On the design of optimized projections for sensing sparse signals in overcomplete dictionaries

Sparse signals can be sensed with a reduced number of random projections and then reconstructed if compressive sensing (CS) is employed. Traditionally, the projection matrix has been chosen as a random Gaussian matrix, but improved reconstruction performance can be obtained by optimizing the projection matrix. In this paper, we are interested in projection matrix designs for sensing sparse signals in overcomplete dictionaries. In particular, we put forth a closed form design that stems from the formulation of an optimization problem, which bypasses the complexity of iterative design approaches.