Iterative CT reconstruction based on ADMM using shearlet sparse regularization

Dayu Xiao; Jianhua Li; Ruotong Zhao; Shouliang Qi; Yan Kang; Dayu Xiao; Jianhua Li; Ruotong Zhao; Shouliang Qi; Yan Kang

doi:10.3934/mbe.2022552

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 11840-11853. doi: 10.3934/mbe.2022552

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Research article Special Issues

Iterative CT reconstruction based on ADMM using shearlet sparse regularization

1.
College of Medicine and Biological Information Engineering, Northeastern University, Shenyang, 110819, China
2.
School of Biological Science and Medical Engineering, Beihang University, Beijing 100191, China
3.
College of Health Science and Environment Engineering, Shenzhen Technology University, Shenzhen 518118, China
Academic editor: Simon James Fong

Received: 17 March 2022 Revised: 01 August 2022 Accepted: 08 August 2022 Published: 16 August 2022
MSC : Reasearcharticle

The total variation (TV) method favors solutions with the piece-wise constant assumption of the desired image from sparse-view sampling, for example, simple geometric images with flat intensity. When the phantoms become more complex and contain complicated textures, for example, high-resolution phantom and lung CT images, the images reconstructed by TV regularization may lose their contrast and fine structures. One of the optimally sparse transforms for images, the shearlet transform, has C² without discontinuities on C² curves, giving excellent sensitive directional information as compared with other wavelet transform approaches. Here, we developed a Shearlet-Sparse Regularization (SSR) algorithm solved with the Alternating Direction Method of Multipliers (ADMM) to overcome this limitation. With the strengthened characteristics of SSR, we performed one simulation experiment and two real experiments using a NeuViz 64 X-ray CT scanning system to measure the performance and properties of proposed algorithm. The results demonstrate that the SSR method exhibits the advantage of providing high-quality directional information and contrast as compared with TV.
- CT reconstruction,
- compressed sensing,
- shearlet regularization,
- ADMM,
- iterative reconstruction
Citation: Dayu Xiao, Jianhua Li, Ruotong Zhao, Shouliang Qi, Yan Kang. Iterative CT reconstruction based on ADMM using shearlet sparse regularization[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 11840-11853. doi: 10.3934/mbe.2022552

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Abstract

The total variation (TV) method favors solutions with the piece-wise constant assumption of the desired image from sparse-view sampling, for example, simple geometric images with flat intensity. When the phantoms become more complex and contain complicated textures, for example, high-resolution phantom and lung CT images, the images reconstructed by TV regularization may lose their contrast and fine structures. One of the optimally sparse transforms for images, the shearlet transform, has C² without discontinuities on C² curves, giving excellent sensitive directional information as compared with other wavelet transform approaches. Here, we developed a Shearlet-Sparse Regularization (SSR) algorithm solved with the Alternating Direction Method of Multipliers (ADMM) to overcome this limitation. With the strengthened characteristics of SSR, we performed one simulation experiment and two real experiments using a NeuViz 64 X-ray CT scanning system to measure the performance and properties of proposed algorithm. The results demonstrate that the SSR method exhibits the advantage of providing high-quality directional information and contrast as compared with TV.

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