Exact Interior Reconstruction with Cone‐Beam CT

Abstract

Using the backprojection filtration (BPF) and filtered backprojection (FBP) approaches, respectively, we prove that with cone-beam CT the interior problem can be exactly solved by analytic continuation. The prior knowledge we assume is that a volume of interest (VOI) in an object to be reconstructed is known in a subregion of the VOI. Our derivations are based on the so-called generalized PI-segment (chord). The available projection onto convex set (POCS) algorithm and singular value decomposition (SVD) method can be applied to perform the exact interior reconstruction. These results have many implications in the CT field and can be extended to other tomographic modalities, such as SPECT/PET, MRI.

Towards Clinical Application of a Laplace Operator-Based Region of Interest Reconstruction Algorithm in C-Arm CT

“…Corresponding algorithms were suggested by Noo et al [6] and Pan et al [7] and are based on the concept of differentiated backprojection (DBP): After backprojecting the derivative of the projection data, these methods require a 1-D finite Hilbert inversion along specific lines in the backprojection result. Later, Defrise et al [8], Ye et al [9], [10], and Kudo et al [11] suggested an extension to the DBP method that solves the Hilbert inversion by iterative projection onto convex sets (POCS). This extension allows a wider class of truncation configurations to be solved accurately, but at the cost of higher computational efforts.…”

Noise Analysis in Computed Tomography (CT) Image Reconstruction using QR-Decomposition Algorithm

“…Specifically, for local CT image reconstruction [5][6], single photon emission tomography [7]- [10], and fluorescent x-ray computed tomography [11]. Moreover, these problems tend to be ill-conditioned and, if the data includes noise, the solution includes large oscillation due to the illconditioned problem and regularization may be considered.…”

Efficient 2D filtering for cone-beam VOI reconstruction

“…Approaches in Noo et al [1], Pan et al [2], Defrise et al [3], Ye et. al [4], [5], Kudo et al [6], Chityala et al [7], Koloditz et al [8], [9] can provide exact or high accurate reconstruction for imaging. But they require either prior information of the object, or additional radiation dose, scans of patient shape and outline.…”