Interior tomography from low-count local projections and associated Hilbert transform data

摘要

This paper presents a statistical interior tomography approach combining an optimization of the truncated Hilbert transform (THT) data. With the introduction of the compressed sensing (CS) based interior tomography, a statistical iteration reconstruction (SIR) regularized by the total variation (TV) has been proposed to reconstruct an interior region of interest (ROI) with less noise from low-count local projections. After each update of the CS based SIR, a THT constraint can be incorporated by an optimizing strategy. Since the noisy differentiated back-projection (DBP) and its corresponding noise variance on each chord can be calculated from the Poisson projection data, an object function is constructed to find an optimal THT of the ROI from the noisy DBP and the present reconstructed image. Then the inversion of this optimized THT on each chord is performed and the resulted ROI will be the initial image of next update for the CS based SIR. In addition, a parameter in the optimization of THT step can be used to determine the stopping rule of the iteration heuristically. Numerical simulations are performed to evaluate the proposed approach. Our results indicate that this approach can reconstruct an ROI with high accuracy by reducing the noise effectively.