The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented.

The development of accurate and efficient algorithms for image reconstruction from helical cone-beam projections remains a subject of active research. In the last few years, a number of quasi-exact and exact algorithms have been developed. Among them, the Katsevich algorithms are of filtered backprojection type and thus possess computational advantages over other existing exact algorithms. In this work, we propose an alternative approach to reconstructing exactly an image from helical cone-beam projections. Based on this approach, we develop an algorithm that requires less data than do the existing quasi-exact and exact algorithms, including the Katsevich algorithms. Our proposed algorithm is also of filtered backprojection type with one-dimensional filtering performed along a PI-line in image space. Therefore, it is (at least) computationally as efficient as the Katsevich algorithms. We have performed a preliminary numerical study to demonstrate and validate the proposed algorithm using computer-simulation data. The implication of the proposed approach and algorithm appears to be significant in that they can naturally address the long object problem as well as the super-short scan problem and, most importantly, in that they provide the opportunity to reconstruct images within any selected region of interest from minimum data, allowing the use of detector with a reduced size, the selection of a minimum number of rotation angles and thus the reduction of radiation dose delivered to the imaged subject.

Flat-panel-detector X-ray cone-beam computed tomography (CBCT) is used in a rapidly increasing host of imaging applications, including image-guided surgery and radiotherapy. The purpose of the work is to investigate and evaluate image reconstruction from data collected at projection views significantly fewer than what is used in current CBCT imaging. Specifically, we carried out imaging experiments by use of a bench-top CBCT system that was designed to mimic imaging conditions in image-guided surgery and radiotherapy; we applied an image reconstruction algorithm based on constrained total-variation (TV)-minimization to data acquired with sparsely sampled view-angles; and we conducted extensive evaluation of algorithm performance. Results of the evaluation studies demonstrate that, depending upon scanning conditions and imaging tasks, algorithms based on constrained TV-minimization can reconstruct images of potential utility from a small fraction of the data used in typical, current CBCT applications. A practical implication of the study is that the optimization of algorithm design and implementation can be exploited for considerably reducing imaging effort and radiation dose in CBCT.

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Recently, we have derived a general formula for image reconstruction from helical cone-beam projections. Based upon this formula, we have also developed an exact algorithm for image reconstruction on PI-line segments from minimum data within the Tam-Danielsson window. This previous algorithm can be referred to as a backprojection-filtration algorithm because it reconstructs an image by first backprojection of the data derivatives and then filtration of the backprojections on PI-line segments. In this work, we propose an alternative algorithm, which reconstructs an image by first filtering the modified data along the cone-beam projections of the PI-lines onto the detector plane and then backprojecting the filtered data onto PI-line segments. Therefore, we refer to this alternative algorithm as the filtered-backprojection algorithm. A preliminary computer-simulation study was performed for validating and demonstrating this new algorithm. Furthermore, we derive a practically useful expression to accurately compute the derivative of the data function for image reconstruction. The proposed filtered-backprojection algorithm can reconstruct the image within any selected ROI inside the helix and thus can handle naturally the long object problem and the super-short scan problem. It can also be generalized to reconstruct images from data acquired with other scanning configurations such as the helical scan with a varying pitch.