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

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.