Edge-adaptive ℓ2 regularization image reconstruction from non-uniform fourier data

Victor Churchill; Rick Archibald; Anne Gelb

doi:10.3934/ipi.2019042

Edge-adaptive ℓ₂ regularization image reconstruction from non-uniform fourier data

Victor Churchill, Rick Archibald, Anne Gelb

Data Analysis and Machine Learning

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Signals and images recovered from edge-sparsity based reconstruction methods may not truely be sparse in the edge domain, and often result in poor quality reconstruction. Iteratively reweighted methods provide some improvement in accuracy, but at the cost of extended runtime. This paper examines such methods when data are acquired as non-uniform Fourier samples, and then presents a new non-iterative weighted regularization method that first pre-processes the data to determine the precise locations of the non-zero values in the edge domain. Our new method is both accurate and efficient, and outperforms reweighted regularization methods in several numerical experiments.

Original language	English
Pages (from-to)	931-958
Number of pages	28
Journal	Inverse Problems and Imaging
Volume	13
Issue number	5
DOIs	https://doi.org/10.3934/ipi.2019042
State	Published - Oct 2019

Funding

Rick Archibald's work is sponsored by the Applied Mathematics Division of ASCR, DOE; in particular under the ACUMEN project (RA). Anne Gelb's work is supported in part by the grants NSF-DMS 1502640, NSF-DMS 1732434, AFOSR FA9550-18-1-0316 and AFOSR FA9550-15-1-0152. 2010 Mathematics Subject Classification. Primary: 68U10, 65F22; Secondary: 42A10. Key words and phrases. Image reconstruction, sparsity constraints, edge detection, iteratively reweighted ℓ1 regularization. Rick Archibald’s work is sponsored by the Applied Mathematics Division of ASCR, DOE; in particular under the ACUMEN project (RA). Anne Gelb’s work is supported in part by the grants NSF-DMS 1502640, NSF-DMS 1732434, AFOSR FA9550-18-1-0316 and AFOSR FA9550-15-1-0152. ∗ Corresponding author: [email protected].

Funders	Funder number
AFOSR FA9550-15-1-0152
AFOSR FA9550-18-1-0316
Applied
NSF-DMS	1502640, 1732434
U.S. Department of Energy	NSF-DMS 1502640, NSF-DMS 1732434, RA
Air Force Office of Scientific Research	FA9550-18-1-0316, FA9550-15-1-0152
Advanced Scientific Computing Research

Keywords

Edge detection
Image reconstruction
Iteratively reweighted ℓ regularization
Sparsity constraints

Access to Document

10.3934/ipi.2019042

Cite this

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abstract = "Signals and images recovered from edge-sparsity based reconstruction methods may not truely be sparse in the edge domain, and often result in poor quality reconstruction. Iteratively reweighted methods provide some improvement in accuracy, but at the cost of extended runtime. This paper examines such methods when data are acquired as non-uniform Fourier samples, and then presents a new non-iterative weighted regularization method that first pre-processes the data to determine the precise locations of the non-zero values in the edge domain. Our new method is both accurate and efficient, and outperforms reweighted regularization methods in several numerical experiments.",

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