The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. Direct inversion leads to unacceptable noise amplification. Usually, the problem is either regularized during the inversion process, or the noise is filtered after deconvolution and decomposition in the wavelet transform domain. Herein, we have developed the second solution, by thresholding the coefficients of a new complex wavelet packet transform

We consider the question of computing Maximum A Posteriori (MAP) assignment in an arbitrary pair-wise Markov Random Field (MRF). We present a randomized iterative algorithm based on simple local updates. The algorithm, starting with an arbitrary initial assignment, updates it in each iteration by first, picking a random node, then selecting an (appropriately chosen) random local neighborhood and optimizing over this local neighborhood. Somewhat surprisingly, we show that this algorithm finds a near optimal assignment within n log 2 n iterations with high probability for any n node pair-wise MRF with geometry (i.e. MRF graph with polynomial growth) with the approximation error depending on (in a reasonable manner) the geometric growth rate of the graph and the average radius of the local neighborhood – this allows for a graceful tradeoff between the complexity of the algorithm and the approximation error. Through extensive simulations, we show that our algorithm finds extremely good approximate solutions for various kinds of MRFs with geometry. 1

Abstract—A method for removing additive Gaussian noise from digital images is described. It is based on statistical modeling of the coefficients of a redundant, oriented, complex multiscale transform. Two types of modeling are used to model the wavelet coefficients. Both are based on Gaussian scale mixture (GSM) modeling of neighborhoods of coefficients at adjacent locations and scales. Modeling of edge and ridge discontinuities is performed using wavelet coefficients derotated by twice the phase of the coefficient at the same location and the next coarser scale. Other areas are modeled using standard wavelet coefficients. An adaptive Bayesian model selection framework is used to determine the modeling applied to each neighborhood. The proposed algorithm succeeds in providing improved denoising performance at structural image features, reducing ringing artifacts and enhancing sharpness, while avoiding degradation in other areas. The method outperforms previously published methods visually and in standard tests. Index Terms—Complex, denoising, image, interscale phase, restoration, wavelet.

Abstract—A selective wavelet shrinkage algorithm for digital image denoising is presented. The performance of this method is an improvement upon other methods proposed in the literature and is algorithmically simple for large computational savings. The improved performance and computational speed of the proposed wavelet shrinkage algorithm is presented and experimentally compared with established methods. The denoising method incorporated in the proposed algorithm involves a two-threshold validation process for real-time selection of wavelet coefficients. The two-threshold criteria selects wavelet coefficients based on their absolute value, spatial regularity, and regularity across multiresolution scales. The proposed algorithm takes image features into consideration in the selection process. Statistically, most images have regular features resulting in connected subband coefficients. Therefore, the resulting subbands of wavelet transformed images in large part do not contain isolated coefficients. In the proposed algorithm, coefficients are selected due to their magnitude, and only a subset of those selected coefficients which exhibit a spatially regular behavior remain for image reconstruction. Therefore, two thresholds are used in the coefficient selection process. The first threshold is used to distinguish coefficients of large magnitude and the second is used to distinguish coefficients of spatial regularity. The performance of the proposed wavelet denoising technique is an improvement upon several other established wavelet denoising techniques, as well as being computationally efficient to facilitate real-time image-processing applications. Index Terms—Image denoising, selective wavelet shrinkage, twothreshold criteria. I.

The wavelet shrinkage denoising approach is able to maintain local regularity of a signal while suppressing noise. However, the conventional wavelet shrinkage based methods are not time-scale adaptive to track the local time-scale variation. In this paper, a new type of Neural Shrinkage (NS) is presented with a new class of shrinkage architecture for speckle reduction in Synthetic Aperture Radar (SAR) images. The numerical results indicate that the new method outperforms the standard filters, the standard wavelet shrinkage despeckling method, and previous NS.

Abstract. This paper focuses on fuzzy image denoising techniques. In particular, we investigate the usage of fuzzy set theory in the domain of image enhancement using wavelet thresholding. We propose a simple but efficient new fuzzy wavelet shrinkage method, which can be seen as a fuzzy variant of a recently published probabilistic shrinkage method [1] for reducing adaptive Gaussian noise from digital greyscale images. Experimental results show that the proposed method can efficiently and rapidly remove additive Gaussian noise from digital greyscale images. Numerical and visual observations show that the performance of the proposed method outperforms current fuzzy non-wavelet methods and is comparable with some recent but more complex wavelets methods. We also illustrate the main differences between this version and the probabilistic version and show the main improvements in comparison to it. 1

Abstract- Clinical research has shown a clear correlation between white matter disorders of the neonatal brain and neuro-motoric handicap at a later age. The visual interpretation of ultrasound images is a proven method to detect White Matter Damage at an early stage. A problem, common to all medical ultrasound images, is the presence of speckle noise, which not only complicates the visual interpretation of images, but also the quantitative measurements. In this article we compare two wavelet based filtering methods which are applied in order to remove speckle noise and preserve details as well. The first one is a new wavelet-based method for image denoising that applies the Bayesian framework, using prior knowledge about the spatial clustering of the wavelet coefficients. Local spatial interactions of the wavelet coefficients are modeled by adopting a Markov Random Field model. The second one is a new filtering method, based on a recursive filtering of detail images obtained from a wavelet decomposition of the image by using spatial filtering which is based on threshold decomposition and simple spatial rules. Key words- Wavelets, denoising, speckle 1.

Denoising of color images can be done on each color component independently. Recent work has shown that exploiting strong correlation between high-frequency content of different color components can improve the denoising performance. We show that for typical color images high correlation also means similarity, and propose to capture inter-color dependency using an optimal luminance/color-difference space projection. Experimental results confirm that performing denoising on the the projected color components yields superior to existing solutions denoising performance, both in PSNR and visual quality sense. We also develop a novel approach to estimate directly from the noisy image data the image and noise statistics, which are required to determine the optimal projection. Index Terms – Image denoising, wavelet thresholding, luminance, color differences, optimal color projection

Contrastive Divergence (CD) is a popular method for estimating the parameters of Markov Random Fields (MRFs) by rapidly approximating an intractable term in the gradient of the log probability. Despite CD’s empirical success, little is known about its theoretical convergence properties. In this paper, we analyze the CD1 update rule for Restricted Boltzmann Machines (RBMs) with binary variables. We show that this update is not the gradient of any function, and construct a counterintuitive “regularization function ” that causes CD learning to cycle indefinitely. Nonetheless, we show that the regularized CD update has a fixed point for a large class of regularization functions using Brower’s fixed point theorem. 1

Markov Random Fields (MRFs) are an important class of probabilistic models which are used for density estimation, classification, denoising, and for constructing Deep Belief Networks. Every application of an MRF requires addressing its inference problem, which can be done using deterministic inference methods or using stochastic Markov Chain Monte Carlo methods. In this paper we introduce a new Markov Chain transition operator that updates all the variables of a pairwise MRF in parallel by using auxiliary Gaussian variables. The proposed MCMC operator is extremely simple to implement and to parallelize. This is achieved by a formal equivalence result between arbitrary pairwise MRFs and a particular type of Restricted Boltzmann Machine. This result also implies that the later can be learned in place of the former without any loss of modeling power, a possibility we explore in experiments. 1