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Methods and costs of preventing cadmium emissions. EIR 6636 EN Vol. III. Environment and quality of life
Nonuniform Sparse Recovery with Subgaussian Matrices
Compressive sensing predicts that sufficiently sparse vectors can be
recovered from highly incomplete information. Efficient recovery methods such
as -minimization find the sparsest solution to certain systems of
equations. Random matrices have become a popular choice for the measurement
matrix. Indeed, near-optimal uniform recovery results have been shown for such
matrices. In this note we focus on nonuniform recovery using Gaussian random
matrices and -minimization. We provide a condition on the number of
samples in terms of the sparsity and the signal length which guarantees that a
fixed sparse signal can be recovered with a random draw of the matrix using
-minimization. The constant 2 in the condition is optimal, and the
proof is rather short compared to a similar result due to Donoho and Tanner
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