Spatially-Adaptive Reconstruction in Computed Tomography Based on Statistical Learning

In this work we explore direct reconstruction algorithms for Computed Tomography, based on principles of Filtered Back-Projection (FBP). Special attention is given to the problem of image reconstruction in Region Of Interest (ROI) from truncated projections. In the proposed linear reconstruction scheme the ramp filter of FBP is replaced with a statistically trained spatially-variant 2-D convolution kernel, combined with a similar post-processing filter. Two types of filter training objectives are considered: (i) Optimizing the reconstruction quality from noisy and truncated projections in a pre-defined ROI for images from a known family; and (ii) Targeting desired properties of the impulse response of the overall projection-reconstruction scheme. We also propose a locally-adaptive reconstruction scheme, which merges several linear reconstructions, adjusting automatically to unknown local smoothness of the image. We devise an analytical such algorithm, as well as one based on a learning machine. Numerical simulations demonstrate efficiency of the proposed approach.