Sparse Reconstruction from Hadamard Matrices: A Lower Bound

03/28/2019

∙

by   Jarosław Błasiok, et al.

∙

0

∙

share

We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. We show that for a N × N Hadamard matrix, one cannot recover all k-sparse vectors unless the number of subsampled rows is Ω(k ^2 N).