Coding theory and compressed sensing through convex relaxations

Arash Saber Tehrani, Alexandros G. Dimakis
We survey recent connections between convex relaxations used in coding theory and in sparse approximation theory. One important conclusion arising from our results is that graph girth can be used to certify that sparse compressed sensing matrices have good sparse approximation guarantees. This allows us to present the first deterministic measurement matrix constructions that have an optimal number of measurements for 1/ 1 sparse approximation.
doi:10.3929/ethz-a-007071467 fatcat:ltn46qh2zbdediq6ryebxttuyq