Piecewise Sparse Recovery via Piecewise Greedy Method

Abstract:

      In some applications, there are signals with piecewise structure to be recovered. In this paper, we propose a piecewise OMP (P\_OMP) method which aims to preserve the piecewise sparse structure (or the small-scaled entries) of piecewise signals. Besides the merits of OMP, the P\_OMP, which is a generalization of the combination of CoSaMP and OMMP (Orthogonal Multi-matching Pursuit) on piecewise sparse recovery, possesses the advantages of comparable approximation error decay as CoSaMP with more relaxed sufficient condition and better recovery success rate. Moreover, the P\_OMP algorithm recovers the piecewise sparse signal according to its piecewise structure, which results in better details preservation. Numerical experiments indicate that compared with CoSaMP, OMP, OMMP and BP methods, the P\_OMP algorithm is more effective and robust for piecewise sparse recovery.