Review of image reconstruction methods in X-ray computed tomography with cone-beam geometry

The article reflects the main task of the X-ray computed tomography and its mathematical description. Direct and inverse Radon transform are given. The methods of image reconstruction in X-ray computed tomography are presented. Their brief classification are given. The author have reviewed classical problem of two-dimensional computed tomography and basics approaches to its solution. Emphasis is placed on back projection algorithm with filtering convolution. The derivation of the algorithm for parallel and fan-beam reconstruction are given. The analysis of the problem of three-dimensional reconstruction are presented. The author describes the additional conditions imposed on the projection data, the computational efficiency of the algorithms and the quality of the images. The basic trajectory of the X-ray source, providing the condition Tuy, are considered. The article gives an overview of existing methods of three-dimensional reconstruction with cone-beam geometry, their advantages, disadvantages, clinical applications. Their brief classification are given. Approximate algorithms of three-dimensional reconstruction are presented. The Feldkamp algorithm, the extended parallel backprojection, and the advanced single-slice rebinning are described. The author raises the question of developing approaches and methods for obtaining images with three-dimensional reconstruction for cone-beam spiral CT.