Motolyha O. Patient radiation dose minimization during X-Ray images acquiring

The task of slices reconstruction in X-ray computed tomography is reduced to the solution of integral equations, or system of algebraic equations in discrete case. It is ill-posed problem because of inconsistencies of number of equations and number of variables and because of errors in experimentally measured data. Therefore, the task of finding the best method of reconstruction is actual. All available methods give approximate results. Two methods of image reconstruction were compared in this research: inverse projection and variation. The comparison is made using the numerical experiment, the goal of experiment was to obtain a relationship between image accuracy and experimental error. As was shown, the image obtained by inverse projection is unstable: there is no convergence of the approximate image to accurately when approaching experimental error to zero. Besides, image obtained by variational method is accurate when there isn’t experimental error. We have proposed a method of the tomographic reconstruction, which is a modification of the method of back-projection and taking into account the theory of ill-posed problems in this article. In original back-projection method filter parameters value is chosen almost arbitrarily. In the proposed method, this choice is justified: the filter parameter is identified as the regularization parameter, which allows us to use the theory of ill-posed problems for its determination, and thus ensure the stability of the reconstructed image. The proposed reconstruction algorithm was tested by a numerical experiment on a virtual mathematical phantom, which simulates the structure of the human brain. The minimum values of the number of projections were calculated for different values of X-ray data error. It was shown that when these minimum values are exceeded, the image quality does not significantly improve. An experimental setup was made to test the proposed method. An image of a test real phantom simulating a thorax and an accreditation mammographic phantom were obtained with it. It was shown that the characteristics of these images are consistent with the data of the numerical experiment according to the developed method.