Model-based reconstruction is a powerful framework for solving a variety of inverse problems in imaging. The method works by combining a forward model of the imaging system with a prior model of the image itself, and the reconstruction is then computed by minimizing a functional consisting of the sum of two terms corresponding to the forward and prior models. In recent years, enormous progress has been made in the problem of denoising, a special case of an inverse problem where the forward model is an identity operator. A wide range of methods including nonlocal means, dictionary-based methods, 3D block matching, TV minimization and kernel-based filtering have proven that it is possible to recover high fidelity images even after a great deal of noise has been added. Similarly, great progress has been made in improving model-based inversion when the forward model corresponds to complex physical measurements in applications such as X-ray CT, electronmicroscopy, MRI, and ultrasound, to name just a few. However, combining state-of-the-art denoising algorithms (i.e., prior models) with state-of-the-art inversion methods (i.e., forward models) has been a challenge for many reasons. In this report, we propose a flexible framework that allows state-of-the-art forward models of imaging systems to be matched with state-of-the-art prior or denoising models. This framework, which we term as Plug-and-Play priors, has the advantage that it dramatically simplifies software integration, and moreover, it allows state-of-the-art denoising methods that have no known formulation as an optimization problem to be used. We demonstrate with some simple examples how Plug-and-Play priors can be used to mix and match a wide variety of existing denoising models with a tomographic forward model, thus greatly expanding the range of possible problem solutions.
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