Results 1 - 10 of 177

Stable recovery of sparse overcomplete representations in the presence of noise

by David L. Donoho, Michael Elad, Vladimir N. Temlyakov - 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 460 (22 self) - Add to MetaCart
the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system. Considering an ideal underlying signal that has a sufficiently sparse representation, it is assumed that only a noisy version of it can be observed. Assuming further

Overcomplete Systems of Wavelet and Related Local Bases for Adaptive Signal Representation and Estimation

by Rainer von Sachs
"... this paper we will discuss the usefulness of overcomplete systems of basis functions, such as wavelets or localized sine and cosine functions, for the adaptive parsimonious representation and estimation of statistical signals which show an inhomogeneous behaviour over time. Typical examples can be f ..."
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this paper we will discuss the usefulness of overcomplete systems of basis functions, such as wavelets or localized sine and cosine functions, for the adaptive parsimonious representation and estimation of statistical signals which show an inhomogeneous behaviour over time. Typical examples can

ATOMIC DECOMPOSITION BY BASIS PURSUIT

by Scott Shaobing Chen , David L. Donoho , Michael A. Saunders , 1995
"... The Time-Frequency and Time-Scale communities have recently developed a large number of overcomplete waveform dictionaries -- stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
Abstract - Cited by 2728 (61 self) - Add to MetaCart
The Time-Frequency and Time-Scale communities have recently developed a large number of overcomplete waveform dictionaries -- stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods

Optimally sparse representation in general (non-orthogonal) dictionaries via ℓ¹ minimization

by David L. Donoho, Michael Elad - PROC. NATL ACAD. SCI. USA 100 2197–202 , 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
Abstract - Cited by 633 (38 self) - Add to MetaCart
considered the special case where D is an overcomplete system consisting of exactly two orthobases, and has shown that, under a condition of mutual incoherence of the two bases, and assuming that S has a sufficiently sparse representation, this representation is unique and can be found by solving a convex

A general framework for object detection

by Constantine P. Papageorgiou, Michael Oren, Tomaso Poggio - Sixth International Conference on , 1998
"... This paper presents a general trainable framework for object detection in static images of cluttered scenes. The detection technique we develop is based on a wavelet representation of an object class derived from a statistical analysis of the class instances. By learning an object class in terms of ..."
Abstract - Cited by 395 (21 self) - Add to MetaCart
of a subset of an overcomplete dictionary of wavelet basis functions, we derive a compact representation of an object class which is used as an input to a suppori vector machine classifier. This representation overcomes both the problem of in-class variability and provides a low false detection rate

FUNCTIONAL APPROXIMATIONS USING OVERCOMPLETE BASE SYSTEMS

by Vítìzslav Veselý
"... In more detail the Hilbert-space expansions in overcomplete systems (frames) are handled in [Ves01] in context with the theory of pseudoinverse operators. Chen et al. deal in [CDS98] the problem of sparse representation of vectors (signals) in a nite-dimensional space using special overcomplete syst ..."
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In more detail the Hilbert-space expansions in overcomplete systems (frames) are handled in [Ves01] in context with the theory of pseudoinverse operators. Chen et al. deal in [CDS98] the problem of sparse representation of vectors (signals) in a nite-dimensional space using special overcomplete

A Trainable System for Object Detection

by Constantine Papageorgiou, Tomaso Poggio , 2000
"... This paper presents a general, trainable system for object detection in unconstrained, cluttered scenes. The system derives much of its power from a representation that describes an object class in terms of an overcomplete dictionary of local, oriented, multiscale intensity differences between adj ..."
Abstract - Cited by 344 (8 self) - Add to MetaCart
This paper presents a general, trainable system for object detection in unconstrained, cluttered scenes. The system derives much of its power from a representation that describes an object class in terms of an overcomplete dictionary of local, oriented, multiscale intensity differences between

Density, overcompleteness, and localization of frames

by Radu Balan, Peter G. Casazza, Christopher Heil, Zeph Landau - I. THEORY, J. FOURIER ANAL. APPL , 2005
"... This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in ..."
Abstract - Cited by 62 (20 self) - Add to MetaCart
This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F

Density, overcompleteness and localization of frames. II. Gabor systems

by Radu Balan, Peter G. Casazza, Christopher Heil, Zeph Landau - J. Fourier Anal. and Applicat , 2005
"... This work develops a quantitative framework for describing the overcompleteness of a large class of frames. A previous article introduced notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of th ..."
Abstract - Cited by 13 (6 self) - Add to MetaCart
and implications are clarified. New results are obtained on the excess and overcompleteness of Gabor frames, on the relationship between frame bounds and density, and on the structure of the dual frame of an irregular Gabor frame. More generally, these results apply both to Gabor frames and to systems of Gabor

Overcomplete Image Representations for Texture Analysis

by Rodrigo Nava , 2014
"... Abstract Computer vision has played an important role in many scientific and technological areas mainly because modern society highlights vision over other senses. At the same time, application requirements and complexity have also increased, so that in many cases, the optimal solution depends on t ..."
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on the intrinsic characteristics of the problem. Therefore, it is difficult to propose a universal image model. In parallel, advances in understanding the human visual system have allowed to suggest sophisticated models that incorporate simple phenomena. This dissertation aims to investigate characteristics
Results 1 - 10 of 177