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Compressive sensing has attracted considerable attention in automotive radar interference mitigation. However, these algorithms usually cannot be applied directly to commercial automotive radar as most of them are computationally intense. In this paper, we therefore introduce a computationally efficient two-dimensional masked residual updates (2D MRU) compressive sensing framework. By utilizing the sparsity of the beat signal in the frequency domain, the range-Doppler (RD) spectrum can be reconstructed with the help of undistorted samples in the beat signal. Unlike the other schemes, where a 2D signal measurement is vectorized into a 1D signal, the proposed 2D MRU can directly take a 2D signal measurement and reconstruct the corresponding RD spectrum. Furthermore, the 2D MRU framework can be easily integrated into well-known optimization schemes such as basis pursuit, iterative hard thresholding, iterative soft thresholding, orthogonal matching pursuit, and approximate message-passing algorithm. In addition to the standard iterative thresholding algorithms, we propose a novel prior-model-based iterative thresholding method to further reduce the computation time and reconstruction error. Theoretical analysis shows that the proposed framework can successfully reconstruct the RD spectrum with high probability. Moreover, numerical experiments demonstrate the superiority of the proposed framework in terms of computational complexity.

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