Grid matching for sparse signal recovery in compressive sensing

Abstract

Abstract—Sparse signal recovery is often performed over an estimation grid whose choice affects the recovery performance. The grid mismatch effect is posed as a total least squares problem based on the errors in variables (EIV) model. An existing ap-proach to model the mismatch namely the interpolation approach is interpreted as an EIV model. The grid mismatch is solved by an alternating descent algorithm, which alternates between basis-pursuit (BP) and least squares (LS) as well as its extension wherein BP is solved by a Bayesian algorithm. These algorithms are compared with respect to the SNR and grid offset for the Nyquist and upsampled grids. Index Terms—Sparse signal recovery, grid mismatch, errors in variables model, total least squares, basis pursuit, fast Laplace, direction of arrival estimation I.