essential for effective cross-subject decoding. Extensive experiments conducted on six MI/ME datasets demonstrate the effectiveness of the proposed method in comparison with other state-of-the-art approaches. Furthermore, ablation study and visualization analyses explain the generalization mechanism of the proposed method and also show neurophysiologically meaningful patterns related to MI/ME.

Attention decoding plays a vital role in daily life, where electroencephalography (EEG) has been widely involved. However, training a universally effective model for everyone is impractical due to substantial interindividual variability in EEG signals. To tackle the above challenge, we propose an end-to-end brain-computer interface (BCI) framework, including temporal and spatial one-dimensional (1D) convolutional neural network and domain-adversarial training strategy, namely DA-TSnet. Specifically, DA-TSnet extracts temporal and spatial features of EEG, while it is jointly supervised by task loss and domain loss. During training, DA-TSnet aims to maximize the domain loss while simultaneously minimizing the task loss. We conduct an offline analysis, simulate online experiments on a self-collected dataset of 85 subjects, and real online experiments on 22 subjects. Main results: DA-TSnet achieves a leave-one-subject-out (LOSO) cross-validation (CV) classification accuracy of 89.40% ± 9.96%, outperforming several state-of-the-art attention EEG decoding methods. In simulated online experiments, DA-TSnet achieves an outstanding accuracy of 88.07% ± 11.22%. In real online experiments, it achieves an average accuracy surpassing 86%. Significance: An end-to-end network framework does not rely on elaborate preprocessing and feature extraction steps, which saves time and human workload. Moreover, our framework utilizes domain-adversarial training neural network (DANN) to tackle the challenge posed by the high interindividual variability in EEG signals, which has significant reference value for handling other EEG signal decoding issues. Last, the performance of the DA-TSnet framework in offline and online experiments underscores its potential to facilitate more reliable applications.

In this paper, a novel spatio-temporal self-constructing graph neural network (ST-SCGNN) is proposed for cross-subject emotion recognition and consciousness detection. For spatio-temporal feature generation, activation and connection pattern features are first extracted and then combined to leverage their complementary emotion-related information. Next, a self-constructing graph neural network with a spatio-temporal model is presented. Specifically, the graph structure of the neural network is dynamically updated by the self-constructing module of the input signal. Experiments based on the SEED and SEED-IV datasets showed that the model achieved average accuracies of 85.90% and 76.37%, respectively. Both values exceed the state-of-the-art metrics with the same protocol. In clinical besides, patients with disorders of consciousness (DOC) suffer severe brain injuries, and sufficient training data for EEG-based emotion recognition cannot be collected. Our proposed ST-SCGNN method for cross-subject emotion recognition was first attempted in training in ten healthy subjects and testing in eight patients with DOC. We found that two patients obtained accuracies significantly higher than chance level and showed similar neural patterns with healthy subjects. Covert consciousness and emotion-related abilities were thus demonstrated in these two patients. Our proposed ST-SCGNN for cross-subject emotion recognition could be a promising tool for consciousness detection in DOC patients.

Objective: Brain-computer interfaces (BCIs) have tremendous application potential in communication, mechatronic control and rehabilitation. However, existing BCI systems are bulky, expensive and require laborious preparation before use. This study proposes a practical and user-friendly BCI system without compromising performance., Methods: A hybrid asynchronous BCI system was developed based on an elaborately designed wearable electroencephalography (EEG) amplifier that is compact, easy to use and offers a high signal-to-noise ratio (SNR). The wearable BCI system can detect P300 signals by processing EEG signals from three channels and operates asynchronously by integrating blink detection., Result: The wearable EEG amplifier obtains high quality EEG signals and introduces preprocessing capabilities to BCI systems. The wearable BCI system achieves an average accuracy of 94.03±4.65%, an average information transfer rate (ITR) of 31.42±7.39 bits/min and an average false-positive rate (FPR) of 1.78%., Conclusion: The experimental results demonstrate the feasibility and practicality of the developed wearable EEG amplifier and BCI system., Significance: Wearable asynchronous BCI systems with fewer channels are possible, indicating that BCI applications can be transferred from the laboratory to real-world scenarios.

Videofluoroscopic swallowing study (VFSS) visualizes the swallowing movement by using X-ray fluoroscopy, which is the most widely used method for dysphagia examination. To better facilitate swallowing assessment, the temporal parameter is one of the most important indicators. However, most information of that acquire is hand-crafted and elaborated, which is time-consuming and difficult to ensure objectivity and accuracy. In this article, we propose to formulate this task as a temporal action localization task and solve it using deep neural networks. However, the action of VFSS has the following characteristics such as small motion targets, small action amplitudes, large sample variances, short duration, and variations in duration. Furthermore, all existing methods often rely on daily behaviors, which makes locating and recognizing micro-actions more challenging. To address the above issues, we first collect and annotate the VFSS micro-action dataset, which includes 847 VFSS data from 71 subjects, due to the lack of benchmarks. We then introduce a coarse-to-fine mechanism to handle the short and repeated nature of micro-actions, which can significantly enhancing micro-action localization accuracy. Moreover, we propose a Variable-Size Window Generator method, which improves the model's characterization performance and addresses the issue of different action timings, leading to further improvements in localization accuracy. The results of our experiments demonstrate the superiority of our method, with significantly improved performance (46.10% vs. 37.70%).

Whole-slide image (WSI) classification is fundamental to computational pathology, which is challenging in extra-high resolution, expensive manual annotation, data heterogeneity, etc. Multiple instance learning (MIL) provides a promising way towards WSI classification, which nevertheless suffers from the memory bottleneck issue inherently, due to the gigapixel high resolution. To avoid this issue, the overwhelming majority of existing approaches have to decouple the feature encoder and the MIL aggregator in MIL networks, which may largely degrade the performance. Towards this end, this paper presents a Bayesian Collaborative Learning (BCL) framework to address the memory bottleneck issue with WSI classification. Our basic idea is to introduce an auxiliary patch classifier to interact with the target MIL classifier to be learned, so that the feature encoder and the MIL aggregator in the MIL classifier can be learned collaboratively while preventing the memory bottleneck issue. Such a collaborative learning procedure is formulated under a unified Bayesian probabilistic framework and a principled Expectation-Maximization algorithm is developed to infer the optimal model parameters iteratively. As an implementation of the E-step, an effective quality-aware pseudo labeling strategy is also suggested. The proposed BCL is extensively evaluated on three publicly available WSI datasets, i.e., CAMELYON16, TCGA-NSCLC and TCGA-RCC, achieving an AUC of 95.6%, 96.0% and 97.5% respectively, which consistently outperforms all the methods compared. Comprehensive analysis and discussion will also be presented for in-depth understanding of the method. To promote future work, our source code is released at: https://github.com/Zero-We/BCL.

Stereoelectroencephalography (SEEG) signals can be obtained by implanting deep intracranial electrodes. SEEG depth electrodes can record brain activity from the shallow cortical layer and deep brain structures, which is not achievable through other recording techniques. Moreover, SEEG has the advantage of a high signal-to-noise ratio (SNR). Therefore, it provides a potential way to establish a highly efficient brain-computer interface (BCI) and aid in understanding human brain activity. In this study, we implemented a P300-based BCI using SEEG signals. A single-character oddball paradigm was applied to elicit P300. To predict target characters, we fed the feature vectors extracted from the signals collected by five SEEG contacts into a Bayesian linear discriminant analysis (BLDA) classifier. Thirteen epileptic patients implanted with SEEG electrodes participated in the experiment and achieved an average online spelling accuracy of 93.85%. Moreover, through single-contact decoding analysis and simulated online analysis, we found that the SEEG-based BCI system achieved a high performance even when using a single signal channel. Furthermore, contacts with high decoding accuracies were mainly distributed in the visual ventral pathway, especially the fusiform gyrus (FG) and lingual gyrus (LG), which played an important role in building P300-based SEEG BCIs. These results might provide new insights into P300 mechanistic studies and the corresponding BCIs.

Achieving high classification performance in electroencephalogram (EEG)-based brain-computer interfaces (BCIs) often entails a large number of channels, which impedes their use in practical applications. Despite the previous efforts, it remains a challenge to determine the optimal subset of channels in a subject-specific manner without heavily compromising the classification performance. In this article, we propose a new method, called spatiotemporal-filtering-based channel selection (STECS), to automatically identify a designated number of discriminative channels by leveraging the spatiotemporal information of the EEG data. In STECS, the channel selection problem is cast under the framework of spatiotemporal filter optimization by incorporating a group sparsity constraints, and a computationally efficient algorithm is developed to solve the optimization problem. The performance of STECS is assessed on three motor imagery EEG datasets. Compared with state-of-the-art spatiotemporal filtering algorithms using full EEG channels, STECS yields comparable classification performance with only half of the channels. Moreover, STECS significantly outperforms the existing channel selection methods. These results suggest that this algorithm holds promise for simplifying BCI setups and facilitating practical utility.

Objective: A challenging task for an electroencephalography (EEG)-based asynchronous brain-computer interface (BCI) is to effectively distinguish between the idle state and the control state while maintaining a short response time and a high accuracy when commands are issued in the control state. This study proposes a novel hybrid asynchronous BCI system based on a combination of steady-state visual evoked potentials (SSVEPs) in the EEG signal and blink-related electrooculography (EOG) signals., Methods: Twelve buttons corresponding to 12 characters are included in the graphical user interface (GUI). These buttons flicker at different fixed frequencies and phases to evoke SSVEPs and are simultaneously highlighted by changing their sizes. The user can select a character by focusing on its frequency-phase stimulus and simultaneously blinking his/her eyes in accordance with its highlighting as his/her EEG and EOG signals are recorded. A multifrequency band-based canonical correlation analysis (CCA) method is applied to the EEG data to detect the evoked SSVEPs, whereas the EOG data are analyzed to identify the user's blinks. Finally, the target character is identified based on the SSVEP and blink detection results., Results: Ten healthy subjects participated in our experiments and achieved an average information transfer rate (ITR) of 105.52 bits/min, an average accuracy of 95.42%, an average response time of 1.34 s and an average false-positive rate (FPR) of 0.8%., Conclusion: The proposed BCI generates multiple commands with a high ITR and low FPR., Significance: The hybrid asynchronous BCI has great potential for practical applications in communication and control.

Energy-resolved computed tomography (ErCT) with a photon counting detector concurrently produces multiple CT images corresponding to different photon energy ranges. It has the potential to generate energy-dependent images with improved contrast-to-noise ratio and sufficient material-specific information. Since the number of detected photons in one energy bin in ErCT is smaller than that in conventional energy-integrating CT (EiCT), ErCT images are inherently more noisy than EiCT images, which leads to increased noise and bias in the subsequent material estimation. In this work, we first deeply analyze the intrinsic tensor properties of two-dimensional (2D) ErCT images acquired in different energy bins and then present a F ull- S pectrum-knowledge-aware Tensor analysis and processing (FSTensor) method for ErCT reconstruction to suppress noise-induced artifacts to obtain high-quality ErCT images and high-accuracy material images. The presented method is based on three considerations: (1) 2D ErCT images obtained in different energy bins can be treated as a 3-order tensor with three modes, i.e., width, height and energy bin, and a rich global correlation exists among the three modes, which can be characterized by tensor decomposition. (2) There is a locally piecewise smooth property in the 3-order ErCT images, and it can be captured by a tensor total variation regularization. (3) The images from the full spectrum are much better than the ErCT images with respect to noise variance and structural details and serve as external information to improve the reconstruction performance. We then develop an alternating direction method of multipliers algorithm to numerically solve the presented FSTensor method. We further utilize a genetic algorithm to tackle the parameter selection in ErCT reconstruction, instead of manually determining parameters. Simulation, preclinical and synthesized clinical ErCT results demonstrate that the presented FSTensor method leads to significant improvements over the filtered back-projection, robust principal component analysis, tensor-based dictionary learning and low-rank tensor decomposition with spatial-temporal total variation methods.

Segmentation of cardiac ventricle from magnetic resonance images is significant for cardiac disease diagnosis, progression assessment, and monitoring cardiac conditions. Manual segmentation is so time consuming, tedious, and subjective that automated segmentation methods are highly desired in practice. However, conventional segmentation methods performed poorly in cardiac ventricle, especially in the right ventricle. Compared with the left ventricle, whose shape is a simple thick-walled circle, the structure of the right ventricle is more complex due to ambiguous boundary, irregular cavity, and variable crescent shape. Hence, effective feature extractors and segmentation models are preferred. In this paper, we propose a dilated-inception net (DIN) to extract and aggregate multi-scale features for right ventricle segmentation. The DIN outperforms many state-of-the-art models on the benchmark database of right ventricle segmentation challenge. In addition, the experimental results indicate that the proposed model has potential to reach expert-level performance in right ventricular epicardium segmentation. More importantly, DIN behaves similarly to clinical expert with high correlation coefficients in four clinical cardiac indices. Therefore, the proposed DIN is promising for automated cardiac right ventricle segmentation in clinical applications.

Accurate estimation of the locations and extents of neural sources from electroencephalography and magnetoencephalography (E/MEG) is challenging, especially for deep and highly correlated neural activities. In this study, we proposed a new fully data-driven source imaging method, source imaging based on spatio-temporal basis function (SI-STBF), which is built upon a Bayesian framework, to address this issue. The SI-STBF is based on the factorization of a source matrix as a product of a sparse coding matrix and a temporal basis function (TBF) matrix, which includes a few TBFs. The prior of the TBF is set in the empirical Bayesian manner. Similarly, for the spatial constraint, the SI-STBF assumes the prior covariance of the coding matrix as a weighted sum of several spatial covariance components. Both the TBFs and the coding matrix are learned from E/MEG simultaneously through variational Bayesian inference. To enable inference on high-resolution source space, we derived a scalable algorithm using convex analysis. The performance of the SI-STBF was assessed using both simulated and experimental E/MEG recordings. Compared with L 2 -norm constrained methods, the SI-STBF is superior in reconstructing extended sources with less spatial diffusion and less localization error. By virtue of the spatio-temporal factorization of source matrix, the SI-STBF also produces more accurate estimations than spatial-only constraint method for high correlated and deep sources.

Objective: This paper presents an asyn-chronous electrooculography (EOG)-based human-machine interface (HMI) for smart home environmental control with the purpose of providing daily assistance for severe spinal cord injury (SCI) patients., Methods: The proposed HMI allows users to interact with a smart home environment through eye blinking. Specifically, several buttons, each corresponding to a control command, randomly flash on a graphical user interface. Each flash of the buttons functions as a visual cue for the user to blink. To issue a control command, the user can blink synchronously with the flashes of the corresponding button. Through detecting blinks based on the recorded EOG signal, the target button and its corresponding control command are determined. Seven SCI patients participated in an online experiment, during which the patients were required to control a smart home environment including household electrical appliances, an intelligent wheelchair, as well as a nursing bed via the proposed HMI., Results: The average false operation ratio in the control state was 4.1%, whereas during the idle state, no false operations occurred., Conclusion: All SCI patients were able to control the smart home environment using the proposed EOG-based HMI with satisfactory performance in terms of the false operation ratio in both the control and the idle states., Significance: The proposed HMI offers a simple and effective approach for patients with severe SCIs to control a smart home environment. Therefore, it is promising to assist severe SCI patients in their daily lives.

Objective: Nonmanual human-machine interfaces (HMIs) have been studied for wheelchair control with the aim of helping severely paralyzed individuals regain some mobility. The challenge is to rapidly, accurately, and sufficiently produce control commands, such as left and right turns, forward and backward motions, acceleration, deceleration, and stopping. In this paper, a novel electrooculogram (EOG) based HMI is proposed for wheelchair control., Methods: A total of 13 flashing buttons, each of which corresponds to a command, are presented in the graphical user interface. These buttons flash on a one-by-one manner in a predefined sequence. The user can select a button by blinking in sync with its flashes. The algorithm detects the eye blinks from a channel of vertical EOG data and determines the user's target button based on the synchronization between the detected blinks and the button's flashes., Results: For healthy subjects/patients with spinal cord injuries, the proposed HMI achieved an average accuracy of 96.7% / 91.7% and a response time of 3.53 s/3.67 s with 0 false positive rates (FPRs)., Conclusion: Using one channel of vertical EOG signals associated with eye blinks, the proposed HMI can accurately provide sufficient commands with a satisfactory response time., Significance: The proposed HMI provides a novel nonmanual approach for severely paralyzed individuals to control a wheelchair. Compared with a newly established EOG-based HMI, the proposed HMI can generate more commands with higher accuracy, lower FPR, and fewer electrodes.

This study proposes an event-related potential (ERP) BCI-based environmental control system that integrates household electrical appliances, a nursing bed, and an intelligent wheelchair to provide daily assistance to paralyzed patients with severe spinal cord injuries (SCIs)., Methods: An asynchronous mode is used to switch the environmental control system on or off or to select a device (e.g., a TV) for achieving selfpaced control. In the asynchronous mode, we introduce several pseudo-keys and a verification mechanism to effectively reduce the false operation rate. By contrast, when the user selects a function of the device (e.g., a TV channel), a synchronous mode is used to improve the accuracy and speed of BCI detection. Two experiments involving six SCI patients were conducted separately in a nursing bed and a wheelchair, and the patients were instructed to control the nursing bed, the wheelchair, and household electrical appliances (an electric light, an air conditioner, and a TV)., Results: The average false rate of BCI commands in the control state was 10.4%, whereas the average false operation ratio was 4.9% (a false BCI command might not necessarily result in a false operation according to our system design). During the idle state, there was an average of 0.97 false positives per minute, which did not result in any false operations., Conclusion: All SCI patients could use the proposed ERP BCIbased environmental control system satisfactorily., Significance: The proposed ERP-based environmental control system could be used to assist patients with severe SCIs in their daily lives.

Goal: Motor imagery-related mu/beta rhythms, which can be voluntarily modulated by subjects, have been widely used in EEG-based brain computer interfaces (BCIs). Moreover, it has been suggested that motor imagery-specific EEG differences can be enhanced by feedback training. However, the differences observed in the EEGs of naive subjects are typically not sufficient to provide reliable EEG control and thus result in unintended feedback. Such feedback can frustrate subjects and impede training. In this study, a hybrid BCI paradigm combining motor imagery and steady-state visually evoked potentials (SSVEPs) has been proposed to provide effective continuous feedback for motor imagery training., Methods: During the initial training sessions, subjects must focus on flickering buttons to evoke SSVEPs as they perform motor imagery tasks. The output/feedback of the hybrid BCI is based on hybrid features consisting of motor imagery- and SSVEP-related brain signals. In this context, the SSVEP plays a more important role than motor imagery in generating feedback. As the training progresses, the subjects can gradually decrease their visual attention to the flickering buttons, provided that the feedback is still effective. In this case, the feedback is mainly based on motor imagery., Results: Our experimental results demonstrate that subjects generate distinguishable brain patterns of hand motor imagery after only five training sessions lasting approximately 1.5 h each., Conclusion: The proposed hybrid feedback paradigm can be used to enhance motor imagery training., Significance: This hybrid BCI system with feedback can effectively identify the intentions of the subjects.

Low energy consumption is crucial for body area networks (BANs). In BAN-enabled ECG monitoring, the continuous monitoring entails the need of the sensor nodes to transmit a huge data to the sink node, which leads to excessive energy consumption. To reduce airtime over energy-hungry wireless links, this paper presents an energy-efficient compressed sensing (CS)-based approach for on-node ECG compression. At first, an algorithm called minimal mutual coherence pursuit is proposed to construct sparse binary measurement matrices, which can be used to encode the ECG signals with superior performance and extremely low complexity. Second, in order to minimize the data rate required for faithful reconstruction, a weighted ℓ1 minimization model is derived by exploring the multisource prior knowledge in wavelet domain. Experimental results on MIT-BIH arrhythmia database reveals that the proposed approach can obtain higher compression ratio than the state-of-the-art CS-based methods. Together with its low encoding complexity, our approach can achieve significant energy saving in both encoding process and wireless transmission.

In this paper, a hybrid brain-computer interface (BCI) system combining P300 and steady-state visual evoked potential (SSVEP) is proposed to improve the performance of asynchronous control. The four groups of flickering buttons were set in the graphical user interface. Each group contained one large button in the center and eight small buttons around it, all of which flashed at a fixed frequency (e.g., 7.5 Hz) to evoke SSVEP. At the same time, the four large buttons of the four groups were intensified through shape and color changes in a random order to produce P300 potential. During the control state, the user focused on a desired group of buttons (target buttons) to evoke P300 potential and SSVEP, simultaneously. Discrimination between the control and idle states was based on the detection of both P300 and SSVEP on the same group of buttons. As an application, this method was used to produce a "go/stop" command in real-time wheelchair control. Several experiments were conducted, and data analysis results showed that combining P300 potential and SSVEP significantly improved the performance of the BCI system in terms of detection accuracy and response time.

Practical brain-computer interface (BCI) systems should require only low training effort for the user, and the algorithms used to classify the intent of the user should be computationally efficient. However, due to inter- and intra-subject variations in EEG signal, intermittent training/calibration is often unavoidable. In this paper, we present an online semi-supervised P300 BCI speller system. After a short initial training (around or less than 1 min in our experiments), the system is switched to a mode where the user can input characters through selective attention. In this mode, a self-training least squares support vector machine (LS-SVM) classifier is gradually enhanced in back end with the unlabeled EEG data collected online after every character input. In this way, the classifier is gradually enhanced. Even though the user may experience some errors in input at the beginning due to the small initial training dataset, the accuracy approaches that of fully supervised method in a few minutes. The algorithm based on LS-SVM and its sequential update has low computational complexity; thus, it is suitable for online applications. The effectiveness of the algorithm has been validated through data analysis on BCI Competition III dataset II (P300 speller BCI data). The performance of the online system was evaluated through experimental results on eight healthy subjects, where all of them achieved the spelling accuracy of 85 % or above within an average online semi-supervised learning time of around 3 min.

To control a cursor on a monitor screen, a user generally needs to perform two tasks sequentially. The first task is to move the cursor to a target on the monitor screen (termed a 2-D cursor movement), and the second task is either to select a target of interest by clicking on it or to reject a target that is not of interest by not clicking on it. In a previous study, we implemented the former function in an EEG-based brain-computer interface system using motor imagery and the P300 potential to control the horizontal and vertical cursor movements, respectively. In this study, the target selection or rejection functionality is implemented using a hybrid feature from motor imagery and the P300 potential. Specifically, to select the target of interest, the user must focus his or her attention on a flashing button to evoke the P300 potential, while simultaneously maintaining an idle state of motor imagery. Otherwise, the user performs left-/right-hand motor imagery without paying attention to any buttons to reject the target. Our data analysis and online experimental results validate the effectiveness of our approach. The proposed hybrid feature is shown to be more effective than the use of either the motor imagery feature or the P300 feature alone. Eleven subjects attended our online experiment, in which a trial involved sequential 2-D cursor movement and target selection. The average duration of each trial and average accuracy of target selection were 18.19 s and 93.99% , respectively, and each target selection or rejection event was performed within 2 s., (© 2011 IEEE)

Two-dimensional cursor control is an important and challenging issue in EEG-based brain-computer interfaces (BCIs). To address this issue, here we propose a new approach by combining two brain signals including Mu/Beta rhythm during motor imagery and P300 potential. In particular, a motor imagery detection mechanism and a P300 potential detection mechanism are devised and integrated such that the user is able to use the two signals to control, respectively, simultaneously, and independently, the horizontal and the vertical movements of the cursor in a specially designed graphic user interface. A real-time BCI system based on this approach is implemented and evaluated through an online experiment involving six subjects performing 2-D control tasks. The results attest to the efficacy of obtaining two independent control signals by the proposed approach. Furthermore, the results show that the system has merit compared with prior systems: it allows cursor movement between arbitrary positions.

In sparse representation, two important sparse solutions, the 0-norm and 1-norm solutions, have been receiving much of attention. The 0-norm solution is the sparsest, however it is not easy to obtain. Although the 1-norm solution may not be the sparsest, it can be easily obtained by the linear programming method. In many cases, the 0-norm solution can be obtained through finding the 1-norm solution. Many discussions exist on the equivalence of the two sparse solutions. This paper analyzes two conditions for the equivalence of the two sparse solutions. The first condition is necessary and sufficient, however, difficult to verify. Although the second is necessary but is not sufficient, it is easy to verify. In this paper, we analyze the second condition within the stochastic framework and propose a variant. We then prove that the equivalence of the two sparse solutions holds with high probability under the variant of the second condition. Furthermore, in the limit case where the 0-norm solution is extremely sparse, the second condition is also a sufficient condition with probability 1.

Multivariate pattern analysis approaches toward detection of brain regions from fMRI data have been gaining attention recently. In this study, we introduce an iterative sparse-representation-based algorithm for detection of voxels in functional MRI (fMRI) data with task relevant information. In each iteration of the algorithm, a linear programming problem is solved and a sparse weight vector is subsequently obtained. The final weight vector is the mean of those obtained in all iterations. The characteristics of our algorithm are as follows: 1) the weight vector (output) is sparse; 2) the magnitude of each entry of the weight vector represents the significance of its corresponding variable or feature in a classification or regression problem; and 3) due to the convergence of this algorithm, a stable weight vector is obtained. To demonstrate the validity of our algorithm and illustrate its application, we apply the algorithm to the Pittsburgh Brain Activity Interpretation Competition 2007 functional fMRI dataset for selecting the voxels, which are the most relevant to the tasks of the subjects. Based on this dataset, the aforementioned characteristics of our algorithm are analyzed, and a comparison between our method with the univariate general-linear-model-based statistical parametric mapping is performed. Using our method, a combination of voxels are selected based on the principle of effective/sparse representation of a task. Data analysis results in this paper show that this combination of voxels is suitable for decoding tasks and demonstrate the effectiveness of our method.

This paper discusses the estimation and numerical calculation of the probability that the 0-norm and 1-norm solutions of underdetermined linear equations are equivalent in the case of sparse representation. First, we define the sparsity degree of a signal. Two equivalence probability estimates are obtained when the entries of the 0-norm solution have different sparsity degrees. One is for the case in which the basis matrix is given or estimated, and the other is for the case in which the basis matrix is random. However, the computational burden to calculate these probabilities increases exponentially as the number of columns of the basis matrix increases. This computational complexity problem can be avoided through a sampling method. Next, we analyze the sparsity degree of mixtures and establish the relationship between the equivalence probability and the sparsity degree of the mixtures. This relationship can be used to analyze the performance of blind source separation (BSS). Furthermore, we extend the equivalence probability estimates to the small noise case. Finally, we illustrate how to use these theoretical results to guarantee a satisfactory performance in underdetermined BSS.

In this paper, we use a two-stage sparse factorization approach for blindly estimating the channel parameters and then estimating source components for electroencephalogram (EEG) signals. EEG signals are assumed to be linear mixtures of source components, artifacts, etc. Therefore, a raw EEG data matrix can be factored into the product of two matrices, one of which represents the mixing matrix and the other the source component matrix. Furthermore, the components are sparse in the time-frequency domain, i.e., the factorization is a sparse factorization in the time frequency domain. It is a challenging task to estimate the mixing matrix. Our extensive analysis and computational results, which were based on many sets of EEG data, not only provide firm evidences supporting the above assumption, but also prompt us to propose a new algorithm for estimating the mixing matrix. After the mixing matrix is estimated, the source components are estimated in the time frequency domain using a linear programming method. In an example of the potential applications of our approach, we analyzed the EEG data that was obtained from a modified Sternberg memory experiment. Two almost uncorrelated components obtained by applying the sparse factorization method were selected for phase synchronization analysis. Several interesting findings were obtained, especially that memory-related synchronization and desynchronization appear in the alpha band, and that the strength of alpha band synchronization is related to memory performance.