Reconstruction of Images with Finite Rate of Innovation from Noisy Tomographic Projections

In this paper, we propose a robust 2D tomographic reconstruction algorithm for classes of piecewise constant images whose edges are defined by curves with finite rate innovation (FRI). The curve is known to satisfy an annihilation relation associated with the derivative of the image. Given limited numbers of noisy projections and inaccurately known angles, unlike conventional methods that are directly reconstructing images from projections, we first recover the curve exploiting the frequency domain annihilation relation. Once the curve is retrieved, we leverage the spatial domain interpretation of the annihilation relation, and formulate the image reconstruction as a regularized optimization problem. To enhance the reconstruction quality, we further refine the angles given the reconstructed image and iterate the process. Experiments show that by doing so, we can robustly reconstruct the 2D image even from limited numbers of severely corrupted projections and highly inaccurate projection angles.