A new reconstruction algorithm in tomography with geometric feature-preserving regularization

We present a new optimization-based reconstruction model with geometric feature-preserving regularization. The previous construction approach of optimization-based requires generally solving a tremendously large discrete linear system. In addition, the analytic algorithms, such as, back-projection related methods, Fourier transform based reconstruction algorithms, are sensitive to noise. These disadvantages motivate us naturally to present a new optimization-based regularization algorithm, as distinct from traditionally constructing a discrete linear system, that is based upon a continuous energy functional model like analytic one. Some theoretical derivations and numerical computing of our model are discussed. Experimental results illustrate the desirable performance of the algorithm under various noiseless data situations. And the geometric feature-preserving regularizer is used in numerical simulations to demonstrate the robustness and effectiveness of the algorithm under various contaminated data scenarios.