Results 1  10
of
1,734,037
Dualization of signal recovery problems
, 2009
"... In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in particular in signal recovery. These problems are not easily amenab ..."
Abstract

Cited by 18 (7 self)
 Add to MetaCart
In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in particular in signal recovery. These problems are not easily
Signal recovery from random measurements via Orthogonal Matching Pursuit
 IEEE TRANS. INFORM. THEORY
, 2007
"... This technical report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous ..."
Abstract

Cited by 780 (9 self)
 Add to MetaCart
previous results for OMP, which require O(m 2) measurements. The new results for OMP are comparable with recent results for another algorithm called Basis Pursuit (BP). The OMP algorithm is faster and easier to implement, which makes it an attractive alternative to BP for signal recovery problems.
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
Abstract

Cited by 496 (2 self)
 Add to MetaCart
that convex relaxation succeeds. As evidence of the broad impact of these results, the paper describes how convex relaxation can be used for several concrete signal recovery problems. It also describes applications to channel coding, linear regression, and numerical analysis.
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
 California Institute of Technology, Pasadena
, 2008
"... Abstract. Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery alg ..."
Abstract

Cited by 766 (12 self)
 Add to MetaCart
Abstract. Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery
1 GradientBased Algorithms with Applications to Signal Recovery Problems
"... This chapter presents in a selfcontained manner recent advances in the design and analysis of gradientbased schemes for specially structured smooth and nonsmooth minimization problems. We focus on the mathematical elements and ideas for building fast gradientbased methods and derive their complex ..."
Abstract
 Add to MetaCart
their complexity bounds. Throughout the chapter, the resulting schemes and results are illustrated and applied on a variety of problems arising in several specific key applications such as sparse approximation of signals, total variationbased image processing problems, and sensor location problems. 1.1
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
Abstract

Cited by 1513 (20 self)
 Add to MetaCart
Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear
Blind Signal Separation: Statistical Principles
, 2003
"... Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mut ..."
Abstract

Cited by 522 (4 self)
 Add to MetaCart
of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach but requires to venture beyond familiar second order statistics. The objective of this paper is to review some of the approaches that have been recently developed to address this exciting problem
Stable recovery of sparse overcomplete representations in the presence of noise
 IEEE TRANS. INFORM. THEORY
, 2006
"... Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes t ..."
Abstract

Cited by 462 (20 self)
 Add to MetaCart
Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
Abstract

Cited by 516 (2 self)
 Add to MetaCart
It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing
Results 1  10
of
1,734,037