Bilinear Recovery Using Adaptive Vector-AMP
Bilinear Recovery Using Adaptive Vector-AMP
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DOI：
10.1109/tsp.2019.2916100
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发表时间：
2018-08
影响因子：
5.4
通讯作者：
Subrata Sarkar;A. Fletcher;S. Rangan;Philip Schniter
中科院分区：
文献类型：
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作者：
Subrata Sarkar;A. Fletcher;S. Rangan;Philip Schniter
我们考虑共同恢复向量$ \ boldsymbol {b} $的问题和矩阵$ \ boldsymbol {c} $从嘈杂测量中$ \ boldsymbol {y} = \ boldsymbol {a} {c} + \ boldsymbol {w} $，其中$ \ boldsymbol {a}（\ cdot）$是$ \ boldsymbol {b} $的已知仿射线性函数（i。 _ {i = 1}^q b_i \ boldsymbol {a} _i $带有已知矩阵$ \ boldsymbol {a} _i $）。此问题在矩阵完成，鲁棒PCA，词典学习，自我校准，盲目卷积，联合通道/符号估计，具有矩阵不确定性的压缩感测以及许多其他任务中都有应用。为了解决这个双线性恢复问题，我们提出了双线性自适应矢量近似消息传递（VAMP）算法。我们从数值上证明，所提出的方法与其他双线性恢复的最先进方法具有竞争力，包括提起的鞋面和双线性通用近似消息传递。
We consider the problem of jointly recovering the vector $\boldsymbol{b}$ and the matrix $\boldsymbol{C}$ from noisy measurements $\boldsymbol{Y} = \boldsymbol{A}(\boldsymbol{b})\boldsymbol{C} + \boldsymbol{W}$, where $\boldsymbol{A}(\cdot)$ is a known affine linear function of $\boldsymbol{b}$ (i.e., $\boldsymbol{A}(\boldsymbol{b})=\boldsymbol{A}_0+\sum _{i=1}^Q b_i \boldsymbol{A}_i$ with known matrices $\boldsymbol{A}_i$). 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 (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 Generalized Approximate Message Passing.