Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

Wavelet based feature extraction for phoneme recognition

Abstract: In an effort to provide a more efficient representation of the acoustical speech signal in the pre classification stage of a speech recognition system, we consider the application of the Best-Basis Algorithm of R.R. Coifman and M.L. Wickerhauser (1992). This combines the advantages of using a smooth, compactly supported wavelet basis with an adaptive time scale analysis, dependent on the problem at hand. We start by briefly reviewing areas within speech recognition where the wavelet transform has been applied with some success. Examples include pitch detection, formant tracking, phoneme classification. Finally, our wavelet based feature extraction system is described and its performance on a simple phonetic classification problem given.

A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration

Abstract: We present a multilevel extension of the popular ldquothresholded Landweberrdquo algorithm for wavelet-regularized image restoration that yields an order of magnitude speed improvement over the standard fixed-scale implementation. The method is generic and targeted towards large-scale linear inverse problems, such as 3-D deconvolution microscopy. The algorithm is derived within the framework of bound optimization. The key idea is to successively update the coefficients in the various wavelet channels using fixed, subband-adapted iteration parameters (step sizes and threshold levels). The optimization problem is solved efficiently via a proper chaining of basic iteration modules. The higher level description of the algorithm is similar to that of a multigrid solver for PDEs, but there is one fundamental difference: the latter iterates though a sequence of multiresolution versions of the original problem, while, in our case, we cycle through the wavelet subspaces corresponding to the difference between successive approximations. This strategy is motivated by the special structure of the problem and the preconditioning properties of the wavelet representation. We establish that the solution of the restoration problem corresponds to a fixed point of our multilevel optimizer. We also provide experimental evidence that the improvement in convergence rate is essentially determined by the (unconstrained) linear part of the algorithm, irrespective of the type of wavelet. Finally, we illustrate the technique with some image deconvolution examples, including some real 3-D fluorescence microscopy data.

Wavelet Frames: Multiresolution Analysis and Extension Principles

Abstract: After reviewing the basic ideas of frame theory from a functional analysis point of view, we discuss two approaches for the construction of (affine) wavelet frames. The theory of Frame Multiresolution Analysis as introduced in [1] is presented in a streamlined form, and the main result of the theory is completed. The interplay between redundancy and robustness in frame expansions is illustrated by a simple example. We then restate Ron and Shen’s Unitary Extension Principle and give a simple direct proof different from the original derivation in [2].