Image Denoising via Nonlocal Low Rank Approximation With Local Structure Preserving

Abstract

The nuclear norm minimization method emerged from a patch-based low-rank model leads to an excellent image denoising performance, where the non-local self-similarity over image patches is exploited. However, natural images are normally with complex and irregular image patches, which cannot be well represented using only a low-rank model, and thus most of them suffer from the over-penalty problem especially for images with lots of local irregular structures (e.g., fine details or sharp edges), and then results in over-smoothing problem after denoising. On the other hand, in order to represent the irregular components, edges defined over pixel level are often exploited. While the total variation (TV) is a well-known prior to remove noises and preserve edges, it might yield undesired staircase artifacts. The total generalized variation (TGV), a generalization of TV, can largely alleviate such staircase artifacts. Consequently, in order to deal with the over-smoothing problem aroused by a low-rank model, we propose a re-weighted TGV regularized nuclear norm minimization model for local structure preserving image denoising. Thanks to the split Bregman method, our proposed model can be effectively solved. A re-weighted strategy is developed to adaptively update the weight parameters of TGV regularization. The encouraging experimental results on noisy images demonstrate the effectiveness of our proposed method. INDEX TERMS Low rank, nuclear norm minimization, total generalized variation, image denoising, local structures preserving.

Nonconvex Low Rank Approximation With Phase Congruency Regularization for Mixed Noise Removal

“…Approaches based on low rank matrix factorization [23], [24] and those based on nuclear norm minimization [22], [25], [26] are two categories of low rank reconstruction from noisy data. Methods in the first category are that the given data matrix is decomposed as a product of two matrices of fixed low rank by matrix factorization.…”

“…On the other hand, methods based on nuclear norm minimization are to estimate rank minimization, such as Robust Principal Component Analysis(RPCA) [27]. Its extensions of RPCA [22], [25], [26], which is a convex optimization framework, have been successfully applied in image denoising. Suppose that Y ∈ R m×n is the observation image, and X denotes its underlying low rank matrix.…”

“…TV norm was incorporated into low rank approximation analysis to achieve structural smoothness and to improve quality of the recovered images by [20], which exploited the low rank property of natural images, enhancing the structural smoothness, detecting and removing large sparse noise. In order to improve high performance and flexibility, reweighted Total Generalized Variation(TGV) regularized nuclear norm minimization model was utilized to preserve local structure in image denoising [21], [22].…”

Mixed Noise Removal Using Adaptive Median Based Non-Local Rank Minimization

“…Rank minimization mechanism, generally known as low rank approximation, is one of the most effective approaches for Gaussian noise removal [4], [6], [32]- [34] in recent years. More recently, in addition to Gaussian noise model, low rank approximation has been successfully applied to a variety of noise models such as speckle noise and seismic noise models [35]- [37].…”

Improved RPCA method via non‐convex regularisation for image denoising

“…Restoring a clean image from its noisy version is a hot research issue in the field of low-level computer vision because the noise can destroy important details in the image and reduce its quality. Image denoising is a broad research subject in the past few decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The extensively studied image denoising algorithms can be divided into two main categories: sparse representation and lowrank matrix recovery (LRMR).…”