Study On Regularization Methods In Cone-beam CT Image Reconstruction

Cone-beam computer tomography(CBCT),uses high-energy X-ray beam to irradiate the objects,the internal structure of the object can be reconstructed by a specific reconstruction algorithm based on the projection data with different angles.However,too much radiation would bring risks to patients' s health.In order to reduce the radiation to the patient,it is necessary to reduce the current of the emitted rays,but that would lead to the degradation of the quality of reconstructed image.Therefore,a reconstruction algorithm that can improve the quality of CBCT reconstruction image is critical.The most popular TV seminorm can preserve the edge of the reconstructed image well,but the TV regularizer leads to the piecewise-constant regions,i.e.the staircase effect.In this work,we proposed and designed three regularizers to avoid the staircase effect,and improve the quality of the reconstructed imageFirstly,we adopted the Hessian Schatten regularizer,which was the Schatten norm of the Hessian matrix for each pixel.We extended the regularizer from two-dimensional case to three-dimensional CBCT image reconstruction.We used the optimization method combined with the MM algorithm and the dual algorithm to optimize its corresponding objective function.Secondly,we used the Structure Tensor Total Variation regularizer to reconstruct the CBCT image.The regularizer utilized the eigenvalues of the structure tensor to detect the geometry characteristics of the image.So the STV calculated the function of the eigenvalues of the structure tensor for each pixel as regularizer.Unlike the Hessian Schatten regularizer,we proposed the simpler gradient descent method to optimize the objective function by deriving the derivative of STV.Finally,we designed a new tensor that can detect the geometric structure of the image,which we called mixed tensor.The mixed tensor utilized the advantages of the different order derivatives of the image to improve the quality of reconstructed image.The square root of the sum of the eigenvalues of the mixed tensor was designed as regularizer for CBCT image reconstruction.At the same time,we proposed an optimization method that combined with the MM algorithm and the conjugate gradient method to optimize the corresponding objective function,and used the MFISTA algorithm to accelerate the MM algorithm.In our work,experiments are carried out on four CBCT models respectively.The CBCT reconstruction image based on three new penalties adopted by us were compared with the reconstruction image based on the most popular TV penalty.