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.

The traditional group sparse optimization method can simultaneously achieve the channel selection and classification for the motor imagery electroencephalogram (EEG) signals, but it doesn’t consider the spatial structure information between the electrode channels. Combining the group sparsity and spatial smoothness of EEG signals, a new EEG classification model is proposed, which is an improvement of group least absolute shrinkage and selection operator (LASSO). We call it fused group LASSO. First, group LASSO is used to model the group sparsity of EEG signals, the features of the same channel are assigned the same weights. Then, based on group LASSO, channel weights are regularized by total variation norm (TV-norm), which constrains the weights of adjacent channels to the same or similar, thereby the spatial smoothness modeling of EEG signals can be achieved. Using the primal-dual theory, an optimization algorithm for the new model is given. In order to verify the effectiveness of the new model, experiments were performed on two public brain-computer interface (BCI) competition data sets and one self-collected data set. Compared with the existing sparse optimization methods, the proposed method has achieved the highest average classification accuracy of 79.24%, 86.64% and 81.09%, respectively, and with better physiological interpretability. Compared with spatial filtering methods with smooth constraints, the proposed method realized global spatial smooth in a data-driver manner, and achieved the highest average classification accuracy of 84.96% in two competition data sets. All the experimental results showed that the proposed method can significantly improve the performance of BCI systems.

Background: Image segmentation is an important part of computer-aided diagnosis (CAD), the segmentation of small ground glass opacity (GGO) pulmonary nodules is beneficial for the early detection of lung cancer. For the segmentation of small GGO pulmonary nodules, an integrated active contour model based on Markov random field energy and Bayesian probability difference (IACM_MRFEBPD) is proposed in this paper. Methods: First, the Markov random field (MRF) is constructed on the computed tomography (CT) images, then the MRF energy is calculated. The MRF energy is used to construct the region term. It can not only enhance the contrast between pulmonary nodule and the background region, but also solve the problem of intensity inhomogeneity using local spatial correlation information between neighboring pixels in the image. Second, the Gaussian mixture model is used to establish the probability model of the image, and the model parameters are estimated by the expectation maximization (EM) algorithm. So the Bayesian posterior probability difference of each pixel can be calculated. The probability difference is used to construct the boundary detection term, which is 0 at the boundary. Therefore, the blurred boundary problem can be solved. Finally, under the framework of the level set, the integrated active contour model is constructed. Results: To verify the effectiveness of the proposed method, the public data of the lung image database consortium and image database resource initiative (LIDC-IDRI) and the clinical data of the Affiliated Jiangmen Hospital of Sun Yat-sen University are used to perform experiments, and the intersection over union (IOU) score is used to evaluate the segmentation methods. Compared with other methods, the proposed method achieves the best results with the highest average IOU of 0.7444, 0.7503, and 0.7450 for LIDC-IDRI test set, clinical test set, and all test sets, respectively. Conclusions: The experiment results show that the proposed method can segment various small GGO pulmonary nodules more accurately and robustly, which is helpful for the accurate evaluation of medical imaging.

In this article, the problem of impulse noise image restoration is investigated. A typical way to eliminate impulse noise is to use an $L_{1}$ 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 $L_{1}$ 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.