A reweighted matrix completion algorithm for sparse inverse synthetic aperture radar imaging

Abstract Sparse inverse synthetic aperture radar (ISAR) imaging can be generally achieved by compressed sensing (CS) methods because sparse sampling disables the approach of conventional range Doppler. However, the CS‐based methods have to convert the matrix into a vector when the random sampling is adopted, which results in huge memory usage and high computational complexity. Note that matrix completion (MC) is suitable for matrix operations, which can recover random sparse data directly based on the low‐rank property of the echo matrix. In order to improve the performance of the conventional MC approaches, a novel reweighted matrix completion method for sparse ISAR imaging is proposed in this paper. To avoid using the same singular value thresholding of the traditional MC method to achieve a low‐rank solution, the reweighted scheme for singular values is applied to restrain the rank. Furthermore, the weights of the current iteration are updated with their singular values obtained in the former iteration, rather than using a fixed value. Then, the alternating direction method of multipliers is utilised to alternatively optimise the proposed model, which has an improved computational efficiency. Once the full data is recovered, the ISAR image can be achieved via the conventional 2D inverse fast Fourier transform. Experimental results based on measured data validate the proposed approach that can result in improving imaging performance within several seconds, which is tens of times faster than some reported low‐rank‐based methods.