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===Wavelets with Composite Dilations===

===Wavelets with Composite Dilations===

Speaker: Vishal Patel -- Date: September 8, 2011

Speaker: [http://www.umiacs.umd.edu/~pvishalm/ Vishal Patel] -- Date: September 8, 2011

Sparse representation of visual information lies at the foundation of many image processing applications, such as image restoration and compression. It is well known that wavelets provide a very sparse representation for a large class of signals and images. For instance, from a continuous perspective, wavelets can be shown to sparsely represent one-dimensional signals that are smooth away from point discontinuities. Unfortunately, separable wavelet transforms have some limitations in higher dimensions. For this reason, in recent years there has been considerable interest in obtaining directionally-oriented image decompositions. Wavelets with composite dilations offer a general and especially effective framework for the construction of such representations.  In this talk, I will discuss the theory and implementation of several recently introduced multiscale directional transforms. Then, I will present a new general scheme for creating an M-channel directional filter bank. An advantage of an M-channel directional filter bank is that it can project the image directly onto the desired basis. Applications in image denoising, deconvolution and image enhancement will be presented.

Sparse representation of visual information lies at the foundation of many image processing applications, such as image restoration and compression. It is well known that wavelets provide a very sparse representation for a large class of signals and images. For instance, from a continuous perspective, wavelets can be shown to sparsely represent one-dimensional signals that are smooth away from point discontinuities. Unfortunately, separable wavelet transforms have some limitations in higher dimensions. For this reason, in recent years there has been considerable interest in obtaining directionally-oriented image decompositions. Wavelets with composite dilations offer a general and especially effective framework for the construction of such representations.  In this talk, I will discuss the theory and implementation of several recently introduced multiscale directional transforms. Then, I will present a new general scheme for creating an M-channel directional filter bank. An advantage of an M-channel directional filter bank is that it can project the image directly onto the desired basis. Applications in image denoising, deconvolution and image enhancement will be presented.