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

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