Collaborative filters perform denoising through transform-domain shrinkage of a group of similar patches extracted from an image. Existing collaborative filters of stationary correlated noise have all used simple approximations of the transform noise power spectrum adopted from methods which do not employ patch grouping and instead operate on a single patch. We note the inaccuracies of these approximations and introduce a method for the exact computation of the noise power spectrum. Unlike earlier methods, the calculated noise variances are exact even when noise in one patch is correlated with noise in any of the other patches. We discuss the adoption of the exact noise power spectrum within shrinkage, in similarity testing (patch matching), and in aggregation. We also introduce effective approximations of the spectrum for faster computation. Extensive experiments support the proposed method over earlier crude approximations used by image denoising filters such as Block-Matching and 3D-filtering (BM3D), demonstrating dramatic improvement in many challenging conditions.

Collaborative filters perform denoising through transform-domain shrinkage of a group of similar blocks extracted from an image. Existing methods for collaborative filtering of stationary correlated noise have all used simple approximations of the transform noise power spectrum adopted from methods which do not employ block grouping. We note the inaccuracies of these approximations and introduce a method for the exact computation and effective approximations of the noise power spectrum. Unlike earlier methods, the calculated noise variances are exact even when noise in one block is correlated with noise in any of the other blocks. We discuss the adoption of the exact noise power spectrum within shrinkage, in similarity testing (block matching), and in aggregation. Extensive experiments support the proposed method over earlier crude approximations used by image denoising filters such as BM3D, demonstrating dramatic improvement in many challenging conditions.

We denoise Poisson images with an iterative algorithm that progressively improves the effectiveness of variance-stabilizing transformations (VST) for Gaussian denoising filters. At each iteration, a combination of the Poisson observations with the denoised estimate from the previous iteration is treated as scaled Poisson data and filtered through a VST scheme. Due to the slight mismatch between a true scaled Poisson distribution and this combination, a special exact unbiased inverse is designed. We present an implementation of this approach based on the BM3D Gaussian denoising filter. With a computational cost at worst twice that of the noniterative scheme, the proposed algorithm provides significantly better quality, particularly at low signal-to-noise ratio, outperforming much costlier state-of-the-art alternatives.

Groups of mutually similar image blocks are the key element in nonlocal image processing. In this work, the spatial coordinates of grouped blocks are leveraged in two distinct parts of the transform-domain collaborative filtering within the BM3D algorithm. First, we introduce an adaptive 1-D transform for 3-D collaborative filtering based on sampling 2-D smooth functions at the positions of grouped blocks. This adaptive transform is applied for improved decorrelation of the 2-D spectra of the grouped blocks. Second, we propose a directional sharpening procedure whose strength varies adaptively according to the relative orientation of the transform basis functions with respect to the group coordinates. Experiments confirm the efficacy of the proposed adaptations, for denoising as well as for sharpening of noisy images.

We introduce an adaptive Gaussian-Cauchy mixture modeling for the likelihood of pairwise mean/standard-deviation scatter points found when estimating signal-dependent noise. The maximization of the likelihood is used to identify the noise-model parameters, following an adaptive mixture parameter that controls the balance between the Gaussian and the heavy-tailed Cauchy. This renders the estimation robust with respect to outliers, typically present in large quantities among the scatter points from images dominated by texture. The modeling is directly suited to describing also observations subject to clipping, i.e. under- or over-exposure. Experiments on a dataset of badly exposed and highly textured images demonstrate the effectiveness of the adaptive Gaussian-Cauchy mixture likelihood for the accurate estimation of the noise standard-deviation curve.

We consider the estimation of signal-dependent noise from a single image. Unlike conventional algorithms that build a scatterplot of local mean-variance pairs from either small or adaptively selected homogeneous data samples, our proposed approach relies on arbitrarily large patches of heterogeneous data extracted at random from the image. We demonstrate the feasibility of our approach through an extensive theoretical analysis based on mixture of Gaussian distributions. A prototype algorithm is also developed in order to validate the approach on simulated data as well as on real camera raw images.