Investigation On Reconstruction Algorithms For Limited-angle CT Based On L₀ Regularization And Guided Filtering

Computed tomography（CT）,as a method of image diagnosis,can reconstruct im-ages,which represent the interior structure features of an object,by utilizing the X-ray projection data from multiple projection views without destroying the scanned object.In mathematics,the essence of CT reconstruction is an inverse problem.When CT sys-tem can obtain complete projection data,high-quality results can be reconstructed by tra-ditional iterative methods,such as the simultaneous algebraic reconstruction technique（SART）.In industrial applications,for fan-beam CT,the high-resolution reconstruction image is mainly reconstructed by analytic algorithm when the scanning angle is greater than or equal to 180°,such as filtering back projection（FBP）.However,in some practice applications,constrained by scanning environment,structure of scanned object,X-ray dose and other practical problems,the scanned angular ranges are insufficient（less than 1800 or scanning angle interval increased）.At this time,the reconstruction results using the traditional methods will lead to slope artifacts,and the image details are easy to be damaged.Therefore,how to reconstruct highly quality images from incomplete projec-tions,which has become a research hotspot and difficulty.In practical applications,in order to make the problem stablilized,many scholars considered using the regularization method in the optimization theory,such as the total variation（TV）algorithm based on the total variation minimization.In this method,the li norm of the image gradient is used as the regularization term.After that,some scholars proposed that using the l₀ gradient as the regularization term can greatly suppress the block artifacts.Inspired by this,the main work of this paper is as follows:To further improve the image quality and protect the edge of image,we propose a coupling method of limited-angle CT reconstruction,that combines l₀ regularization and guided image filtering（GIF）method.l₀ regularization method can effectively preserve edge information and prevent over smoothing.The GIF method can smooth the input image in the local region and preserve the details of guided image in the edge part.An intermediate result obtained by gradient minimization is regarded as a guidance image of GIF,then GIF is used to filter the result reconstructed by simultaneous algebraic recon-struction technique（SART）with nonnegative constraint.It should be stressed that the guidance image is dynamically updated as the iteration process,and the edge information can be transferred to the filtered image to ensure that the output image is similar to the input image as a whole and the edge details and structure are similar to the guided image.Then some numerical experiments experiments are used to evaluate the proposed method.For the simulation data experiment,we have carried out the experimental research under three scanning angles（[0,90°],[0120°]and[0150°]）,compared the quantified results between different algorithms,and given the horizontal profile of reconstruction results and sensi-tivity analysis of parameters.For real data experiments,we conducted experiments in the scanning range of[0,90°]and[0120°],and then the quantified results were given.Exper-imental results show that our method owns some advantages in suppressing the artifacts of limited angle CT and in preserving the edge of image.