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Most existing regression based classification methods for robust face recognition usually characterize the representation error using L 1 -norm or Frobenius-norm for the pixel-level noise or nuclear norm for the image-level noise, and code the coefficients vector by l 1 -norm or l 2 -norm. To our best knowledge, nuclear norm can be used to describe the low-rank structural information but may lead to the suboptimal solution, while l 1 -norm or l 2 -norm can promote the sparsity or cooperativity but may neglect the prior information (e.g., the locality and similarity relationship) among data. To solve these drawbacks, we propose two weighted sparse coding regularized nonconvex matrix regression models including w eighted s parse coding regularized matrix γ -norm based m atrix r egression (WS γ MR) for the structural noise and w eighted s parse coding regularized matrix γ -norm plus m inimax concave plus (MCP) function based m atrix r egression (WS γ M 2 R) for the mixed noise (e.g, structural noise plus sparse noise). The MCP induced nonconvex function can overcome the imbalanced penalization of different singular values and entries of the error image matrix, and the weighted sparse coding can consider the prior information by borrowing a novel distance metric. The variants of inexact augmented Lagrange multiplier (iALM) algorithm including nonconvex iALM (NCiALM) and majorization-minimization iALM (MMiALM) are developed to solve the proposed models, respectively. The matrix γ -norm based classifier is devised for classification. Finally, experiments on four popular face image databases can validate the superiority of our methods compared with the-state-of-the-art regression methods. [ABSTRACT FROM AUTHOR]

Compressive sensing (CS) based computed tomography (CT) image reconstruction aims at reducing the radiation risk through sparse-view projection data. However, it is challenging to achieve satisfying image quality from incomplete projections. Recent works demonstrate the promising potential of nonconvex L 1 / 2 -norm in CS problem, while the applications on medical imaging are constrained by its nonconvexity. In this paper, we develop an L 1 / 2 -regularized nonlocal self-similarity (NSS) denoiser based CT reconstruction model, which combines with low-rank approximation and group sparse coding (GSC) framework. Concretely, we firstly split the CT reconstruction problem into two subproblems, then improve CT image quality furtherly using our proposed denoiser. Instead of optimizing the nonconvex problem under the perspective of GSC, we particularly reconstruct CT image via low-rank minimization based on two simple yet essential schemes, which build the equivalent relationship between GSC based denoiser and low-rank minimization. Furtherly, the weighted singular value thresholding (WSVT) operator is utilized to optimize the resulting nonconvex L 1 / 2 minimization problem. Following this, our proposed denoiser is integrated with the CT reconstruction problem by alternating direction method of multipliers (ADMM) framework. Extensive experimental results on typical clinical CT images have demonstrated that our approach can further achieve better performance than popular approaches. [ABSTRACT FROM AUTHOR]

Linear regression-based and extended methods have been widely used in pattern classification. These methods can be roughly divided into two categories: reconstruction error-based methods and discriminative methods. The reconstruction error-based methods search the target label by learning the representation coefficients to compute the minimal reconstruction error. The goal of the discriminative methods is to learn the projection matrix to predict the target label of the image. To combine the advantages of these two kinds of regression-based methods, this paper presents a dual robust regression framework (DualRR) for pattern classification. In the training stage, a double low-rank robust regression model (DLR) is proposed to learn the projection matrix. In DLR, low-rank robust regression motivates us to model the data as the sum of a low-rank clean data and sparse noise matrix. The low-rank is further used to constrain the projection matrix to enhance the discriminative performance. In the testing stage, the proposed framework employs a robust regression representation model to learn the optimal representation coefficients and obtain the reconstruction sample to approximate the test sample. We thus apply the reconstruction sample to search the classification label by using the projection matrix learned in the training stage. Extensive experiments are conducted on six public available databases, namely, LFW, FRGC, CUHK Sketch, PolyU Palm, NUST-RF and Caltech 101, demonstrating the merits of the proposed model over state-of-the-art regression-based classification methods. [ABSTRACT FROM AUTHOR]