Restricted Isometry Constants Where $\ell ^{p}$ Sparse Recovery Can Fail for $0≪ p \leq 1$

This paper investigates conditions under which the solution of an underdetermined linear system with minimal lscrp norm, 0 < p les 1, is guaranteed to be also the sparsest one. Matrices are constructed with restricted isometry constants (RIC) delta2m arbitrarily close to 1/radic2 ap 0.707 where sparse recovery with p = 1 fails for at least one m-sparse vector, as well as matrices with delta2m arbi...