14 research outputs found
Sparse Signal Separation in Redundant Dictionaries
We formulate a unified framework for the separation of signals that are
sparse in "morphologically" different redundant dictionaries. This formulation
incorporates the so-called "analysis" and "synthesis" approaches as special
cases and contains novel hybrid setups. We find corresponding coherence-based
recovery guarantees for an l1-norm based separation algorithm. Our results
recover those reported in Studer and Baraniuk, ACHA, submitted, for the
synthesis setting, provide new recovery guarantees for the analysis setting,
and form a basis for comparing performance in the analysis and synthesis
settings. As an aside our findings complement the D-RIP recovery results
reported in Cand\`es et al., ACHA, 2011, for the "analysis" signal recovery
problem: minimize_x ||{\Psi}x||_1 subject to ||y - Ax||_2 \leq {\epsilon}, by
delivering corresponding coherence-based recovery results.Comment: Proc. of IEEE International Symposium on Information Theory (ISIT),
Boston, MA, July 201
A survey of uncertainty principles and some signal processing applications
The goal of this paper is to review the main trends in the domain of
uncertainty principles and localization, emphasize their mutual connections and
investigate practical consequences. The discussion is strongly oriented
towards, and motivated by signal processing problems, from which significant
advances have been made recently. Relations with sparse approximation and
coding problems are emphasized
Disjoint sparsity for signal separation and applications to hybrid inverse problems in medical imaging
The main focus of this work is the reconstruction of the signals f and gi, i=1,\u2026,N, from the knowledge of their sums hi=f+gi, under the assumption that f and the gi's can be sparsely represented with respect to two different dictionaries Af and Ag. This generalizes the well-known \u201cmorphological component analysis\u201d to a multi-measurement setting. The main result of the paper states that f and the gi's can be uniquely and stably reconstructed by finding sparse representations of hi for every i with respect to the concatenated dictionary [Af,Ag], provided that enough incoherent measurements gi are available. The incoherence is measured in terms of their mutual disjoint sparsity. This method finds applications in the reconstruction procedures of several hybrid imaging inverse problems, where internal data are measured. These measurements usually consist of the main unknown multiplied by other unknown quantities, and so the disjoint sparsity approach can be directly applied. As an example, we show how to apply the method to the reconstruction in quantitative photoacoustic tomography, also in the case when the Gr\ufcneisen parameter, the optical absorption and the diffusion coefficient are all unknown
A survey of uncertainty principles and some signal processing applications
The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, highlight their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and motivated by signal processing problems, from which significant advances have been made recently. Relations with sparse approximation and coding problems are emphasized