access icon free Robust GNC approach for quantised compressed sensing

Practical acquisition of compressed sensing measurements involves a finite-range finite-precision quantisation step. To solve the sparse recovery problem and handle the quantisation distortion, this Letter proposes a non-smooth graduated-non-convexity approach that follows a path of gradually improved solutions along a sequence of non-smooth non-convex optimisation problems that progressively promote quantisation consistency (QC) and sparsity. We consider two classes of multi-scale continuous approximation functions to depict intermediate QC degrees and sparsity-inducing strengths, respectively, and apply recent proximal splitting methods to solve the resulting subproblem at each refinement scale. The simulations demonstrate the convergence of intermediate solutions to a nearly optimal estimation, in terms of accuracy and support recovery.

Inspec keywords: optimisation; compressed sensing; approximation theory

Other keywords: finite-range finite-precision quantisation step; multiscale continuous approximation functions; robust GNC approach; nonsmooth graduated-nonconvexity approach; sparse recovery problem; quantised compressed sensing

Subjects: Optimisation techniques; Signal processing and detection; Interpolation and function approximation (numerical analysis); Signal processing theory; Interpolation and function approximation (numerical analysis); Optimisation techniques

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      • 6. Elleuch, I., Abdelkefi, F., Siala, M., Hamila, R., Al-Dhahir, N.: ‘Quasi-sparsest solutions for quantized compressed sensing by graduated-non-convexity based reweighted 1 minimization’. EUSIPCO, Budapest, Hungary, 29 August – 2 September 2016, pp. 473477.
http://iet.metastore.ingenta.com/content/journals/10.1049/el.2017.0925
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Erratum: Robust GNC approach for quantised compressed sensing