Research On Image Reconstruction Algorithm Based On Hessian Schatten-Norm Regularization

Computed tomography(CT),as an important detection technique,can reconstruct the two-dimensional or three-dimensional images of the internal and external structure of the object by using projection data from multiple projection angles.It is widely applied in building crack analysis,industrial flaw detection and seismic exploration with the characteristics of non-destructive and high precision.In order to get accurate reconstructed images,the traditional analytic algorithm usually requires complete projection data.However,in some practical applications,due to some factors such as the external environment and other factors,the obtained projection data are sometimes incomplete,which brings great challenges to the reconstruction of high quality images.The problem of incomplete projection data reconstruction is of great academic value and practical application value.The algebraic iterative reconstruction algorithm is a very important image reconstruction algorithm,which has the characteristics of simple and easy to implement and good reconstruction effect.It is suitable for the reconstruction of incomplete projection data,especially when the projection data is less.But the iterative algorithm has a large amount of computation and slow convergence.In order to improve the quality of image reconstruction,In this paper,we study the Hessian Schatten-norm and image reconstruction algorithm of Hessian Schatten-norm under incomplete proection data.Because of the presence of noise in the projection data the essence of Hessian Schatten-norm added is noise removal,Hessian Schatten norm has two order derivative invariance and piecewise smooth solution.Added it to the target function (?).The process of solving the new model minx(?),p is the process of image reconstruction based on Hessian Schatten-norm regularization.According to the simulation data and real data,the results show that the Hessian Schatten-norm can effectively improve the quality of reconstructed images when the projection data are incomplete.