Research On CT Incomplete Data Reconstruction Algorithms Based On Mojette Transform

Computerized tomography(CT)obtains cross-section information of an object by means of X-ray projection measurements at different angles.With the advantage of the non-contact and non-destructive property,the internal structure of objects can be reconstructed with high precision.It has been widely used in medical imaging and industrial non-destructive testing.However,constrained by scanning environment or the scanning object,in some cases only sparse-view projection data or limited-angle projection data can be collected for CT image reconstruction,called incomplete data reconstruction problem.Although some important progress has been made in traditional CT reconstruction technology based on Radon transform,the imprecise reconstruction problem of the back-projection reconstruction based on Radon transform is still one of the difficult and key problems for image reconstruction in the case of incomplete projection data.On the basis of above considerations,this dissertation studies the CT incomplete projection data reconstruction algorithm based on Mojette transform.From the perspective of discrete geometry,the discrete image domain,discrete projection domain and back-projection process can be directly correlated with the digital CT system by means of Mojette transform,which can provide the precise solution in the sense of discretization,instead of an approximate solution due to finite Radon sampling.Although the CT reconstruction method based on Mojette transform has many favorable properties,some challenging problems still remain to be addressed,such as noise sensitivity in Mojette reconstruction process,optimal projection selection in sparse angle condition,model design problem of limited-angle Mojette reconstruction and so on.Aiming at addressing such key problems in CT incomplete projection data reconstruction based on Mojette transform,this dissertation conducts in-depth research and the main contributions are given as follows:(1)Aiming at addressing the problem of noise sensitivity in Mojette reconstruction process,the sparse-view Mojette reconstruction method with minimum noise accumulation is proposed.The proposed algorithm traverses all projections in each iteration and counts the number of pixels that each projection can reconstruct,aming at prioritizing projections according to the number of pixels.In each iteration,the projection which can obtain the maximum number of pixels is selected to reconstruct the image,thus minimizing the number of iterations for image reconstruction.The fewer number of iterations for image reconstruction,the fewer number of noise propagation.Thus,the accumulation noise in the middle area of the reconstructed image is smaller.On the premise of sparse projections,the proposed sparse-view Mojette reconstruction can effectively suppress the noise accumulation and obtain high-quality images.The experimental results show that the proposed method can resist noise within a certain level.(2)Aiming at addressing the problem of the low effciency reconstruction,which is caused by traversing all projections using sparse-view Mojette reconstruction with minimum accumulation noise in each iteration,it is necessary to find the optimal projections corresponding to the least iterative path.Therefore,this dissertation proposes two efficient projection selection criterions,which are based on the relationship among the projection direction,the number of samples and the image size.The proposed selection criterions can overcome the shortcomings of the typical traversal search method.The first criterion is to select the projection directions with the maximum sum of their horizontal and vertical components.The above projections are easiest to solve the reconstructed pixels,so that the image reconstruction can be completed within the minimum number of iterations,leading to effectively reducing the accumulation noise.The second criterion is to find the minimal number of projections to complete image reconstruction within the minimum number of iterations.Furthermore,we find that there are many projection sets satisfying the above selection criterions.Since the reconstructed images from these projection sets have the same noise level but different distributions,the noise-offsetting reconstruction algorithm can be used to recover the final CT image from these projection sets.Finally,the degraded images caused by the accumulation noise in the CT image can be improved.(3)For limited angle CT reconstruction problem,the projection data are collected in a limited-angle range with relatively scarce information,thus its algorithm implementation is more difficult than sparse-view CT reconstruction.Therefore,according to the spatial and frequency domain properties of Mojette projection transform,the limited-angle CT reconstruction algorithm with minimum redundancy coverage in Mojette frequency domain is proposed.The minimum redundancy coverage in frequency domain is equivalent to the minimum spatial projection sampling,that is to say,the number of projections required to reconstruct an image is the least and the efficiency is the highest.Furthermore,the equivalent relationship of Mojette projection data in its frequency domain is found.The projection angles are compressed in a little angle range to achieve the limited-angle CT image reconstruction.The experimental results show that the proposed algorithm can obtain high precision image reconstruction using the projections in a relatively small limited-angle range.