Regularization Based Image Reconstruction Algorithms For Limited-angle CT

X-ray computed tomography(CT)is an imaging method that non-invasively acquires images of the interior of an object for which the features cannot be observed directly,and has been widely applied in clinical fields,non-destructive testing,archaeology and biology,etc..The fundamental problem of X-ray CT is to reconstruct a slice image from its projections,which is referred to as an inverse problem in mathematics.The filtered back-projection(FBP)algorithm,which has been commonly utilized in commercial CT,can reconstruct images accurately when the projections obtained are complete.For fan-beam CT,the scanned angular range should be larger than 0180 plus a fan-angle to reconstruct a high quality image.However,in some practical applications of CT imaging,constrained by scanning environment,scanned object or X-ray dose,etc.,it is likely that the object is only scanned in a limited angular range(less than 0180 plus a fan-angle),then,the projections are incomplete.For example: imaging of a pipeline in service which is attached to wall or is installed on the ground,imaging of dental CT,imaging of C-arm CT,imaging of the chest and breasts,etc..To reduce the scanning time or radiation dose,the object is also scanned in a limited angular range.In these situations,limited-angle CT image reconstruction using the FBP algorithm,will lead to slope artifacts(i.e.limited-angle artifacts).Therefore,how to steady reconstruct an image with high quality when only limited-angle projections are utilized,which has not only important academic significance but also important commercial value,is a hot research topic.The limited-angle CT image reconstruction is a seriously ill-posed problem due to the projections are incomplete.To stabilize the reconstruction process of limited-angle CT image reconstruction problem,some regularization strategies based on optimization theory may be considered.In recent years,wavelet tight frames have been used in image reconstruction.The basic idea for wavelet tight frames based approaches is that images can be sparsely approximated by properly designed wavelet tight frames.The wavelet tight frames with multiresolution can provide abundant multilevel redundancy information in sparsifying the image.The two dimension masks of wavelet tight frames correspond to the discretized high-order partial derivatives,then,the wavelet tight frames transform can be considered as a generalization of total variation.Therefore,we focus on the regularization based limited-angle CT reconstruction algorithms under the wavelet tight frames.The main works of this thesis are in the following:1.The model of 0? regularization for wavelet tight frames based for image restoration is modified by adding a 2? regularization term of image(the energy term of image),and we propose a novel reconstruction model that based on 0? and 2? regularization for limited-angle CT reconstruction problem.The existence of a solution for the original problem will be obtained by considering a family of problems.To suppress the slope artifacts,we develop a limited-angle CT reconstruction algorithm based on 0? and 2? regularization,the convergence analysis of our algorithm under certain conditions is given.We prove that the sequence,which is generated by our algorithm,exists a subsequence that is convergent to a local minimizer.For a typical case of our algorithm,we analyze the error bounds between the reconstructed image and the reference image,and the stability of solution is shown in theory.Some simulated experiments and practical data experiments are used to evaluate our algorithm.The experimental results show that our algorithm can reconstruct an image with high quality in a certain degree.In terms of reconstructed image,our algorithm outperforms ASD-POCS(Adaptive Steepest Descent-Projection onto Convex Sets)algorithm in suppressing the noise and slope artifacts,and can improve the quality of reconstructed image.2.The high-frequency of a prior image is considered as a prior information and applied to limited-angle CT reconstruction problem,and we propose a novel reconstruction model that based on 0? regularization and prior image for limited-angle CT reconstruction problem.The reconstruction model is solved by alternating iteration fashion and a limited-angle CT reconstruction algorithm that based on 0? regularization and prior image is developed,and the convergence analysis of our algorithm under certain conditions is given.We prove that the bounded sequence,which is generated by our algorithm,exists a subsequence that is convergent to a critical or a stationary point.Some simulated experiments and practical data experiments are used to evaluate our algorithm.The experimental results show that our algorithm can reconstruct an image as almost good as the PICCS(Prior Image Constrained Compressed Sensing)algorithm in terms of reconstructed image,what's more,our algorithm can reconstruct a higher quality image than PICCS algorithm according to the quantified results.3.To reduce the difficulty of parameter selection in the limited-angle CT reconstruction process,inspired by the L-curve method,we propose a limited-angle CT reconstruction algorithm based on adapted iteration hard thresholding under the wavelet tight frames.Some simulated experiments and practical data experiments are used to evaluate our algorithm,the experimental results show that the reconstructed results using our algorithm with adapted iteration hard thresholding are almost as good as those using the non-adapted parameter method in terms of visual inspection.However,our algorithm has an advantage over the non-adapted parameter method in adaptively choosing the parameter.