Shrinkage for Redundant Representations
نویسنده
چکیده
Shrinkage is a well known and appealing denoising technique. The use of shrinkage is known to be optimal for Gaussian white noise, provided that the sparsity on the signal’s representation is enforced using a unitary transform. Still, shrinkage is also practiced successfully with non-unitary, and even redundant representations. In this paper we shed some light on this behavior. We show that simple shrinkage could be interpreted as the first iteration of an algorithm that solves the basis pursuit denoising (BPDN) problem. Thus, this work leads to a sequential shrinkage algorithm that can be considered as a novel and effective pursuit method.
منابع مشابه
Softening the Multiscale Product Method for Adaptive Noise Reduction
The goal of denoising is to remove the noise while preserving the important features as much as possible. By exploring the power of parsimonious wavelet basis representation and statistical decision methods, Donoho and Johnstone [5] pioneered the wavelet shrinkage. However, the performance of traditional wavelet shrinkage is not even as good as that of a simple multiscale product method (MPM) [...
متن کاملRedundant Representations in Evolutionary Computation
This paper discusses how the use of redundant representations influences the performance of genetic and evolutionary algorithms. Representations are redundant if the number of genotypes exceeds the number of phenotypes. A distinction is made between synonymously and non-synonymously redundant representations. Representations are synonymously redundant if the genotypes that represent the same ph...
متن کاملIterative Shrinkage Algorithms and Their Acceleration for L1-L2 Signal and Image Processing Applications
Sparse, redundant representations offer a powerful emerging model for signals. This model approximates a data source as a linear combination of few atoms from a pre-speci ed and over-complete dictionary. Often such models are t to data by solving mixed `1-`2 convex optimization problems. Iterative Shrinkage algorithms constitute a new family of highly effective numerical methods for handling t...
متن کاملA Wide-Angle View at Iterated Shrinkage Algorithms
Sparse and redundant representations – an emerging and powerful model for signals – suggests that a data source could be described as a linear combination of few atoms from a pre-specified and over-complete dictionary. This model has drawn a considerable attention in the past decade, due to its appealing theoretical foundations, and promising practical results it leads to. Many of the applicati...
متن کاملSparse and Redundant Representations for Inverse Problems and Recognition
Title of dissertation: Sparse and Redundant Representations for Inverse Problems and Recognition Vishal M. Patel, Doctor of Philosophy, 2010 Dissertation directed by: Professor Rama Chellappa Department of Electrical and Computer Engineering Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertatio...
متن کامل