A Generalized Construction Model for CT Projection-Wise Filters on the SDBP Technique

Yiming Jiang, Jintao Zhao, Xiaodong Hu and Jing Zou
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Yiming Jiang: School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China
Jintao Zhao: Tianjin Key Laboratory of Information Sensing and Intelligent Control, Tianjin University of Technology and Education, Tianjin 300222, China
Xiaodong Hu: School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China
Jing Zou: School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China

Mathematics, 2022, vol. 10, issue 4, 1-18

Abstract: Nowadays, with the rapid development of computed tomography (CT), the theoretical expansion of CT reconstruction has become the crucial ingredient to break through technical bottlenecks. This article supplements relevant knowledge of the method for constructing CT projection-wise filters. From the perspective of the mathematical principle of CT reconstruction, the second-order divided-difference back projection (SDBP) technique is firstly proposed, which is an implementation of accurate and efficient inverse Radon transform. On the basis of the SDBP technique, a brand new computational model for filter expressions is derived. The model reveals the correlation between the convolution kernel for data restoration and the filter expression and also specifies the principle of filter construction. On the proposed filter construction model, the decomposition form of filters is discovered for the first time. A series of basic filters are acquired, which can be used to compose filters in actual need. According to the superposition principle, the properties of a filter depend on the decomposed basic filters. The selection of the kernel function on the properties of basic filters clarifies the general rule of filter construction. These theories proposed in this article are of reference value for the filter optimization research in the CT reconstruction field.

Keywords: inverse Radon transform; CT reconstruction; SDBP; filter construction; kernel function; Hilbert transform; basic filters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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