The Projection Matrix And Anti-alias Research On 3-D Cone-beam Iterative Arithmetic

In iterative algorithm, it is very important to make a precise projection matrix . But because of the calculated complexity of projection matrix, especially in 3-D cone-beam CT, the development of iterative algorithm is subjected to restriction. For solving this problem, author makes some researches on the aspects of anti-alias disposal and calculation projection matrix more precisely,more quickly.In the thesis, it briefly introduces the computer tomography theory and the methods of image reconstruction, introduce the theory of algebraic reconstruction technique, and then educe the definition of projection matrix in iterative algorithm.It introduces the calculation of projection matrix in 3-D cone beam iterative algorithm, and makes a particular programme implementation for the length projection matrix arithmetic; At last it gives the result of simulated projection date.Based on Splatting theory it presents a method of calculation projection matrix in iterative algorithm。This algorithm is based on the 3-D cone-beam scanning , using cubic B spline local basis function as interpolation kernel, and utilizing footprint function of filter kernel to interpolate the volume to calculate projection matrix. Compared with the constant-size interpolation, it can reconstruct high-resolution image in the same experiment condition. In the thesis, it gives the practical realization of splatting algebraic adapting to 3-D cone-beam reconstruction, and uses the 3-D Sheep-Logan phantom to simulate reconstruction.In the period of X rays traverse the object, signals will be mixed because of the sampling interval of voxels to rays can't be satisfied with the Nyqust sampling theorem. For solving this problem, the theory analyzes the condition of alias signals appearance and makes a suitable transform of interpolating function based on utilizing the splatting algorithm to evaluate projection matrix in iterative algorithm, lastly it gives a anti-alias process method applied for 3-D cone beam CT system using circular trace.