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This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via ell1 minimisation, or more precisely the problem of identifying a dictionary dico from a set of training samples Y knowing that $ ...
With the flood of information available today the question how to deal with high dimensional data/signals, which are cumbersome to handle, to calculate with and to store, is highly important. One approach to reducing this flood is to find sparse signal rep ...
We propose a new method for imaging sound speed in breast tissue from measurements obtained by ultrasound tomography (UST) scan- ners. Given the measurements, our algorithm finds a sparse image representation in an overcomplete dictionary that is adapted t ...
In this paper, we propose the use of (adaptive) nonlinear approximation for dimensionality reduction. In particular, we propose a dimensionality reduction method for learning a parts based representation of signals using redundant dictionaries. A redundant ...
Many recent works have shown that if a given signal admits a sufficiently sparse representation in a given dictionary, then this representation is recovered by several standard optimization algorithms, in particular the convex ℓ1 minimization approac ...
We develop an efficient learning framework to construct signal dictionaries for sparse representation by selecting the dictionary columns from multiple candidate bases. By sparse, we mean that only a few dictionary elements, compared to the ambient signal ...
This article extends the concept of it compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic ...
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 ...
In this article we present a signal model for classification based on a low dimensional dictionary embedded into the high dimensional signal space. We develop an alternate projection algorithm to find the embedding and the dictionary and finally test the c ...
This paper shows introduces the use sensing dictionaries for p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We do both a worst case and average case recovery analyses of this ...
