Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction

Iterative methods for tomographic image reconstruction have the computational cost of each iteration dominated by the computation of the (back)projection operator, which take roughly O(N³) floating point operations (flops) for N × N pixels images. Furthermore, classical iterative algorithms may take too many iterations in order to achieve acceptable images, thereby making the use of these techniques unpractical for high-resolution images. Techniques have been developed in the literature in order to reduce the computational cost of the (back)projection operator to O(N²logN) flops. Also, incremental algorithms have been devised that reduce by an order of magnitude the number of iterations required to achieve acceptable images. The present paper introduces an incremental algorithm with a cost of O(N²logN) flops per iteration and applies it to the reconstruction of very large tomographic images obtained from synchrotron light illuminated data.