论文标题
将广义期望一致的近似值用于MR图像恢复
Denoising Generalized Expectation-Consistent Approximation for MR Image Recovery
论文作者
论文摘要
为了解决反问题，请插件（PNP）方法用呼叫特定于应用程序的DeNoiser在凸优化算法中替换近端步骤，通常是使用深神经网络（DNN）实现的。尽管这种方法得出了准确的解决方案，但可以改进它们。例如，Denoiser通常经过设计/训练以消除白色高斯噪声，但是PNP算法中的Dinoiser输入误差通常远非白色或高斯。近似消息传递（AMP）方法提供了白色和高斯DEOISER输入误差，但仅当正向操作员足够随机时。在这项工作中，对于基于傅立叶的远期运营商，我们提出了一种基于普遍的期望一致性（GEC）近似（GEC）的近似（AMP的近乎表亲）的PNP算法，该算法在每次迭代时提供了可预测的错误统计信息，以及一个新的DNN Denoiser，利用了这些统计数据。我们将方法应用于磁共振（MR）图像恢复，并证明其优于现有的PNP和AMP方法。
To solve inverse problems, plug-and-play (PnP) methods replace the proximal step in a convex optimization algorithm with a call to an application-specific denoiser, often implemented using a deep neural network (DNN). Although such methods yield accurate solutions, they can be improved. For example, denoisers are usually designed/trained to remove white Gaussian noise, but the denoiser input error in PnP algorithms is usually far from white or Gaussian. Approximate message passing (AMP) methods provide white and Gaussian denoiser input error, but only when the forward operator is sufficiently random. In this work, for Fourier-based forward operators, we propose a PnP algorithm based on generalized expectation-consistent (GEC) approximation -- a close cousin of AMP -- that offers predictable error statistics at each iteration, as well as a new DNN denoiser that leverages those statistics. We apply our approach to magnetic resonance (MR) image recovery and demonstrate its advantages over existing PnP and AMP methods.
