Short-and-Sparse Deconvolution Via Rank-One Constrained Optimization (Roco)

Short-and-sparse deconvolution (SaSD) aims to recover a short kernel and a long and sparse signal from their convolution. In the literature, formulation of blind deconvolution is either a convex programming via a matrix lifting of convolution, or a bilinear Lasso. Optimization solvers are typically based on bilinear factorizations. In this paper, we formulate SaSD as a non-convex optimization with a rank-one matrix constraint, hence referred to as Rank-One Constrained Optimization (ROCO). The solver is based on alternating direction method of multipliers (ADMM). It operates on the full rank-one matrix rather than bilinear factorizations. Closed form updates are derived for the efficiency of ADMM. Simulations include both synthetic data and real images. Results show substantial improvements in recovery accuracy (at least 19dB in PSNR for real images) and comparable runtime compared with benchmark algorithms based on bilinear factorization.