Nonlocally Centralized Sparse Representation for Image Restoration

Abstract

Abstract:The sparse representation models code an image patch as a linear combination of a few atoms chosen out from an over-complete dictionary, and they have shown promising results in various image restoration applications. However, due to the degradation of the observed image (e.g., noisy, blurred and/or downsampled), the sparse representations by conventional models may not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation based image restoration, in this paper the concept of sparse coding noise is introduced, and the goal of image restoration turns to how to suppress the sparse coding noise. To this end, we exploit the image nonlocal self-similarity to obtain good estimates of the sparse coding coefficients of the original image, and then centralize the sparse coding coefficients of the observed image to those estimates. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, while our extensive experiments on various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed NCSR algorithm.

Sparse Representation for Color Image Super-Resolution with Image Quality Difference Evaluation

“…Referring to Dong's algorithm [14], putting the images 1-3 (shown in the test dataset in Fig. 3) as examples, we plot the trend chart of the variation of PSNR and the two features during 640 iterations which is shown in Fig.…”

“…Because of the noise and blur, α y is not exactly equal with α x , the sparse representation coefficient of the original high-resolution image x, so Dong et al [14] proposed NCSR model introducing sparse code noise:…”

“…In Dong's algorithm [14], one most suitable subdictionary trained by K-means PCA will be selected adaptively for each patch, so the coding coefficients of this patch over the other sub-dictionaries are 0 and α is already sparse. Therefore, the sparsity regularization term ||α|| 1 can be removed and the NCSR model is formulated as follows:…”

“…In 2011, Dong et al [13] proposed a SR method based on adaptive sparse domain selection and adaptive regularization (ASDS-AReg). In 2013, they proposed another model called Nonlocally Centralized Sparse Representation (NCSR), which turns the goal of image SR to how to suppress the sparse coding noise [14]. These methods adopt iterative shrinkage algorithm to solve l 1 -norm minimization problem.…”

Non-Local Sparse Image Inpainting for Document Bleed-Through Removal

“…A number of non-local regularization terms, exploiting the non-local self-similarity, are employed in solving inverse problems [29,30]. Fusing image sparsity with non-local self-similarity produces better results in recently reported image restoration techniques [31,32]. The underlying assumption in such methods is that similar patches share the same dictionary atoms.…”