Solution existence, uniqueness, and stability of discrete basis sinograms in multispectral CT

• URL: http://arxiv.org/abs/2305.03330v1
• Date: Fri, 5 May 2023 07:22:20 GMT
• Title: Solution existence, uniqueness, and stability of discrete basis sinograms in multispectral CT
• Authors: Yu Gao and Xiaochuan Pan and Chong Chen
• Abstract summary: This work investigates conditions for quantitative image reconstruction in multispectral computed tomography (MSCT) An empirical, but highly effective, two-step data-domain-decomposition (DDD) method has been developed and used widely for quantitative image reconstruction in MSCT.
• Score: 4.084909224028198
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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