An MTL1TV non-convex regularization model for MR Image reconstruction using the alternating direction method of multipliers

Xuexiao You; Ning Cao; Wei Wang; Xuexiao You; Ning Cao; Wei Wang

doi:10.3934/era.2024159

Electronic Research Archive

2024, Volume 32, Issue 5: 3433-3456. doi: 10.3934/era.2024159

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Research article

An MTL1TV non-convex regularization model for MR Image reconstruction using the alternating direction method of multipliers

1.
College of Information Science and Engineering, Hohai University, Nanjing 210098, China
2.
School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
3.
Key Laboratory of Clinical Engineering, School of Biomedical Engineering and Informatics, Nanjing Medical University, Nanjing 211166, China

Received: 20 November 2023 Revised: 24 February 2024 Accepted: 09 May 2024 Published: 28 May 2024

The acquisition time of magnetic resonance imaging (MRI) is relatively long. To achieve high-quality and fast reconstruction of magnetic resonance (MR) images, we proposed a non-convex regularization model for MR image reconstruction with the modified transformed $ {l_1} $ total variation (MTL1TV) regularization term. We addressed this new model using the alternating direction method of multipliers (ADMM). To evaluate the proposed MTL1TV model, we performed numerical experiments on several MR images. The numerical results showed that the proposed model gives reconstructed images of improved quality compared with those obtained from state of the art models. The results indicated that the proposed model can effectively reconstruct MR images.
- MR Image reconstruction,
- transformed $ {l_1} $ penalty,
- non-convex regularization,
- total variation,
- ADMM
Citation: Xuexiao You, Ning Cao, Wei Wang. An MTL1TV non-convex regularization model for MR Image reconstruction using the alternating direction method of multipliers[J]. Electronic Research Archive, 2024, 32(5): 3433-3456. doi: 10.3934/era.2024159

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Abstract

The acquisition time of magnetic resonance imaging (MRI) is relatively long. To achieve high-quality and fast reconstruction of magnetic resonance (MR) images, we proposed a non-convex regularization model for MR image reconstruction with the modified transformed $ {l_1} $ total variation (MTL1TV) regularization term. We addressed this new model using the alternating direction method of multipliers (ADMM). To evaluate the proposed MTL1TV model, we performed numerical experiments on several MR images. The numerical results showed that the proposed model gives reconstructed images of improved quality compared with those obtained from state of the art models. The results indicated that the proposed model can effectively reconstruct MR images.

References

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