This paper describes a dual certificate condition on a linear measurement operator A (defined on a Hilbert space H and having finite-dimensional range) which guarantees that an atomic norm minimization, in a certain sense, will be able to approximately recover a structured signal v0∈H from measurements Av0. Put very streamlined, the condition implies that peaks in a sparse decomposition of v0 are close the the support of the atomic decomposition of the solution v∗. The condition applies in a relatively general context - in particular, the space H can be infinite-dimensional. The abstract framework is applied to several concrete examples, one example being super-resolution. In this process, several novel results which are interesting on its own are obtained.
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.
No comments:
Post a Comment