"Plug-and-Play" Edge-Preserving Regularization

In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated algorithms are complex and require a good knowledge of large-scale optimization algorithms, and they involve certain tolerances that the user must choose. We present a simpler approach that relies only on standard computational building blocks in matrix computations, such as orthogonal transformations, preconditioned iterative solvers, Kronecker products, and the discrete cosine transform -- hence the term "plug-and-play." We do not attempt to improve on TV reconstructions, but rather provide an easy-to-use approach to computing reconstructions with similar properties.Comment: 14 pages, 7 figures, 3 table

Image reconstruction from nonuniformly spaced samples in spectral-domain optical coherence tomography

In spectral-domain optical coherence tomography (SD-OCT), data samples are collected nonuniformly in the wavenumber domain, requiring a measurement re-sampling process before a conventional fast Fourier transform can be applied to reconstruct an image. This re-sampling necessitates extra computation and often introduces errors in the data. Instead, we develop an inverse imaging approach to reconstruct an SD-OCT image. We make use of total variation (TV) as a constraint to preserve the image edges, and estimate the two-dimensional cross-section of a sample directly from the SD-OCT measurements rather than processing for each A-line. Experimental results indicate that compared with the conventional method, our technique gives a smaller noise residual. The potential of using the TV constraint to suppress sensitivity falloff in SD-OCT is also demonstrated with experiment data

Plug-and-play priors for model based reconstruction

Abstract-Model-based reconstruction is a powerful framework for solving a variety of inverse problems in imaging. 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. 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, electron-microscopy, MRI, and ultrasound, to name just a few. However, combining state-of-theart 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 paper, we propose a flexible framework that allows state-of-the-art forward models of imaging systems to be matched with state-of-the-art priors 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