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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.
Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the state-of-the-art performance of PnP algorithms using pre-trained deep ne
Recent frameworks, such as the so-called plug-and-play, allow us to leverage the developments in image denoising to tackle other, and more involved, problems in image processing. As the name suggests, state-of-the-art denoisers are plugged into an it
This paper presents a novel deformable registration framework, leveraging an image prior specified through a denoising function, for severely noise-corrupted placental images. Recent work on plug-and-play (PnP) priors has shown the state-of-the-art p
Plug-and-play priors (PnP) is an image reconstruction framework that uses an image denoiser as an imaging prior. Unlike traditional regularized inversion, PnP does not require the prior to be expressible in the form of a regularization function. This
Since the seminal work of Venkatakrishnan et al. (2013), Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging. These methods derive Minimum Mean Square Error (MMSE) or Maximum A Posteriori (MAP) estimators for inverse problems in imag