Approximate message passing algorithm for complex separable compressed imaging
Approximate message passing algorithm for complex separable compressed imaging
复制标题
复杂可分离压缩成像的近似消息传递算法
DOI：
10.1109/apsipa.2013.6694378
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Kazushi Mimura
中科院分区：
文献类型：
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作者：
Akira Hirabayashi;Jumpei Sugimoto; Kazushi Mimura
提出了一种用于复可分压缩成像的近似消息传递（AMP）算法.压缩感知的标准公式使用一维信号，而图像通常通过光栅扫描重塑成这样的向量，这需要一个巨大的矩阵。然而，在可分离的情况下，如离散傅立叶变换（DFT），可以使用两个中等大小的矩阵来公式化感测过程，这两个矩阵被乘以来自两侧的图像。我们利用这个公式在我们的AMP算法。由于我们假设传感过程为DFT，其中测量很复杂，因此我们的公式适用于目标信号和测量都很复杂的情况。实验结果表明，该算法能够很好地重建128×128的图像，而在相同的计算环境下，光栅扫描方法无法处理这类图像。我们还表明，所提出的算法的压缩率是大致相同的所谓的弱阈值。
We propose the approximate message passing (AMP) algorithm for complex separable compressed imaging. The standard formulation of compressed sensing uses one-dimensional signals while images are usually reshaped into such vectors by raster scan, which requires a huge matrix. In separable cases like discrete Fourier transform (DFT), however, sensing processes can be formulated using two moderate size matrices which are multiplied to images from the both sides. We exploit this formulation in our AMP algorithm. Since we suppose DFT for the sensing process, in which measurements are complex, our formulation applies to cases in which both target signals and measurements are complex. We show that the proposed algorithm perfectly reconstructs a 128×128 image, which could not be handled by the raster scan approach on the same computational environment. We also show that the compression rate of the proposed algorithm is mostly same as the so-called weak threshold.