Adaptive filtered-back-projection for computed tomography

We propose an extension of the Filtered Back-Projection (FBP) algorithm for reconstruction of attenuation images in Computed Tomography (CT). In our scheme, the standard filtering of projections with windowed ramp kernel is replaced by an adaptive, spatially-variant linear filter, based on a structured bank of 2D convolution kernels. In addition, the proposed scheme includes a post-processing step of image filtering by convolution with a 2D adaptive filter. Both filters are trained for specified reconstruction task via an optimization of corresponding objective function. The reconstruction task is defined through (i) a representative set of specific family of images; (ii) data acquisition conditions (partial set of projections, noise level); and (iii) a Region-Of-Interest (ROI) to be recovered. The resulting adaptive scheme absorbs various imperfections of reconstruction algorithm and specializes to given task, effectively improving the reconstruction quality.