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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 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)
Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting(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)
Scaling functions and orthogonal wavelets are created from the coeecients of a lowpass and highpass lter (in a two-band orthogonal lter bank). For \multiilters" those coeecients are matrices. This gives a new block structure for the lter bank, and leads to multiple scaling functions and wavelets. Geronimo, Hardin, and Massopust constructed two scaling(More)
This paper gives an overview of recent achievements of the multiwavelet theory. The construction of multiwavelets is based on a mul-tiresolution analysis with higher multiplicity generated by a scaling vector. The basic properties of scaling vectors such as L 2-stability, approximation order and regularity are studied. Most of the proofs are sketched. §1.(More)
An important object in wavelet theory is the scaling function (t), satisfying a dilation equation (t) = P C k (2t ? k). Properties of a scaling function are closely related to the properties of the symbol or mask P (!) = P C k e ?i!k. The approximation order provided by (t) is the number of zeros of P (!) at ! = , or in other words the number of factors(More)
We present a simple denoising technique for geometric data represented as a semiregular mesh, based on locally adaptive Wiener filtering. The degree of denoising is controlled by a single parameter (an estimate of the relative noise level) and the time required for denoising is independent of the magnitude of the estimate. The performance of the algorihm is(More)