Information Theoretic Discrepancy based Iterative Reconstruction (IDIR) Algorithm for Limited Angle Tomography

The X-ray tomosynthesis that measures several low dose projections over a limited angular range has been investigated as an alternative method of X-ray mammography for breast cancer screening. An extension of the scan coverage increases the vertical resolution by mitigating the interplane blurring. The implementation of a wide angle tomosynthesis equipment, however, may not be straightforward, mainly due to the image deterioration from the statistical noise in exterior projections. In this paper, we adopt the voltage modulation scheme to enlarge the coverage of the tomosynthesis scan. The higher tube voltages are used for outer angles, which offers the sufficient penetrating power for outlying frames in which the pathway of X-ray photons is elongated. To reconstruct 3D information from voltage modulated projections, we propose a novel algorithm, named information theoretic discrepancy based iterative reconstruction (IDIR) algorithm, which allows to account for the polychromatic acquisition model. The generalized information theoretic discrepancy (GID) is newly employed as the objective function. Using particular features of the GID, the cost function is derived in terms of imaginary variables with energy dependency, which leads to a tractable optimization problem without using the monochromatic approximation. In preliminary experiments using simulated and experimental equipment, the proposed imaging architecture and IDIR algorithm showed superior performances over conventional approaches.