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首页> 外文期刊>IEEE Transactions on Information Theory >Analysis of Approximate Message Passing With Non-Separable Denoisers and Markov Random Field Priors
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Analysis of Approximate Message Passing With Non-Separable Denoisers and Markov Random Field Priors

机译：具有不可分离的降噪器和马尔可夫随机场先验的近似消息传递分析

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摘要

Approximate message passing (AMP) is a class of low-complexity, scalable algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal from noisy, linear measurements. AMP is an iterative algorithm that performs estimation by updating an estimate of the unknown signal at each iteration and the performance of AMP (quantified, for example, by the mean squared error of its estimates) depends on the choice of a "denoiser" function that is used to produce these signal estimates at each iteration. An attractive feature of AMP is that its performance can be tracked by a scalar recursion referred to as state evolution. Previous theoretical analysis of the accuracy of the state evolution predictions has been limited to the use of only separable denoisers or block-separable denoisers, a class of denoisers that underperform when sophisticated dependencies exist between signal entries. Since signals with entrywise dependencies are common in image/video-processing applications, in this work we study the high-dimensional linear regression task when the dependence structure of the input signal is modeled by a Markov random field prior distribution. We provide a rigorous analysis of the performance of AMP, demonstrating the accuracy of the state evolution predictions, when a class of non-separable sliding-window denoisers is applied. Moreover, we provide numerical examples where AMP with sliding-window denoisers can successfully capture local dependencies in images.
机译：近似消息传递（AMP）是一类低复杂度，可扩展的算法，用于解决高维线性回归任务，其中人们希望从嘈杂的线性测量中恢复未知信号。 AMP是一种迭代算法，通过在每次迭代时更新未知信号的估计值来执行估计，并且AMP的性能（例如，通过其估计值的均方误差进行量化）取决于“降噪器”函数的选择，用于在每次迭代时产生这些信号估计。 AMP的一个吸引人的特征是它的性能可以通过称为状态演化的标量递归进行跟踪。以前对状态演化预测的准确性进行的理论分析仅限于仅使用可分离的去噪器或块可分离的去噪器，当信号条目之间存在复杂的依存关系时，这类去噪器的性能将下降。由于具有输入依存关系的信号在图像/视频处理应用程序中很常见，因此在本工作中，当我们通过马尔可夫随机场先验分布对输入信号的依存结构进行建模时，我们研究高维线性回归任务。当应用一类不可分离的滑动窗口降噪器时，我们对AMP的性能进行了严格的分析，证明了状态演化预测的准确性。此外，我们提供了数值示例，其中带滑动窗口降噪器的AMP可以成功捕获图像中的局部依存关系。

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