Abstract—We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2-D image fragments (e.g., blocks) into 3-D data arrays which we call “groups. ” Collaborative filtering is a special procedure developed to deal with these 3-D groups. We realize it using the three successive steps: 3-D transformation of a group, shrinkage of the transform spectrum, and inverse 3-D transformation. The result is a 3-D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality. Index Terms—Adaptive grouping, block matching, image denoising, sparsity, 3-D transform shrinkage. I.

Abstract—The shape-adaptive discrete cosine transform (SA-DCT) transform can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable block-DCT (B-DCT). Despite the near-optimal decorrelation and energy compaction properties, application of the SA-DCT has been rather limited, targeted nearly exclusively to video compression. In this paper, we present a novel approach to image filtering based on the SA-DCT. We use the SA-DCT in conjunction with the Anisotropic Local Polynomial Approximation—Intersection of Confidence Intervals technique, which defines the shape of the transform’s support in a pointwise adaptive manner. The thresholded or attenuated SA-DCT coefficients are used to reconstruct a local estimate of the signal within the adaptive-shape support. Since supports corresponding to different points are in general overlapping, the local estimates are averaged together using adaptive weights that depend on the region’s statistics. This approach can be used for various image-processing tasks. In this paper, we consider, in particular, image denoising and image deblocking and deringing from block-DCT compression. A special structural constraint in luminance-chrominance space is also proposed to enable an accurate filtering of color images. Simulation experiments show a state-of-the-art quality of the final estimate, both in terms of objective criteria and visual appearance. Thanks to the adaptive support, reconstructed edges are clean, and no unpleasant ringing artifacts are introduced by the fitted transform. Index Terms—Anisotropic, deblocking, denoising, deringing, discrete cosine transform (DCT), shape adaptive.

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We propose an effective color image denoising method that exploits ltering in highly sparse local 3D transform domain in each channel of a luminance-chrominance color space. For each image block in each channel, a 3D array is formed by stacking together blocks similar to it, a process that we call “grouping”. The high similarity between grouped blocks in each 3D array enables a highly sparse representation of the true signal in a 3D transform domain and thus a subsequent shrinkage of the transform spectra results in effective noise attenuation. The peculiarity of the proposed method is the application of a “grouping constraint ” on the chrominances by reusing exactly the same grouping as for the luminance. The results demonstrate the effectiveness of the proposed grouping constraint and show that the developed denoising algorithm achieves state-of-the-art performance in terms of both peak signal-to-noise ratio and visual quality. Index Terms — color image denoising, adaptive grouping, blockmatching, shrinkage. 1.

One of the promising recent directions in nonparametric regression concerns the spatially adaptive estimation, which can be treated as an extended model selection problem where the basis as well as the basis supports are selected simultaneously.

We propose a new algorithm for multispectral image denoising. The algorithm is based on the state-of-the-art Block Matching 3-D lter. For each “reference ” 3-D block of multispectral data (sub-array of pixels from spatial and spectral locations) we nd similar 3-D blocks using block matching and group them together to form a set of 4-D groups of pixels in spatial (2-D), spectral (1-D) and “temporally matched ” (1-D) directions. Each of these groups is transformed using 4-D separable transforms formed by a xed 2-D transform in spatial coordinates, a xed 1-D transform in “temporal ” coordinate, and 1-D PCA transform in spectral coordinates. Denoising is performed by shrinking these 4-D spectral components, applying an inverse 4-D transform to obtain estimates for all 4-D blocks and aggregating all estimates together. The effectiveness of the proposed approach is demonstrated on the denoising of real images captured with multispectral camera.