Bilinear Recovery using Adaptive Vector-AMP
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We consider the problem of jointly recovering the vector b and the matrix C from noisy measurements Y = A(b)C + W, where A(·) is a known affine linear function of b (i.e., A(b)=A_0+∑_i=1^Q b_i A_i with known matrices A_i). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks. To solve this bilinear recovery problem, we propose the Bilinear Adaptive Vector Approximate Message Passing (BAd-VAMP) algorithm. We demonstrate numerically that the proposed approach is competitive with other state-of-the-art approaches to bilinear recovery, including lifted VAMP and Bilinear GAMP.
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