Spatially-Adaptive Reconstruction in Computed Tomography Based on Statistical Learning

Abstract: We propose a direct reconstruction algorithm for Computed Tomography, based on a local fusion of a few preliminary image estimates by means of a non-linear fusion rule. One such rule is based on a signal denoising technique which is spatially adaptive to the unknown local smoothness. Another, more powerful fusion rule, is based on a neural network trained off-line with a high-quality training set of images. Two types of linear reconstruction algorithms for the preliminary images are employed for two different reconstruction tasks. For an entire image reconstruction from full projection data, the proposed scheme uses a sequence of Filtered Back-Projection algorithms with a gradually growing cut-off frequency. To recover a Region Of Interest only from local projections, statistically-trained linear reconstruction algorithms are employed. Numerical experiments display the improvement in reconstruction quality when compared to linear reconstruction algorithms.