Study On Optimized Reconstruction Algorithm Of X-ray Computed Tomography With Sparse Projection

X-CT(X-ray Computed Tomography) is an advanced nondestructive testing equipment. It has been widely used in many fields. With the rapid development of CT technology, research on how to reconstruct high quality CT image with the condition of incomplete projection data becomes a hot research point. The traditional CT image reconstruction algorithms such as Filter Backprojection(FBP), Algebraic Reconstruction Technique(ART), Simultaneous Algebraic Reconstruction Techniques(SART), etc. cannot meet requirements without changing the way of obtaining data. Compressed Sensing(CS) was came up with and made it possible to reconstruct high quality CT image with sparse projection data. As a starting point, this thesis focus on the shortages of the reconstruction algorithm based on Total Variation(TV) minimum under the framework of image compressed sensing, we study the image sparse representation method and solving method of optimization equation, and propose two CT image reconstruction algorithms which are a CT reconstruction algorithm based on Diagonal Total Variation(DTV) and a CT reconstruction algorithm based on Non-Aliasing Contourlet Transform(NACT). The experimental results indicate that the proposed algorithms are available to reconstruct CT image with sparse data.Thesis study content mainly contains:① Proposed a CT reconstruction algorithm based on DTV. The reconstruction algorithm based on TV which only uses x-coordinate and y-coordinate gradient transform as its sparse representation approach hasn’t made the best of the edge and directivity of CT image. Based on this, we brought in DTV which uses the diagonal direction gradient to constraint reconstructed image and was operated when the reconstructed image has no change after a set number of TV gradient descent. We try to obtain sparser representation of CT image under the help of multi-direction information. Through numerical simulation we found that the proposed algorithm can reconstruct high-quality CT image, which is more suitable when the sparse sampling.② Proposed a CT reconstruction algorithm based on NACT. To improve the sparse representation of CT image, we bring in NACT in case of it can be available to express high-dimensional singularity of images, propose a CT reconstruction algorithm which combines NACT and TV, then use the Split-Bregman method to solve the optimization problem. Finally, the simulation results show that the proposed algorithm has lower Root Mean Square Error(RMSE) and higher Universal Quality Index(UQI) than ART and TV under the condition of small projection data and iteration numbers. The proposed algorithm maintains the edge details better, and is more effectively in suppressing noise and artefacts.This work was supported in part by the National Natural Science Foundation of China(No. 61201346), the Fundamental Research Funds for the Central Universities(No. CDJZR14125501). We study on optimized reconstruction algorithm of X-ray CT with sparse projection and obtain a series of high-level research achievements which further improve the CT image reconstruction algorithm, reducing the X-ray radiation under the CT scanning, promoting the development of medical CT, which has very important significance no matter in theory or in practical application.