Inverse Problem in Non - linear Partial Volume Effect

Non-linear partial volume effect is still an unsolved problem in the theory and application of computed tomography reconstruction. In this work,an optimization-based reconstruction algorithm for effectively solving this effect was studied and developed. The discrete non-linear X-ray projection transformation model was established,when the inverse problem of X-ray projection transformation was transformed into a non-convex optimization. A non-linear iterative reconstruction algorithm was formulated to solve the non-convex optimization problem by tailoring the first-order primal-dual algorithm developed originally for solving convex optimization problems. Using computer-simulation studies,the convergence and reconstruction accuracy of the algorithm was demonstrated in this investigation. Images reconstructed were examined first through visual inspection with extremely narrow display window for revealing a contrast level of less than 1%, and then assessed with quantitative metrics such as the normalized l(2)-norm of the difference relative to its truth images. The simulation results show that the non-linear reconstruction algorithm can converge to the real image within the range of calculation accuracy,and the reconstructed image can also be displayed for the details with image contrast less than 1%. This would provide a reference for the design of computed tomography imaging application algorithm which can effectively compensate the non-linear partial volume effect artifacts.