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This article presents an alteration of greedy algorithms like thresholding or (Orthogonal) Matching Pursuit which improves their performance in finding sparse signal representations in redundant dictionaries. These algorithms can be split into a sensing an ...
This paper analyzes the performance of the simple thresholding algorithm for sparse signal representations. In particular, in order to be more realistic we introduce a new probabilistic signal model which assumes randomness for both the amplitude and also ...
Consider a scenario where a distributed signal is sparse and is acquired by various sensors that see different versions. Thus, we have a set of sparse signals with both some common parts, and some variations. The question is how to acquire such signals and ...
In the last decade we observed an increasing interaction between data compression and sparse signals approximations. Sparse approximations are desirable because they compact the energy of the signals in few elements and correspond to a structural simplific ...
Numerous applications demand that we manipulate large sets of very high-dimensional signals. A simple yet common example is the problem of finding those signals in a database that are closest to a query. In this paper, we tackle this problem by restricting ...
Real-world phenomena involve complex interactions between multiple signal modalities. As a consequence, humans are used to integrate at each instant perceptions from all their senses in order to enrich their understanding of the surrounding world. This par ...
Recent results in compressed sensing or compressive sampling suggest that a relatively small set of measurements taken as the inner product with universal random measurement vectors can well represent a source that is sparse in some fixed basis. By adaptin ...
Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007
There has been an intense activity recently in the field of sparse approximations with redundant dictionaries, largely motivated by the practical performances of algorithms such as Matching Pursuit and Basis Pursuit. However, most of the theoretical result ...
Approximating a signal or an image with a sparse linear expansion from an overcomplete dictionary of atoms is an extremely useful tool to solve many signal processing problems. Finding the sparsest approximation of a signal from an arbitrary dictionary is ...
Low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. The advantages of wavelet bases lie in their ...