Cauchy non-convex sparse feature selection method for the high-dimensional small-sample problem in motor imagery EEG decoding.

Introduction: The time, frequency, and space information of electroencephalogram (EEG) signals is crucial for motor imagery decoding. However, these temporal-frequency-spatial features are high-dimensional small-sample data, which poses significant challenges for motor imagery decoding. Sparse regularization is an effective method for addressing this issue. However, the most commonly employed sparse regularization models in motor imagery decoding, such as the least absolute shrinkage and selection operator (LASSO), is a biased estimation method and leads to the loss of target feature information. Methods: In this paper, we propose a non-convex sparse regularization model that employs the Cauchy function. By designing a proximal gradient algorithm, our proposed model achieves closer-to-unbiased estimation than existing sparse models. Therefore, it can learn more accurate, discriminative, and effective feature information. Additionally, the proposed method can perform feature selection and classification simultaneously, without requiring additional classifiers. Results: We conducted experiments on two publicly available motor imagery EEG datasets. The proposed method achieved an average classification accuracy of 82.98% and 64.45% in subject-dependent and subject-independent decoding assessment methods, respectively. Conclusion: The experimental results show that the proposed method can significantly improve the performance of motor imagery decoding, with better classification performance than existing feature selection and deep learning methods. Furthermore, the proposed model shows better generalization capability, with parameter consistency over different datasets and robust classification across different training sample sizes. Compared with existing sparse regularization methods, the proposed method converges faster, and with shorter model training time.

A new difference of anisotropic and isotropic total variation regularization method for image restoration.

Total variation (TV) regularizer has diffusely emerged in image processing. In this paper, we propose a new nonconvex total variation regularization method based on the generalized Fischer-Burmeister function for image restoration. Since our model is nonconvex and nonsmooth, the specific difference of convex algorithms (DCA) are presented, in which the subproblem can be minimized by the alternating direction method of multipliers (ADMM). The algorithms have a low computational complexity in each iteration. Experiment results including image denoising and magnetic resonance imaging demonstrate that the proposed models produce more preferable results compared with state-of-the-art methods.

Impulse Noise Image Restoration Using Nonconvex Variational Model and Difference of Convex Functions Algorithm.

In this article, the problem of impulse noise image restoration is investigated. A typical way to eliminate impulse noise is to use an L1 norm data fitting term and a total variation (TV) regularization. However, a convex optimization method designed in this way always yields staircase artifacts. In addition, the L1 norm fitting term tends to penalize corrupted and noise-free data equally, and is not robust to impulse noise. In order to seek a solution of high recovery quality, we propose a new variational model that integrates the nonconvex data fitting term and the nonconvex TV regularization. The usage of the nonconvex TV regularizer helps to eliminate the staircase artifacts. Moreover, the nonconvex fidelity term can detect impulse noise effectively in the way that it is enforced when the observed data is slightly corrupted, while is less enforced for the severely corrupted pixels. A novel difference of convex functions algorithm is also developed to solve the variational model. Using the variational method, we prove that the sequence generated by the proposed algorithm converges to a stationary point of the nonconvex objective function. Experimental results show that our proposed algorithm is efficient and compares favorably with state-of-the-art methods.

The CSP-Based New Features Plus Non-Convex Log Sparse Feature Selection for Motor Imagery EEG Classification.

The common spatial pattern (CSP) is a very effective feature extraction method in motor imagery based brain computer interface (BCI), but its performance depends on the selection of the optimal frequency band. Although a lot of research works have been proposed to improve CSP, most of these works have the problems of large computation costs and long feature extraction time. To this end, three new feature extraction methods based on CSP and a new feature selection method based on non-convex log regularization are proposed in this paper. Firstly, EEG signals are spatially filtered by CSP, and then three new feature extraction methods are proposed. We called them CSP-wavelet, CSP-WPD and CSP-FB, respectively. For CSP-Wavelet and CSP-WPD, the discrete wavelet transform (DWT) or wavelet packet decomposition (WPD) is used to decompose the spatially filtered signals, and then the energy and standard deviation of the wavelet coefficients are extracted as features. For CSP-FB, the spatially filtered signals are filtered into multiple bands by a filter bank (FB), and then the logarithm of variances of each band are extracted as features. Secondly, a sparse optimization method regularized with a non-convex log function is proposed for the feature selection, which we called LOG, and an optimization algorithm for LOG is given. Finally, ensemble learning is used for secondary feature selection and classification model construction. Combing feature extraction and feature selection methods, a total of three new EEG decoding methods are obtained, namely CSP-Wavelet+LOG, CSP-WPD+LOG, and CSP-FB+LOG. Four public motor imagery datasets are used to verify the performance of the proposed methods. Compared to existing methods, the proposed methods achieved the highest average classification accuracy of 88.86, 83.40, 81.53, and 80.83 in datasets 1-4, respectively. The feature extraction time of CSP-FB is the shortest. The experimental results show that the proposed methods can effectively improve the classification accuracy and reduce the feature extraction time. With comprehensive consideration of classification accuracy and feature extraction time, CSP-FB+LOG has the best performance and can be used for the real-time BCI system.

A primal-dual algorithm framework for convex saddle-point optimization.

In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate [Formula: see text] in the ergodic and nonergodic senses is also given, where t denotes the iteration number.