Average performance of the sparsest approximation using a general dictionary
نویسندگان
چکیده
l00 26 07 07 , v er si on 1 4 M ar 2 00 8 Average performance of the sparsest approximation using a general dictionary François Malgouyres and Mila Nikolova ⋆ LAGA/L2TI, Université Paris 13, CNRS, 99 avenue J.B. Clément, 93430 Villetaneuse, France; (33/0) 1-49-40-35-83, [email protected] ⋄ CMLA, ENS Cachan, CNRS, PRES UniverSud, 61 Av. President Wilson, F-94230 Cachan, France (33/0) 1 47 50 59 08 [email protected] March 4, 2008
منابع مشابه
Average performance of the sparsest approximation in a dictionary
Given data d ∈ R , we consider its representation u involving the least number of non-zero elements (denoted by l0(u∗)) using a dictionary A (represented by a matrix) under the constraint ‖Au− d‖ ≤ τ , for τ > 0 and a norm ‖.‖. This (nonconvex) optimization problem leads to the sparsest approximation of d. We assume that data d are uniformly distributed in θBfd (1) where θ>0 and Bfd (1) is the ...
متن کاملMaximal Sparsity Representation via l1 Minimization
Finding a sparse representation of signals is desired in many applications. For a representation dictionary D and a given signal S ∈ span{D}, we are interested in finding the sparsest vector γ such that Dγ = S. Previous results have shown that if D is composed of a pair of unitary matrices, then under some restrictions dictated by the nature of the matrices involved, one can find the sparsest r...
متن کاملSpeaker Recognition via Block Sparse Bayesian Learning
In order to demonstrate the effectiveness of sparse representation techniques for speaker recognition, a dictionary of feature vectors belonging to all speakers is constructed by total variability i-vectors. Each feature vector from unknown utterance is expressed as linear weighted sum of a dictionary. The weights are calculated using Block Sparse Bayesian Learning (BSBL) where the sparsest sol...
متن کاملA New Method for Speech Enhancement Based on Incoherent Model Learning in Wavelet Transform Domain
Quality of speech signal significantly reduces in the presence of environmental noise signals and leads to the imperfect performance of hearing aid devices, automatic speech recognition systems, and mobile phones. In this paper, the single channel speech enhancement of the corrupted signals by the additive noise signals is considered. A dictionary-based algorithm is proposed to train the speech...
متن کاملHighly sparse representations from dictionaries are unique and independent of the sparseness measure by
The purpose of this paper is to study sparse representations of signals from a general dictionary in a Banach space. For so-called localized frames in Hilbert spaces, the canonical frame coefficients are shown to provide a near sparsest expansion for several sparseness measures. However, for frames which are not localized, this no longer holds true and sparse representations may depend strongly...
متن کامل