Research On Algorithm For Identification Problem In SPECT Based On Adjoint State Method

Single photon emission computed tomography(SPECT),which is widely used in clin-ical application.The identification problem of SPECT is using only SPECT sampling data to reconstruct both the radionactive distribution f and attenuation coefficient ?.It can overcome the disadvantages of using XCT technology to obtain the attenuation coefficient ?.In this paper,we study numerical algorithm of adjoint state method for identification problem of SPECT.Firstly,we present some basic knowledges of mathematics that will be used later,we also give a brief introduction to the basic principle of SPECT imaging,common SPECT image reconstruction methods and the identification problem of SPECT.Secondly,we need to solve different partial differential equations in different direc-tions to implement adjoint state method and the computational complexity is high.In order to avoid this problem,we turn the partial differential equations to ordinary differ-ential equations by rotating the coordinate axes,thus,the unified numerical algorithm is obtained.It requires less computation overhead,and it is simpler to implement.Due to the descenting direction and the reconstructed ? and f obtained by the adjoint state method are inaccurate,we need to be dealt with further.Because TV regularization can eliminate or reduce noise and artifacts,while maintaining the edge characteristics of the image.Therefore,we use the total variation(TV)regularization method to regularize the descending directions and the further reconstruction of ? and f.In order to improve the quality of the reconstructed image,in the specific reconstruction,we distribute the projection data in different directions.Lastly,in this paper,numerical experiments of different numerical templates have been done.The experimental results show that the algorithm proposed in this paper can effectively solve the adjoint state method and get high quality reconstructed images.