Regularization Reconstruction Of Axially Symmetric Object Based On Tight Frame

Computer tomography(CT)can obtain the structure information of the object noninvasively,and it is widely used in medical and industrial field.The traditional CT image reconstruction method needs to collect the projection data of the measured object in all directions,which takes a relatively long time.When the structure of the object changes rapidly with time,the traditional CT imaging technology cannot obtain high-quality images.In this thesis,CT technique is used to reconstruct the internal structure of special(axisymmetric)objects.At this time,the internal structure of the axisymmetric object can be reconstructed from only one angle of projection data,and the data collection can be completed instantaneously.In order to reduce the reconstruction scale and computational complexity,the traditional three-dimensional CT reconstruction method is the hierarchical reconstruction of three-dimensional objects.However,when the projected data are obtained by cone-beam X-ray,this reconstruction method ignores the thickness information,which will lead to reconstruction artifacts and inaccurate reconstruction structure.This thesis proposes an adaptive regularization reconstruction method for threedimensional axisymmetric objects.This method is based on algebraic reconstruction model,which simultaneously reconstructs the structural information of three-dimensional objects.In order to reduce the influence of noise and detector blurring on the reconstructed image,an adaptive tight frame regularization reconstruction model is adopted and the primitive dual algorithm is used to solve the model.In this thesis,one of the cores in numerical algorithm is the efficient computational method for imaging matrix.Since the object has axisymmetric structure,the 3D reconstruction of axis-symmetric object is a 2D problem.Firstly,the region where the axisymmetric object is located is discretized into layers and radial,and each layer is composed of concentric rings.Then,the corresponding imaging matrix can be obtained by calculating the intersection length of each X-ray path and each concentric ring on each layer.This thesis proposes a fast calculation method for the intersection length of X-rays and concentric rings.Numerical experiments show that the reconstruction images are better structured by the adaptive tight frame regularization method.