Study Of Image Reconstruction Algorithms

In medicine and earthquake, image reconstruction has been widely used,the mathematicalbackground can be attributed to mathematical transform, such as Radon transform, Hilberttransform, Fourier transform and their inversion transform.so people have got some image re-construction algorithms, in so many algorithms, FBP(Filtered back projection)have more widelyapplication. this paper, in the set of fan-beam and cone-beam FBP, we apply X-ray and singlephotonγ-ray to scan image, in order to speed up the computation, improve the image qualityand reduce the image artifact, we lead in n-pi-line, and extend the Novikov's inversion formulaby applying generalized Radon transform. So we get exact reconstruction algorithm, in theorywe optimize FBP reconstruction algorithm. This thesis is composed of four chapters as follows:In chapter 1, we systematic introduce this article research background and main researchwork.In chapter 2, we study n-pi-line application question in CT reconstruction algorithm.In chapter 3, we study a general scanning trajectory question in ROI CT reconstructionalgorithm.In chapter 4, on the base of Novikov's inversion formula ,we study attenuated Radon trans-form and exponential Radon transform in practical problem's application of CT reconstruction.