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