Dynamical Sparse Recovery with Finite-time Convergence

Lei Yu 1 Gang Zheng 2 Jean-Pierre Barbot 3
2 DEFROST - Deformable Robots Simulation Team
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : Even though Sparse Recovery (SR) has been successfully applied in a wide range of research communities, there still exists a barrier to real applications because of the inefficiency of the state-of-the-art algorithms. In this paper, we propose a dynamical approach to SR which is highly efficient and with finite-time convergence property. Firstly, instead of solving the ℓ1 regularized optimization programs that requires exhausting iterations, which is computer-oriented, the solution to SR problem in this work is resolved through the evolution of a continuous dynamical system which can be realized by analog circuits. Moreover, the proposed dynamical system is proved to have the finite-time convergence property, and thus more efficient than LCA (the recently developed dynamical system to solve SR) with exponential convergence property. Consequently, our proposed dynamical system is more appropriate than LCA to deal with the time-varying situations. Simulations are carried out to demonstrate the superior properties of our proposed system.
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Submitted on : Monday, November 27, 2017 - 3:00:49 PM
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Lei Yu, Gang Zheng, Jean-Pierre Barbot. Dynamical Sparse Recovery with Finite-time Convergence. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2017, 65 (23), pp.6146-6157. ⟨10.1109/TSP.2017.2745468⟩. ⟨hal-01649419⟩

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