Survey of image denoising techniques <s> b. Statistical Modeling of Wavelet Coefficients <s> We develop a probability model for natural images, based on empirical observation of their statistics in the wavelet transform domain. Pairs of wavelet coefficients, corresponding to basis functions at adjacent spatial locations, orientations, and scales, are found to be non-Gaussian in both their marginal and joint statistical properties. Specifically, their marginals are heavy-tailed, and although they are typically decorrelated, their magnitudes are highly correlated. We propose a Markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties, and show that it accounts for the statistics of a wide variety of images including photographic images, graphical images, and medical images. In order to directly demonstrate the power of the model, we construct an image coder called EPWIC (embedded predictive wavelet image coder), in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model. Bitplanes are ordered using a greedy algorithm that considers the MSE reduction per encoded bit. The decoder uses the statistical model to predict coefficient values based on the bits it has received. Despite the simplicity of the model, the rate-distortion performance of the coder is roughly comparable to the best image coders in the literature. <s> BIB001 </s> Survey of image denoising techniques <s> b. Statistical Modeling of Wavelet Coefficients <s> ABSTRACT Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hiddenMarkov tree (HMT) model captures the key features of the joint density of the wavelet coefficients of real-world data. Onepotential drawback to the HMT framework is the need for cornputationallv expensive iterative training (using the Expectation-Iaximization algorithm, for example). In this paper, we propose two reduced-parameter HMT models that capture the generalstructure of a broad class of real-world images. In the image HMT (iHMT) model we use the fact that for a large class ofimages the structure of the HMT is self-similar across scale. This allows us to reduce the complexity of the iHMT to justnine easily trained parameters (independent of the size of the image and the number of wavelet scales). In the universal HMT(uHMT) we take a Bayesian approach and fix these nine parameters. The uHMT requires no training of any kind. Whilesimple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of thekey structure modeled by the full HvIT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperformsall other wavelet-based estimators in the current literature. both in mean-square error and visual metrics. <s> BIB002
This approach focuses on some more interesting and appealing properties of the Wavelet Transform such as multiscale correlation between the wavelet coefficients, local correlation between neighborhood coefficients etc. This approach has an inherent goal of perfecting the exact modeling of image data with use of Wavelet Transform. A good review of statistical properties of wavelet coefficients can be found in BIB001 and BIB002 . The following two techniques exploit the statistical properties of the wavelet coefficients based on a probabilistic model.