### 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 l_{1}-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.

Language | English |
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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 | |

State | 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 |
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Country | Korea, Republic of |

City | Jeju |

Period | 16/12/13 → 16/12/16 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Information Systems
- Signal Processing

### Cite this

*2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016*[7820788] Institute of Electrical and Electronics Engineers Inc.. DOI: 10.1109/APSIPA.2016.7820788

**High accuracy reconstruction algorithm for CS-MRI using SDMM.** / Shibata, Motoi; Inamuro, Norihito; Ijiri, Takashi; Hirabayashi, Akira.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016.*, 7820788, Institute of Electrical and Electronics Engineers Inc., 2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016, Jeju, Korea, Republic of, 16/12/13. DOI: 10.1109/APSIPA.2016.7820788

}

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

BT - 2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -