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We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter(More)
We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We develop an efficient algorithm for synthesizing random images(More)
We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multi-scale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter(More)
We describe a statistical model for images decomposed in an overcomplete wavelet pyramid. Each coefficient of the pyramid is modeled as the product of two independent random variables: an element of a Gaussian random field, and a hidden multiplier with a marginal log-normal prior. The latter modulates the local variance of the coefficients. We assume(More)
We describe an efficient generalized expectation maximization algorithm for estimating the spectral features of a noise source corrupting an observed image. We use a statistical model for images decomposed in an overcomplete oriented pyramid. Each neighborhood of clean pyramid coefficients is modeled as a Gaussian scale mixture, whereas the noise is assumed(More)
Gabor schemes of multiscale image representation are useful in many computer vision applications. However, the classic Gabor expansion is computationally expensive due to the lack of orthogonality of Gabor functions. Some alternative schemes, based on the application of a bank of Gabor filters, have important advantages such as computational efficiency and(More)
We present a universal statistical model for texture images in the context of an over-complete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coeecients corresponding to basis functions at adjacent spatial locations , orientations, and scales. We develop an eecient algorithm for synthesizing random images(More)
Sparse optimization in overcomplete frames has been widely applied in recent years to ill-conditioned inverse problems. In particular, analysis-based sparse optimization consists of achieving a certain trade-off between fidelity to the observation and sparsity in a given linear representation, typically measured by some &#x2113;<inf>p</inf> quasi-norm.(More)
We present an efficient linear minimum mean square error (LMMSE) method for reconstructing full color images from single sensor color filter array (CFA) data. We use a representative set of full color images to estimate the joint spatial-chromatic covariance among pixel color components. Then, we derive from it a set of joint color-space, small linear(More)