论文标题
可插入的先验与MMSE DEOISER的可证明的融合
Provable Convergence of Plug-and-Play Priors with MMSE denoisers
论文作者
论文摘要
插入式先验（PNP）是一种正规图像重建的方法，可以通过图像Denoiser指定先验。尽管PNP算法对于执行后验概率（MAP）估计的DENOISER的DENOISER已被充分理解，但尚未分析它们的最小平均误差（MMSE）DENOISERS。这封信通过建立迭代收缩/阈值算法（ISTA）的第一个理论收敛结果来解决这一差距。我们表明，PNP-ISTA产生的迭代率具有MMSE DeOiser，将其收敛到某些全球成本函数的固定点。我们通过比较两种类型的Denoiser，即确切的MMSE Denoiser和通过训练深层神经网络获得的近似MMSE DeOiser来验证压缩感测的稀疏信号回收分析。
Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.
