Bilinear Adaptive Generalized Vector Approximate Message Passing
Bilinear Adaptive Generalized Vector Approximate Message Passing
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DOI：
10.1109/access.2018.2887261
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发表时间：
2018-10
期刊：
影响因子：
3.9
通讯作者：
Xiangming Meng;Jiang Zhu
中科院分区：
文献类型：
--
作者：
Xiangming Meng;Jiang Zhu
本文考虑了广义的双线性恢复问题，该问题旨在共同恢复向量B和矩阵x，从componentwise nonelear测量$ {\ text {y}} \ sim p（{\ text {y text {y}}} | }）= \ prod \ limits _ {i，j} p（y_ {ij} | z_ {ij}）$，其中$ {\ text {z}} = {\ text {a}}}}（{\ text {b}}}} x}} $，$ {\ text {a}}（\ cdot）$是B的已知仿射线性函数，并且$ p（y_ {ij} | z_ {ij}）$是标量的条件分布，可以对一般输出变换进行建模。从非线性测量值，一位矩阵完成以及关节通道和数据解码的广泛的双线性恢复，可以用矩阵不确定性，盲目的自我校准和词典学习，例如，具有矩阵不确定性，盲目的自我校准和词典学习，可以用矩阵不确定性，盲目的自我校准和词典学习，可以将广泛的压缩感测量化，可以作为广义的双线性回收率施加问题。为了解决这个问题，我们提出了一种新型算法，称为双线性自适应广义矢量传递（BAD-GVAMP），该算法扩展了最近提出的双线性自适应矢量AMP AMP算法，以在输出变换上结合任意分布。各种应用的数值结果证明了所提出的坏网状算法的有效性。
This paper considers the generalized bilinear recovery problem, which aims to jointly recover the vector b and the matrix X from componentwise nonlinear measurements ${\text {Y}}\sim p({\text {Y}}|{\text {Z}})=\prod \limits _{i,j}p(Y_{ij}|Z_{ij})$ , where ${\text {Z}}={\text {A}}({\text {b}}){\text {X}}$ , ${\text {A}}(\cdot)$ is a known affine linear function of b, and $p(Y_{ij}|Z_{ij})$ is a scalar conditional distribution that 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, and joint channel and data decoding, 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 algorithm to incorporate arbitrary distributions on the output transform. The numerical results on various applications demonstrate the effectiveness of the proposed BAd-GVAMP algorithm.