Abstract
We propose a high accuracy algorithm for compressed sensing magnetic resonance imaging (CS-MRI) using a convex optimization technique. Lustig et al. proposed CS-MRI technique based on the minimization of a cost function defined by the sum of the data fidelity term, the 11-norm of sparsifying transform coefficients, and a total variation (TV). This function is not differentiable because of both l1-norm and TV. Hence, they used approximations of the non-differentiable terms and a nonlinear conjugate gradient algorithm was applied to minimize the approximated cost function. The obtained solution was also an approximated one, thus of low-quality. In this paper, we propose an algorithm that obtains the exact solution based on the simultaneous direction method of multipliers (SDMM), which is one of the convex optimization techniques. A simple application of SDMM to CS-MRI cannot be implemented because the transformation matrix size is proportional to the square of the image size. We solve this problem using eigenvalue decompositions. Simulations using real MR images show that the proposed algorithm outperforms the conventional one regardless of compression ratio and random sensing patterns.
| Original language | English |
|---|---|
| Title of host publication | 2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| ISBN (Electronic) | 9789881476821 |
| DOIs | |
| Publication status | Published - 2017 Jan 17 |
| Externally published | Yes |
| Event | 2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016 - Jeju, Korea, Republic of Duration: 2016 Dec 13 → 2016 Dec 16 |
Other
| Other | 2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016 |
|---|---|
| Country | Korea, Republic of |
| City | Jeju |
| Period | 16/12/13 → 16/12/16 |
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ASJC Scopus subject areas
- Artificial Intelligence
- Computer Science Applications
- Information Systems
- Signal Processing
Cite this
High accuracy reconstruction algorithm for CS-MRI using SDMM. / Shibata, Motoi; Inamuro, Norihito; Ijiri, Takashi; Hirabayashi, Akira.
2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016. Institute of Electrical and Electronics Engineers Inc., 2017. 7820788.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - High accuracy reconstruction algorithm for CS-MRI using SDMM
AU - Shibata, Motoi
AU - Inamuro, Norihito
AU - Ijiri, Takashi
AU - Hirabayashi, Akira
PY - 2017/1/17
Y1 - 2017/1/17
N2 - We propose a high accuracy algorithm for compressed sensing magnetic resonance imaging (CS-MRI) using a convex optimization technique. Lustig et al. proposed CS-MRI technique based on the minimization of a cost function defined by the sum of the data fidelity term, the 11-norm of sparsifying transform coefficients, and a total variation (TV). This function is not differentiable because of both l1-norm and TV. Hence, they used approximations of the non-differentiable terms and a nonlinear conjugate gradient algorithm was applied to minimize the approximated cost function. The obtained solution was also an approximated one, thus of low-quality. In this paper, we propose an algorithm that obtains the exact solution based on the simultaneous direction method of multipliers (SDMM), which is one of the convex optimization techniques. A simple application of SDMM to CS-MRI cannot be implemented because the transformation matrix size is proportional to the square of the image size. We solve this problem using eigenvalue decompositions. Simulations using real MR images show that the proposed algorithm outperforms the conventional one regardless of compression ratio and random sensing patterns.
AB - We propose a high accuracy algorithm for compressed sensing magnetic resonance imaging (CS-MRI) using a convex optimization technique. Lustig et al. proposed CS-MRI technique based on the minimization of a cost function defined by the sum of the data fidelity term, the 11-norm of sparsifying transform coefficients, and a total variation (TV). This function is not differentiable because of both l1-norm and TV. Hence, they used approximations of the non-differentiable terms and a nonlinear conjugate gradient algorithm was applied to minimize the approximated cost function. The obtained solution was also an approximated one, thus of low-quality. In this paper, we propose an algorithm that obtains the exact solution based on the simultaneous direction method of multipliers (SDMM), which is one of the convex optimization techniques. A simple application of SDMM to CS-MRI cannot be implemented because the transformation matrix size is proportional to the square of the image size. We solve this problem using eigenvalue decompositions. Simulations using real MR images show that the proposed algorithm outperforms the conventional one regardless of compression ratio and random sensing patterns.
UR - http://www.scopus.com/inward/record.url?scp=85013797784&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85013797784&partnerID=8YFLogxK
U2 - 10.1109/APSIPA.2016.7820788
DO - 10.1109/APSIPA.2016.7820788
M3 - Conference contribution
AN - SCOPUS:85013797784
BT - 2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016
PB - Institute of Electrical and Electronics Engineers Inc.
ER -