Dynamic parallel MRI reconstruction via weighted nuclear norm plus sparse decomposition model

Lei Xue; Benxin Zhang; Jianqun Yang; Lei Xue; Benxin Zhang; Jianqun Yang

doi:10.3934/era.2025192

Electronic Research Archive

2025, Volume 33, Issue 7: 4241-4258. doi: 10.3934/era.2025192

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Research article

Dynamic parallel MRI reconstruction via weighted nuclear norm plus sparse decomposition model

1.
School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin, China
2.
Shenzhen Campus of Sun Yat-sen University, Shenzhen, China
3.
Shenzhen Institute of Advanced Technology, Shenzhen, China

Received: 11 March 2025 Revised: 29 June 2025 Accepted: 08 July 2025 Published: 18 July 2025

The dynamic parallel magnetic resonance imaging (MRI) reconstruction presents additional challenges due to the multi-coil acquisition process and an increase in data dimensions, which lead to a more ill-posed inverse problem compared to single coil dynamic MRI. Relevant optimization strategies usually involve solving the model after convex relaxation, which often leads to suboptimal solutions that either overshrink important signals or fail to adequately promote low-rankness and sparsity. In this paper, we propose a dynamic parallel MRI reconstruction model based on weighted nuclear norm and $ L_{1} $ norm regularization in the framework of low-rank plus sparse (L+S) decomposition. The introduced weighted nuclear norm imposes nonuniform penalties on singular values and has a more flexible approximation to a low-rank property. To solve the resulting non-convex optimization problem, we employ the alternating direction method of multipliers (ADMM) based on variable splitting. The experimental results on multi-coil dynamic datasets show that this method provides a higher reconstruction quality than the traditional convex method.
- dynamic parallel magnetic resonance imaging,
- low-rank plus sparse decomposition,
- weighted nuclear norm,
- ADMM
Citation: Lei Xue, Benxin Zhang, Jianqun Yang. Dynamic parallel MRI reconstruction via weighted nuclear norm plus sparse decomposition model[J]. Electronic Research Archive, 2025, 33(7): 4241-4258. doi: 10.3934/era.2025192

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Abstract

The dynamic parallel magnetic resonance imaging (MRI) reconstruction presents additional challenges due to the multi-coil acquisition process and an increase in data dimensions, which lead to a more ill-posed inverse problem compared to single coil dynamic MRI. Relevant optimization strategies usually involve solving the model after convex relaxation, which often leads to suboptimal solutions that either overshrink important signals or fail to adequately promote low-rankness and sparsity. In this paper, we propose a dynamic parallel MRI reconstruction model based on weighted nuclear norm and $ L_{1} $ norm regularization in the framework of low-rank plus sparse (L+S) decomposition. The introduced weighted nuclear norm imposes nonuniform penalties on singular values and has a more flexible approximation to a low-rank property. To solve the resulting non-convex optimization problem, we employ the alternating direction method of multipliers (ADMM) based on variable splitting. The experimental results on multi-coil dynamic datasets show that this method provides a higher reconstruction quality than the traditional convex method.

References

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