A plug-and-play synthetic data deep learning for undersampled magnetic resonance image reconstruction

Magnetic resonance imaging (MRI) plays an important role in modern medical diagnostic but suffers from prolonged scan time. Current deep learning methods for undersampled MRI reconstruction exhibit good performance in image de-aliasing which can be tailored to the specific kspace undersampling scenario. But it is very troublesome to configure different deep networks when the sampling setting changes. In this work, we propose a deep plug-and-play method for undersampled MRI reconstruction, which effectively adapts to different sampling settings. Specifically, the image de-aliasing prior is first learned by a deep denoiser trained to remove general white Gaussian noise from synthetic data. Then the learned deep denoiser is plugged into an iterative algorithm for image reconstruction. Results on in vivo data demonstrate that the proposed method provides nice and robust accelerated image reconstruction performance under different undersampling patterns and sampling rates, both visually and quantitatively.Comment: 5 pages, 3 figure

A Variational Inequality Model for Learning Neural Networks

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent training procedure consists of minimizing highly non-convex objectives based on data sets of huge dimension. In this context, current methodologies are not guaranteed to produce global solutions. We present an alternative approach which foregoes the optimization framework and adopts a variational inequality formalism. The associated algorithm guarantees convergence of the iterates to a true solution of the variational inequality and it possesses an efficient block-iterative structure. A numerical application is presented

Image Restoration using Plug-and-Play CNN MAP Denoisers

Plug-and-play denoisers can be used to perform generic image restoration tasks independent of the degradation type. These methods build on the fact that the Maximum a Posteriori (MAP) optimization can be solved using smaller sub-problems, including a MAP denoising optimization. We present the first end-to-end approach to MAP estimation for image denoising using deep neural networks. We show that our method is guaranteed to minimize the MAP denoising objective, which is then used in an optimization algorithm for generic image restoration. We provide theoretical analysis of our approach and show the quantitative performance of our method in several experiments. Our experimental results show that the proposed method can achieve 70x faster performance compared to the state-of-the-art, while maintaining the theoretical perspective of MAP.Comment: Code and models available at https://github.com/DawyD/cnn-map-denoiser . Accepted for publication in VISAPP 202

On the Contractivity of Plug-and-Play Operators

In plug-and-play (PnP) regularization, the proximal operator in algorithms such as ISTA and ADMM is replaced by a powerful denoiser. This formal substitution works surprisingly well in practice. In fact, PnP has been shown to give state-of-the-art results for various imaging applications. The empirical success of PnP has motivated researchers to understand its theoretical underpinnings and, in particular, its convergence. It was shown in prior work that for kernel denoisers such as the nonlocal means, PnP-ISTA provably converges under some strong assumptions on the forward model. The present work is motivated by the following questions: Can we relax the assumptions on the forward model? Can the convergence analysis be extended to PnP-ADMM? Can we estimate the convergence rate? In this letter, we resolve these questions using the contraction mapping theorem: (i) for symmetric denoisers, we show that (under mild conditions) PnP-ISTA and PnP-ADMM exhibit linear convergence; and (ii) for kernel denoisers, we show that PnP-ISTA and PnP-ADMM converge linearly for image inpainting. We validate our theoretical findings using reconstruction experiments.Comment: Errors in the proof of Lemma 1 and the statement of Theorem 2 were identified after the publication; these have been rectified in the revised version (v2