Fast communication: A short note on compressed sensing with partially known signal support

摘要: This short note studies a variation of the compressed sensing paradigm introduced recently by Vaswani et al., i.e., recovery sparse signals from certain number linear measurements when signal support is partially known. In this framework, we propose reconstruction method based on convex minimization program coined innovative Basis Pursuit DeNoise (or iBPDN). Under common @?"2-fidelity constraint made available measurements, optimization promotes (@?"1) sparsity candidate over complement known part. particular, paper extends results al. to cases compressible and noisy showing that iBPDN @?"2-@?"1 instance optimal. The corresponding proof relies small adaption Candes in 2008 for characterizing stability (BPDN) program. We also emphasize an interesting link between our recent work Davenport @d-stable embeddings cancel-then-recover strategy applied problem. For both approaches, reconstructions are indeed stabilized matrix respects Restricted Isometry Property same order.