Fast Algorithms for Sparse Recovery with Perturbed Dictionary

Details Fast Algorithms for Sparse Recovery with Perturbed Dictionary Fast Algorithms for Sparse Recovery with Perturbed Dictionary

2011-11-27

arxiv.org/abs/1111.6237v1

Computer Science

Information Theory

9 pages, 13 figures

Scientific paper

In this paper, for sparse recovery of large underdetermined linear systems, we propose a new kind of fast algorithms, based on totally least square (TLS) method and FOCUSS (FOCal Underdetermined System Solver). The problem about sparse recovery was considered, when perturbations appear in both the measurements and the dictionary (sensing matrix) (here we can call the system model as TLS model). The objective function to be optimized is deduced through a maximum a posteriori (MAP) estimation. Then a new FOCUSS algorithm, named TLS-FOCUSS, is extended with main idea of TLS, to reduce the impact of the perturbation of dictionary and measurements to the performance of sparse recovery. Compared with other recovery algorithms on TLS model, TLS-FOCUSS algorithm is not only near-optimum but also fast, thus fit for large scale computation. In order to reduce the complexity of algorithm further, another suboptimal algorithm named SD-FOCUSS is proposed. Another breakthrough of the paper is that SD-FOCUSS can be applied in MMV (multiple measurement vectors) TLS model which field is not researched at present. The convergence of the TLS-FOCUSS algorithm and SD-FOCUSS algorithm is established with mathematical proof. The new algorithms based on TLS model are proved to be efficient and high-performance. The simulation results illustrate the advantage of TLS-FOCUSS and SD-FOCUSS on accuracyand stability compared with the other algorithms.

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