Solution existence, uniqueness, and stability of discrete basis sinograms in multispectral CT
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912002360737792 |
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| author | Gao, Yu Pan, Xiaochuan Chen, Chong |
| author_facet | Gao, Yu Pan, Xiaochuan Chen, Chong |
| contents | This work investigates conditions for quantitative image reconstruction in multispectral computed tomography (MSCT), which remains a topic of active research. In MSCT, one seeks to obtain from data the spatial distribution of linear attenuation coefficient, referred to as a virtual monochromatic image (VMI), at a given X-ray energy, within the subject imaged. As a VMI is decomposed often into a linear combination of basis images with known decomposition coefficients, the reconstruction of a VMI is thus tantamount to that of the basis images. An empirical, but highly effective, two-step data-domain-decomposition (DDD) method has been developed and used widely for quantitative image reconstruction in MSCT. In the two-step DDD method, step (1) estimates the so-called basis sinogram from data through solving a nonlinear transform, whereas step (2) reconstructs basis images from their basis sinograms estimated. Subsequently, a VMI can readily be obtained from the linear combination of basis images reconstructed. As step (2) involves the inversion of a straightforward linear system, step (1) is the key component of the DDD method in which a nonlinear system needs to be inverted for estimating the basis sinograms from data. In this work, we consider a {\it discrete} form of the nonlinear system in step (1), and then carry out theoretical and numerical analyses of conditions on the existence, uniqueness, and stability of a solution to the discrete nonlinear system for accurately estimating the discrete basis sinograms, leading to quantitative reconstruction of VMIs in MSCT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03330 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solution existence, uniqueness, and stability of discrete basis sinograms in multispectral CT Gao, Yu Pan, Xiaochuan Chen, Chong Numerical Analysis Computer Vision and Pattern Recognition Medical Physics 65R32, 94A08, 65F22, 65J22, 65D18 This work investigates conditions for quantitative image reconstruction in multispectral computed tomography (MSCT), which remains a topic of active research. In MSCT, one seeks to obtain from data the spatial distribution of linear attenuation coefficient, referred to as a virtual monochromatic image (VMI), at a given X-ray energy, within the subject imaged. As a VMI is decomposed often into a linear combination of basis images with known decomposition coefficients, the reconstruction of a VMI is thus tantamount to that of the basis images. An empirical, but highly effective, two-step data-domain-decomposition (DDD) method has been developed and used widely for quantitative image reconstruction in MSCT. In the two-step DDD method, step (1) estimates the so-called basis sinogram from data through solving a nonlinear transform, whereas step (2) reconstructs basis images from their basis sinograms estimated. Subsequently, a VMI can readily be obtained from the linear combination of basis images reconstructed. As step (2) involves the inversion of a straightforward linear system, step (1) is the key component of the DDD method in which a nonlinear system needs to be inverted for estimating the basis sinograms from data. In this work, we consider a {\it discrete} form of the nonlinear system in step (1), and then carry out theoretical and numerical analyses of conditions on the existence, uniqueness, and stability of a solution to the discrete nonlinear system for accurately estimating the discrete basis sinograms, leading to quantitative reconstruction of VMIs in MSCT. |
| title | Solution existence, uniqueness, and stability of discrete basis sinograms in multispectral CT |
| topic | Numerical Analysis Computer Vision and Pattern Recognition Medical Physics 65R32, 94A08, 65F22, 65J22, 65D18 |
| url | https://arxiv.org/abs/2305.03330 |