We propose an image restoration technique exploiting regularized inversion and the recent block-matching and 3D
filtering (BM3D) denoising filter. The BM3D employs a non-local modeling of images by collecting similar image
patches in 3D arrays. The so-called collaborative filtering applied on such a 3D array is realized by transformdomain
shrinkage. In this work, we propose an extension of the BM3D filter for colored noise, which we use in
a two-step deblurring algorithm to improve the regularization after inversion in discrete Fourier domain. The
first step of the algorithm is a regularized inversion using BM3D with collaborative hard-thresholding and the
seconds step is a regularized Wiener inversion using BM3D with collaborative Wiener filtering. The experimental
results show that the proposed technique is competitive with and in most cases outperforms the current best
image restoration methods in terms of improvement in signal-to-noise ratio.
We present a novel approach to still image denoising based on effective filtering in 3D transform domain by combining sliding-window transform processing with block-matching. We process blocks within the image in a sliding manner and utilize the block-matching concept by searching for blocks which are similar to the currently
processed one. The matched blocks are stacked together to form a 3D array and due to the similarity between them, the data in the array exhibit high level of correlation. We exploit this correlation by applying a 3D decorrelating unitary transform and effectively attenuate the noise by shrinkage of the transform coefficients. The subsequent inverse 3D transform yields estimates of all matched blocks. After repeating this procedure for all image blocks in sliding manner, the final estimate is computed as weighed average of all overlapping blockestimates. A fast and efficient algorithm implementing the proposed approach is developed. The experimental
results show that the proposed method delivers state-of-art denoising performance, both in terms of objective criteria and visual quality.
The shape-adaptive DCT (SA-DCT) can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable block 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. It has been recently proposed by the authors<sup>8</sup> to employ the SA-DCT for still image denoising. We use the SA-DCT in conjunction with the directional LPA-ICI technique, which defines the shape of the transform's support in a pointwise adaptive manner. The thresholded or modified 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. In this paper we further develop this novel approach and extend it to more general restoration problems, with particular emphasis on image deconvolution. 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.