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PCM-TV-TFV: A Novel Two-Stage Framework for Image Reconstruction from Fourier Data Guo, Weihong
Description
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).
Item Metadata
Title |
PCM-TV-TFV: A Novel Two-Stage Framework for Image Reconstruction from Fourier Data
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-06-27T16:24
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Description |
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).
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Extent |
39.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Case Western Reserve University
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Series | |
Date Available |
2019-12-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0387360
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International