Sparse Recovery Using Tight Frames and Minimax Concave Penalty

Kurzfassung

Sparse signal recovery is an important problem in compressed sensing, signal/image processing, computational imaging and machine learning. The design of the sensing matrix is crucial in compressed sensing. While random Gaussian sensing matrices are relatively easier to construct, it is known that matrices constituting a tight frame provide superior reconstruction performance. We formulate the problem of sparse signal recovery using a new data-fidelity term that effectively "tightens" the sensing matrix, and incorporate the minimax concave penalty (MCP) instead of the ℓ1-norm for promoting sparsity. We carry out the optimization using a proximal gradient method and its Nesterov accelerated counterpart. Simulation results demonstrate that the proposed algorithms result in up to three times faster convergence and superior reconstruction accuracy over benchmark methods.