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.

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 consider the scenario where additive, independent and identically distributed (i.i.d) noise in an image is removed using an overcomplete set of linear transforms and thresholding. Rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates provided by denoising with each of the transforms, we formulate the optimal combination as a conditional linear estimation problem and solve it for optimal estimates. Our approach is independent of the utilized transforms and the thresholding scheme, and as we illustrate using oracle based denoisers, it extends established work by exploiting a separate degree of freedom that is in general not reachable using previous techniques. Our derivation of the optimal estimates specifically relies on the assumption that the utilized transforms provide sparse decompositions. At the same time, our work is robust as it does not require any assumptions about image statistics beyond sparsity. Unlike existing work which tries to devise ever more sophisticated transforms and thresholding algorithms to deal with the myriad types of image singularities, our work uses basic tools to obtain very high performance on singularities by taking better advantage of the sparsity that surrounds them. With well-established transforms we obtain results that are competitive with state-of-the-art methods. EDICS: RST-DNOI, FLT-LFLT

We study the denoising of signals from clipped noisy observations, such as digital images of an under- or over-exposed scene. From a precise mathematical formulation and analysis of the problem, we derive a set of homomorphic transformations that enable the use of existing denoising algorithms for non-clipped data (including arbitrary denoising Þlters for additive independent and identically distributed (i.i.d.) Gaussian noise). Our results have general applicability and can be "plugged " into current Þltering implementations, to enable a more accurate and better processing of clipped data. Experiments with synthetic images and with real raw data from charge-coupled device (CCD) sensor show the feasibility and accuracy of the approach. Key words: denoising; noise modeling; signal-dependent noise; heteroskedasticity; raw data; overexposure; underexposure; clipping; censoring; homomorphic transformations; variance stabilization. 1.

Abstract — We propose an image denoising method that exploits nonlocal image modeling, principal component analysis (PCA), and local shape-adaptive anisotropic estimation. The nonlocal modeling is exploited by grouping similar image patches in 3-D groups. The denoising is performed by shrinkage of the spectrum of a 3-D transform applied on such groups. The effectiveness of the shrinkage depends on the ability of the transform to sparsely represent the true-image data, thus separating it from the noise. We propose to improve the sparsity in two aspects. First, we employ image patches (neighborhoods) which can have data-adaptive shape. Second, we propose PCA on these adaptive-shape neighborhoods as part of the employed 3-D transform. The PCA bases are obtained by eigenvalue decomposition of empirical second-moment matrices that are estimated from groups of similar adaptive-shape neighborhoods. We show that the proposed method is competitive and outperforms some of the current best denoising methods, especially in preserving image details and introducing very few artifacts. I.

We propose an image denoising method that exploits both nonlocal image modeling and locally adaptive anisotropic estimation. The method uses grouping of adaptive-shape neighborhoods whose surrounding square supersets have been found similar by a blockmatching procedure. The data deÞned on these grouped neighborhoods is stacked together, resulting in 3-D data structures which are generalized cylinders with adaptive-shape cross sections. Because of the similarity, which follows from the matching, and because of the adaptive selection of the shape of the neighborhoods, these 3-D groups are characterized by a high correlation along all the three dimensions. We apply a 3-D decorrelating transform, computed as a separable composition of the Shape-Adaptive DCT (SA-DCT) and a 1-D orthonormal transform, and subsequently attenuate the noise by spectrum shrinkage with hard-thresholding or Wiener Þltering. Inversion of the 3-D transform produces individual estimates for all grouped neighborhoods. These estimates are returned to their original locations and aggregated with other estimates coming from different groups. Overall, this method generalizes two existing Þlters: the BM3D Þlter, which uses grouping of Þxed-size square blocks, and the Poinwise SA-DCT Þlter, which exploits shrinkage on adaptive-shape supports. We show that the developed method inherits the strengths of both Þlters, resulting in a very effective and ßexible tool for image denoising. 1.

In this paper we review and discuss some of the theoretical and practical aspects, the problems, and the considerations that pushed our research from the one-dimensional LPA-ICI (local polynomial approximation- interesection of conÞdence intervals) algorithm [27] to the development of powerful transform-based methods for anisotropic image

This paper presents a novel effective method for denoising of images corrupted by signal-dependent noise. Denoising is performed by coefÞcient shrinkage in the shape-adaptive DCT (SA-DCT) transform-domain. The Anisotropic Local Polynomial Approximation (LPA)- Intersection of ConÞdence Intervals (ICI) technique is used to deÞne the shape of the transform’s support in a pointwise adaptive manner. The use of such an adaptive transform support enables both a simpler modelling of the noise in the transform domain and a sparser decomposition of the signal. Consequently, coefÞcient shrinkage is very effective and the reconstructed estimate’s quality is high, in terms of both numerical error-criteria and visual appearance, with sharp detail preservation and clean edges. Simulation experiments demonstrate the superior performance of the proposed algorithm for a wide class of noise models with a signaldependent variance, including Poissonian (photon-limited imaging), Þlm-grain, and speckle noise. 1.

We outline the evolution of the nonparametric regression modelling in imaging from the local Nadaraya-Watson estimates to the nonlocal means and further to the latest nonlocal block-matching techniques based on transform-domain Þltering. The considered methods are classiÞed mainly according to two leading features: local/nonlocal and pointwise/multipoint. Here nonlocal is an alternative to local, and multipoint is alternative to pointwise. The alternatives, though an obvious simpliÞcation, allow to impose a fruitful and transparent classiÞcation of the basic ideas in the advanced techniques. Within this framework, we introduce a novel multiplemodel interpretation of the basic modelling used in the BM3D algorithm [11], highlighting a source of the outstanding performance of this type of algorithms. 1.

Abstract—In this paper, we present a patch-based variational Bayesian framework for video processing and demonstrate its potential in denoising, inpainting and deinterlacing. Unlike previous methods based on explicit motion estimation, we propose to embed motion-related information into the relationship among video patches and develop a nonlocal sparsity-based prior for typical video sequences. Specifically, we first extend block matching (Nearest Neighbor search) into patch clustering (k-Nearest-Neighbor search), which represents motion in an implicit and distributed fashion. Then we show how to exploit the sparsity constraint by sorting and packing similar patches, which can be better understood from a manifold perspective. Under the Bayesian framework, we treat both patch clustering result and unobservable data as latent variables and solve the inference problem via variational EM algorithms. A weighted averaging strategy of fusing diverse inference results from overlapped patches is also developed. The effectiveness of patch-based video models is demonstrated by extensive experimental results on a wider range of video materials. Index Terms—video processing, patch-based models, sparsitybased priors, variational Bayesian, variational EM, weighted averaging.