Image denoising based on the edge-process model

Abstract

In this paper a novel stochastic image model in the transform domain is presented and its performance in image denoising application is experimentally validated. The proposed model exploits local subband image statistics and is based on geometrical priors. Contrarily to models based on local correlations, or mixture models, the proposed model performs a partition of the image into non-overlapping regions with distinctive statistics. A close form analytical solution of the image denoising problem for an additive white Gaussian noise (AWGN) is derived and its performance bounds are analyzed. Despite being very simple, the proposed stochastic image model provides a number of advantages in comparison to the existing approaches: (a) simplicity of stochastic image modeling; (b) completeness of the model, taking into account multiresolution, spatially adaptive image behavior, geometrical priors and providing an accurate fit to the global image statistics; (c) very low complexity of the algorithm; (d) tractability of the model and of the obtained results due to the closed-form solution and to the existence of analytical performance bounds; (e) extensibility to different transform domains, such as orthogonal, biorthogonal and overcomplete data representations.

Multivariate Statistical Models for Image Denoising in the Wavelet Domain

“…Some recent studies started to investigate the statistics of natural images belonging to different categories (Torralba et al, 2003) and realize the necessity to establishing 'object-based' model (Srivastava et al, 2003). More recently, Voloshynovskiy et al (2005) developed a novel image model that assumes an image can be represented as a union of a number of statistically homogeneous regions of different intensity levels, and treats the data inside each region as a stationary Gaussian with some variances. Despite being very simple, the model presented excellent performance for image denoising.…”

Practical Bounds on Image Denoising: From Estimation to Information

“…Another point to note is that we assume knowledge of the noise variance in our estimation of the covariance matrix in (8). However, in practice, this needs to be estimated from the given noisy image.…”

“…[8] provided a brief analysis of maximum a posteriori (MAP) based denoising methods. Recently, Treibitz et al [9] studied the limits of denoising, among other ill-posed image processing problems, as limits to recovering particular objects or image regions.…”

A fast computation method for time scale signal denoising

“…Let A 2 J the approximation band at the coarsest scale level J , {H 2 j } 1≤ j≤J and {V 2 j } 1≤ j≤J , respectively, the horizontal and vertical sub-bands at scale level j, as defined in Eqs. (33), (34) and (35). For each row of the vertical sub-bands and for each column of the horizontal sub-bands at each scale level j apply the algorithm in section 3.2 from point 1 to point 4.…”

“…The literature is rich of de-noising methodologies and strategies (see for instance [1,2,[4][5][6][7][8][9][10][11][12][13][14]17,18,[21][22][23][24][25][26]28,29,31,[33][34][35][36][37][38][39][40][41]), that formulate a model for the noise and/or for the original signal in suitable spaces where the differences between them are emphasized. They are mainly based on two observations: (i) noise and clean signal show different behaviors in a multi-scale representation; (ii) significant geometrical components of an image (edges) or time structures of a signal (sharp transitions) over-exceed noise information, especially at low resolution.…”