Magnetic resonance image restoration via least absolute deviations measure with isotropic total variation constraint

Xiaolei Gu; Wei Xue; Yanhong Sun; Xuan Qi; Xiao Luo; Yongsheng He; Xiaolei Gu; Wei Xue; Yanhong Sun; Xuan Qi; Xiao Luo; Yongsheng He

doi:10.3934/mbe.2023468

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 10590-10609. doi: 10.3934/mbe.2023468

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Magnetic resonance image restoration via least absolute deviations measure with isotropic total variation constraint

1.
Department of Radiology, Maanshan People's Hospital, Maanshan, China
2.
School of Computer Science and Technology, Anhui University of Technology, Maanshan, China
3.
School of Civil Engineering and Architecture, Anhui University of Technology, Maanshan, China

Received: 06 January 2023 Revised: 23 March 2023 Accepted: 30 March 2023 Published: 12 April 2023

This paper presents a magnetic resonance image deblurring and denoising model named the isotropic total variation regularized least absolute deviations measure (LADTV). More specifically, the least absolute deviations term is first adopted to measure the violation of the relation between the desired magnetic resonance image and the observed image, and to simultaneously suppress the noise that may corrupt the desired image. Then, in order to preserve the smoothness of the desired image, we introduce an isotropic total variation constraint, yielding the proposed restoration model LADTV. Finally, an alternating optimization algorithm is developed to solve the associated minimization problem. Comparative experiments on clinical data demonstrate the effectiveness of our approach to synchronously deblur and denoise magnetic resonance image.
- magnetic resonance image restoration,
- image deblurring,
- image denoising,
- least absolute deviations,
- isotropic total variation
Citation: Xiaolei Gu, Wei Xue, Yanhong Sun, Xuan Qi, Xiao Luo, Yongsheng He. Magnetic resonance image restoration via least absolute deviations measure with isotropic total variation constraint[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10590-10609. doi: 10.3934/mbe.2023468

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Abstract

This paper presents a magnetic resonance image deblurring and denoising model named the isotropic total variation regularized least absolute deviations measure (LADTV). More specifically, the least absolute deviations term is first adopted to measure the violation of the relation between the desired magnetic resonance image and the observed image, and to simultaneously suppress the noise that may corrupt the desired image. Then, in order to preserve the smoothness of the desired image, we introduce an isotropic total variation constraint, yielding the proposed restoration model LADTV. Finally, an alternating optimization algorithm is developed to solve the associated minimization problem. Comparative experiments on clinical data demonstrate the effectiveness of our approach to synchronously deblur and denoise magnetic resonance image.

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