Performance analysis for unconstrained analysis based approaches*The work was supported by NSFC (Nos.11901037, 11871109, 61932010, 61932011, 11771162, 12001067), CAEP Foundation (Grant No. CX20200027). (1st September 2022) - Ge, Huanmin; Chen, Wengu; Li, Dongfang; Wu, Fengyan
Abstract: Efficient recovery of sparse signals from underdetermined linear systems has received extensive attentions in recent decade. This paper considers the stable recovery of a signal x, which is not k -sparse itself but is k -sparse in terms of a Parseval frame D, from the observations y = Ax + e via three unconstrained minimization approaches. We show that if the sensing matrix A satisfies the restricted isometry property adapted to D with δ t k < t − 1 t + 8 for any t > 1, then these three approaches can stably recover x . As a consequence, when t = 2 and 3, our result significantly improves existing best sufficient conditions. Furthermore, we theoretically characterize the recovery errors of these methods.