Stability (over time) of regularized modified CS (noisy) for recursive causal sparse reconstruction

Abstract

LIST OF FIGURES 3.1 (a) Sorted MRI signal coefficient values in Wavelet domain (b) Sorted proposed signal model coefficient values in Wavelet domain. .. .. .. 4.1 Normalized MSE (NMSE), number of extras and number of misses over time for CS, modified CS, modified BPDN, and regularized modified CSN. In part (b) and (c), NMSE for CS was more than 20%.

Regularized Modified BPDN for Noisy Sparse Reconstruction With Partial Erroneous Support and Signal Value Knowledge

“…On the other end, we are also working on obtaining conditions under which it will remain "stable" (its error will be bounded by a time-invariant and small value) for a recursive recovery problem. In [30], this has been done for the constrained version of reg-mod-BPDN. That result uses the restricted isometry constants (RIC) and the restricted orthogonality constants (ROC) [17], [11] in its sufficient conditions and bounds.…”

“…We briefly discuss here the stability of dynamic reg-mod-BPDN (reconstruction error and support estimation errors bounded by a time-invariant and small value at all times). Using an approach similar to that of [30], it should be possible to show the following. If (i) ρ is large enough (so thatN t does not falsely detect any element that got removed from N t ); (ii) the newly added elements to the current support, N t , either get added at a large enough value to get detected immediately, or within a finite delay their magnitude becomes large enough to get detected; and (iii) the matrix A satisfies certain conditions (for a given support size and support change size); reg-mod-BPDN will be stable.…”

Stability (over time) of Regularized modified CS(noisy) for recursive causal sparse reconstruction

“…In this work [17], we first propose two convex optimization problem, reg-mod-CSN and reg-mod-BPDN, to use these extra information for signal recovery. Regularized modified CS(noisy)(reg-mod-CSN) is the noisy relaxation of regularized modified CS (reg-mod-cs) proposed in [16].…”

Opportunistic sensor activation in the face of data deluge

“…In [23], [24], the authors propose techniques for recursive sparse reconstruction of dynamic natural signal/image sequences for small changes in sparsity with time. In [20], the authors address the problem of stability of the aforementioned techniques. All the aforementioned work assume an apriori knowledge about the sparsity of the signal.…”