Fast Reconstruction Algorithm For Limited Angle Projection Based On OPED

Computed Tomography (CT) is a nondestructive and exact imaging technology which obtains image from X-ray or electron beam projection data by computer processing. With decades of development, CT has became one of the most advanced medical imaging technologies, and be widely used in modern medical treatment and industrial non-destructive testing area. However, CT provides convenient diagnostic methods as well as radiation, that can not be ignored. with wide application of CT, this problem has become more prominent. Reducing CT radiation dose is an important way to reduce the radiation. the main method is to change the original hardware scan architecture, only scanning within limited angle and then reconstructing image by the projection data. The incomplete data problem discussed in the article is reconstructed image from the limited angle projection data to reduce the radiation dose.The most widely used CT reconstruction algorithm is Filtered Back Projection (FBP) algorithm. But FBP requires rigorous condition of projection data. Artifact appears in condition of the lack of projection views, the damage of projection data or too much noise. Moreover, to reduce dose is an urgent task, because of high dose rising carcinogenic risk. Unfortunately, inherent drawbacks of FBP block the further dose decrease. So researchers have been exploring more ideal reconstruction algorithms for incomplete project data.For the incomplete data problem, fast reconstruction method of limited angle Radon projections is proposed for CT reconstruction based on Orthogonal Polynomial Expansions on the Disk algorithm (OPED). By solving linear system equations to estimate the missing data, Fast Fourier Transform (FFT) and linear interpolation method are applied for limited angle problem to reduce the computation time. The article provides the OPED mathematical model, derivations and numerical examples for one-side and both-side limited projection reconstruction are given, respectively. The results indicate that the accuracy of the algorithm changes little when the fast implementation for limited problem is used.