Bilinear Adaptive Generalized Vector Approximate Message Passing
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This paper considers the generalized bilinear recovery problem which aims to jointly recover the vector b and the matrix X from componentwise nonlinear measurements Y∼ p( Y| Z)=∏_i,jp(Y_ij|Z_ij), where Z= A( b) X, A(·) is a known affine linear function of b (i.e., A( b)= A_0+∑_i=1^Qb_i A_i with known matrices A_i.), and p(Y_ij|Z_ij) is a scalar conditional distribution which models the general output transform. A wide range of real-world applications, e.g., quantized compressed sensing with matrix uncertainty, blind self-calibration and dictionary learning from nonlinear measurements, one-bit matrix completion, etc., can be cast as the generalized bilinear recovery problem. To address this problem, we propose a novel algorithm called the Bilinear Adaptive Generalized Vector Approximate Message Passing (BAd-GVAMP), which extends the recently proposed Bilinear Adaptive Vector AMP (BAd-VAMP) algorithm to incorporate arbitrary distributions on the output transform. Numerical results on various applications demonstrate the effectiveness of the proposed BAd-GVAMP algorithm.
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