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Image denoising using mixtures of Gaussian scale mixtures

Image denoising using mixtures of Gaussian scale mixtures,10.1109/ICIP.2008.4711817,Jose A. Guerrero-colon,Eero P. Simoncelli,Javier Portilla

Image denoising using mixtures of Gaussian scale mixtures   (Citations: 8)
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The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures (GSMs). In that model, each spatial neighborhood of coefficients is described as a Gaussian random vector modulated by a random hidden positive scaling variable. Here, we introduce a more powerful model in which neighborhoods of each subband are described as a finite mixture of GSMs. We develop methods to learn the mixing densities and covariance matrices associated with each of the GSM components from a single image, and show that this process naturally segments the image into regions of similar content. The model parameters can also be learned in the presence of additive Gaussian noise, and the resulting fitted model may be used as a prior for Bayesian noise removal. Simulations demonstrate this model substantially outperforms the original GSM model.
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    • ...The Gaussian scale mixture (GSM) model and its expansion has been shown to produce results that are significantly better than HMM models [4][12-13]...

    Xiang-Yang Wanget al. A new image denoising in shiftable complex directional pyramid domain

    • ...In this sense, the paper further builds upon the MGSM model from [18], [22], [25] and is also a continuation of our previous work in [26]...
    • ...This approach combines the GSM model with a Markov Random Field model and currently yields better denoising performance on average than MGSM (see [25], [33])...
    • ...4Very recently, in parallel to our research, in [25] a similar result is obtained for the noise-free House image...
    • ...As noted in [25], under-utilized mixture components may attribute to a large part of the computation time...
    • ...MGSM model from [25] when we chooseq = d and identity matrices for the projection bases Vk = I. This is equivalent to not incorporating dimension reductions into the model, hence the third layer in Fig. 1 is missing...

    Bart Goossenset al. Image Denoising Using Mixtures of Projected Gaussian Scale Mixtures

    • ...There has been significant prior work in describing the statistics of wavelet coefficients for a single image [1] [2] . A Gaussian scale mixture (GSM) distribution has been shown to be a good model for describing the statistics of wavelet coefficients for single images [3]...

    Rajiv Soundararajanet al. Statistical modeling of multi-camera images

    • ...What about nonlinear image models? Apart from the non-parametric approaches, a large number of nonlinear image models has been proposed over the years which are capable to capture signicantly more statistical regularities of natural images than linear ICA can do (e.g. [59; 60; 56; 61; 62; 63; 64; 65; 66])...

    Jan Eichhornet al. Natural Image Coding in V1: How Much Use is Orientation Selectivity?

    • ...Some of the most recent and successful advances are based on: Gaussian scale mixtures (GSM) modeling in overcomplete multiscale transform domain [9], [15], [8]; learned dictionaries of atoms to Þlter small square neighborhoods [6]; steering kernel regression [16] (also combined with learned dictionaries [2]); shape-adaptive DCT (SA-DCT) on neighborhoods whose shapes are adaptive to the image structures [7]; nonlocal Þltering ...

    Kostadin Dabovet al. BM3D Image Denoising with Shape-Adaptive Principal Component Analysis

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