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Low-rank matrix restoration, which aims to recover low-rank structures from degraded observation matrices, has been extensively studied in computer vision. However, the existing methods always suffer from data information loss caused by over shrinkage of the rank component or heavy computation burden brought by singular value decomposition. To simultaneously account for these two issues, in this work we propose a low-rank restoration model based on the bilinear factorization for image denoising. Specifically, the essence of the weighted Schatten 2/3 quasi-norm is defined as the hybrid norm of weighted Frobenius/nuclear, thus is extended to a more solvable optimization problem by harnessing the convexity of both factor matrix terms. Moreover, the weights are introduced to ℓ p norm with p = 2 / 3 , which both leverages the solvability of the ℓ 2 / 3 norm and mitigates the over shrinkage problem. Furthermore, for effectively preserving the edge features of image, the total variation (TV) norm is also integrated into the proposed weighted low-rank restoration model. Collectively, above rationally introduced ingredients enables our algorithm to enhance the structural smoothness and effectively remove large sparse noise in the case of natural images with low rank attributes. Finally, the experiments on several data sets show that the proposed method significantly improve the quality of reconstructed images, compared with existing low-rank methods, which confirms the desired roles of introduced ingredients and the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

A major threat to satellites is space debris, which are observed in orbit for a short time due to their low mass and high rotational speed. This major limitation causes them not to be fully illuminated in one snapshot, resulting in their incomplete image reconstruction and identification. In this paper, we propose a method to decrease the number of snapshots in a given observation time and use a limited number of spot beams per snapshot, which we call the encoded aperture. To recover the space debris images, an inverse problem is defined based on compressive sensing methods. Also, we show that for satellite imaging the Total Variation (TV) norm is more appropriate. We develop a procedure to recover space debris and satellites using L 1 and TV norms. Using simulation results, the proposed method is compared with the well-known Sparse Bayesian Learning (SBL) and S L 0 methods in terms of the number of snapshots, minimum Mean Square Error (MSE), Signal-to-Noise Ratio (SNR), and running time. It is shown that the proposed method can successfully recover the images of space objects using a fewer number of snapshots. [ABSTRACT FROM AUTHOR]

Group sparse coding (GSC) uses the non-local similarity of images as constraints, which can fully exploit the structure and group sparse features of images. However, it only imposes the sparsity on the group coefficients, which limits the effectiveness of reconstructing real images. Low-rank regularized group sparse coding (LR-GSC) reduces this gap by imposing low-rankness on the group sparse coefficients. However, due to the use of non-local similarity, the edges and details of the images are over-smoothed, resulting in the blocking artifact of the images. In this paper, we propose a low-rank matrix restoration model based on sparse coding and dual weighting. In addition, total variation (TV) regularization is integrated into the proposed model to maintain local structure smoothness and edge features. Finally, to solve the problem of the proposed optimization, an optimization method is developed based on the alternating direction method. Extensive experimental results show that the proposed SDWLR-GSC algorithm outperforms state-of-the-art algorithms for image restoration when the images have large and sparse noise, such as salt and pepper noise. [ABSTRACT FROM AUTHOR]

Natural images often have intrinsic low-rank structures and are susceptible to interference from outliers or perturbation noise, especially mixed noise. Low-rank matrix recovery via outlier estimation (ROUTE) has been proposed to determine the location of gross corruption by estimating the outliers; however, this approach ignores local structural smoothness. In this paper, we incorporate TV norm regularization into the ROUTE model of low-rank matrix recovery, which is called SSROUTE. This model can ensure structural smoothness in image denoising that is vulnerable to outlier noise and additive white Gaussian noise simultaneously. In addition, to solve the reformulated optimal problem, we develop an algorithm based on the alternating direction method of multipliers. Experimental results show that the proposed algorithm achieves a competitive denoising performance, especially for mixed noise. [ABSTRACT FROM AUTHOR]

Group sparse coding (GSC) uses the non-local similarity of images as constraints, which can fully exploit the structure and group sparse features of images. However, it only imposes the sparsity on the group coefficients, which limits the effectiveness of reconstructing real images. Low-rank regularized group sparse coding (LR-GSC) reduces this gap by imposing low-rankness on the group sparse coefficients. However, due to the use of non-local similarity, the edges and details of the images are over-smoothed, resulting in the blocking artifact of the images. In this paper, we propose a low-rank matrix restoration model based on sparse coding and dual weighting. In addition, total variation (TV) regularization is integrated into the proposed model to maintain local structure smoothness and edge features. Finally, to solve the problem of the proposed optimization, an optimization method is developed based on the alternating direction method. Extensive experimental results show that the proposed SDWLR-GSC algorithm outperforms state-of-the-art algorithms for image restoration when the images have large and sparse noise, such as salt and pepper noise.

In this paper, we propose a multi-matrices low-rank decomposition method for image denoising. In this new method, the total variation (TV) norm is incorporated into low-rank approximation analysis to achieve structural smoothness and to improve quality of the recovered images. Our proposed mathematical framework for multi-matrices low-rank decomposition combines the nuclear norm, TV norm, and $\mathcal {L}_{1}$ norm, which allows us to exploit the low-rank property of natural images, enhance the structural smoothness, and detect and remove large sparse noise. Based on the iterative alternating direction method, we develop an algorithm to solve the proposed challenging optimization problem. We conduct extensive experiments and perform evaluations on multi-images denoising and multi-frames video prediction. Our experimental results demonstrate that the proposed method outperforms the state-of-the-art low-rank matrix recovery methods, particularly for images with large sparse noise. [ABSTRACT FROM AUTHOR]