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Motivated by recent work on two dimensional (2D) harmonic component recoveryvia atomic norm minimization (ANM), a fast 2D direction of arrival (DOA)off-grid estimation based on ANM method was proposed. By introducing a matrixatomic norm the 2D DOA estimation problem is turned into matrix atomic normminimization (MANM) problem. Since the 2D-ANM gridless DOA estimation isprocessed by vectorizing the 2D into 1D estimation and solved via semi-definiteprogramming (SDP), which is with high computational cost in 2D processing whenthe number of antennas increases to large size. In order to overcome thisdifficulty, a detail formulation of MANM problem via SDP method is offered inthis paper, the MANM method converts the original $MN+1$ dimensions probleminto a $M+N$ dimensions SDP problem and greatly reduces the computationalcomplexity. In this paper we study the problem of 2D line spectrally-sparsesignal recovery from partial noiseless observations and full noisyobservations, both of which can be solved efficiently via MANM method andobtain high accuracy estimation of the true 2D angles. We give a sufficientcondition of the optimality condition of the proposed method and prove an upbound of the expected error rate for denoising. Finally, numerical simulationsare conducted to show the efficiency and performance of the proposed method,with comparisons against several existed sparse methods.

Fast Two-Dimensional Atomic Norm Minimization in Spectrum Estimation and Denoising