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 |
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Pages (from-to) | 931-958 |
Number of pages | 28 |
Journal | Inverse Problems and Imaging |
Volume | 13 |
Issue number | 5 |
DOIs | |
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 |
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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