The Study On Computed Tomography Image Reconstruction Algorithm Based On Compressed Sensing Theory

Computed tomography technique has made it possible to detect the interior structure of object without any damage. As a lot of state-of-art reconstruction algorithms have been proposed and after five generations of updating CT devices, the practicability of CT theories has reached to a high level. The CT technology has been widely applied to the field of medical imaging and industrial detection. But the present technologies still require large amounts of samplings to obtain good results, which easily lead to high dose radiation and artifacts, so explore methods to reconstruct clear object under sparse angular, short time and low dose is very important and meaningful, challenging at the same time.The proposal of Compressed Sensing broke the authority of Nyquist Sampling Theory, express the content that one can obtain ideal results by the method Projection on Convex on the premise of sampling in a field which is incoherence with the sparse representation field. Once this theory is proposed, the field of signal Processing, Compressed transmission and image reconstruction evoked a worldwide response, and a lot of researchers has made it successful to reconstruct original signal with 20 times lower sampling rates than traditional, but the research progress on this topic still remains in initial phase. How to find sparser representation basis, how to find the non-stochastic sensing matrix and design reconstruction algorithm which can lead to better results come to the point.On the basis of Compressed Sensing theory, we explored both the sampling design and the reconstruction algorithm。In this paper, we explored a discrete exact reconstruction algorithm which is a special form of Discrete Radon transform, The Mojette transform has successfully avoided irregular and redundant pixel sampling by variant sampling rate. Based on such transform, we proposed a method to find the best projection vector and reconstruction path, corresponding simulation experiment has proved the effectiveness of the method. Besides, we also discussed a practical method to transfer Radon projections to Mojette projections, and how to set up our experimental stage and how to sample and preprocess the projection data before reconstruction. The algorithm has been tested in both simulator and practical experimental environment, and they proved the validity of the practical transfer scheme.But the Mojette transform itself has some inevitable drawbacks, such as sensitive to noise, needs large amounts of detectors, so there still exists a lot of areas be worthy of researching in order to improve the reconstructed results.