Javier Portilla

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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 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)
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)
Dept. de Ciencia Computacional Ctr. for Neural Science, and Lab. Info. & Decision Systems Universidad de Granada Courant Inst. Math. Sciences Dept. Elec. Eng. & Comp. Sci. Spain New York University Mass. Inst. of Technology javier@decsai.ugr.es {eero,vstrela}@cns.nyu.edu mjwain@mit.edu Published in: Proceedings of the 8th International Conference on Image(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 a parametric statistical characterization of texture images in the context of an overcomplete complex wavelet frame. The characterization consists of the local autocorrelation of the coefficients in each subband, the local autocorrelation of the cofficent magnitudes, and the crosscorrelation of coefficient magnitudes at all orientations and(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)
Gaussian scale mixtures (GSM) capture two basic properties of the wavelet coefficients responding to natural images, namely 1) high kurtosis marginals, and 2) positive covariance between neighbor coefficient amplitudes. These features are not shared by Gaussian or lower kurtosis noise sources. Therefore, GSM models provide a means to separate the noise from(More)