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

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

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

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

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

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

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

Progressive coding of 3D objects based on

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

We consider the familiar scenario where independent and identically distributed (i.i.d) noise in an image is removed using a set of overcomplete linear transforms and thresholding. Rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates