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PCM-TV-TFV: A Novel Two-Stage Framework for Image Reconstruction from Fourier Data

Banff International Research Station for Mathematical Innovation and Discovery

We propose in this paper a novel two-stage projection correction modeling (PCM) framework for image reconstruction from (nonuniform) Fourier measurements. PCM consists of a projection stage (P-stage) motivated by the multiscale Galerkin method and a correction stage (C-stage) with an edge guided regularity fusing together the advantages of total variation and total fractional variation. The P-stage allows for continuous modeling of the underlying image of interest. The given measurements are projected onto a space in which the image is well represented. We then enhance the reconstruction result at the C-stage that minimizes an energy functional consisting of a delity in the transformed domain and a novel edge guided regularity. We further develop ecient proximal algorithms to solve the corresponding optimization problem. Various numerical results in both one-dimensional signals and two-dimensional images have also been presented to demonstrate the superior performance of the proposed two-stage method to other classical one-stage methods. This is a joint work with Yue Zhang (now at Siemens Corporate Research) and Guohui Song (Clarkson University).

Mathematics; Functional analysis; Calculus of variations and optimal control; optimization; Numerical analysis

video/mp4

Author affiliation: Case Western Reserve University

2019-12-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72999

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/