Stationary computed tomography with source and detector in linear symmetric geometry: Direct filtered backprojection reconstruction

Purpose Inverse-geometry computed tomography (IGCT) could have great potential in medical applications and security inspections, and has been actively investigated in recent years. In this work, we explore a special architecture of IGCT in a stationary configuration: symmetric-geometry computed tomography (SGCT), where the x-ray source and detector are linearly distributed in a symmetric design. A direct filtered backprojection (FBP)-type algorithm is developed to analytically reconstruct images from the SGCT projections. Methods In our proposed SGCT system, a big number of x-ray source points equally distributed along a straight-line trajectory will sequentially fire in an ultra-fast manner in one side, and an equispaced detector whose total length is comparable to that of the source will continuously collect data in the opposite side, as the object to be scanned moves into the imaging plane. We firstly present the overall design of SGCT. An FBP-type reconstruction algorithm is then derived for this unique imaging configuration. With finite length of x-ray source and detector arrays, projection data from one segment of SGCT scan are insufficient for an exact reconstruction. As a result, in practical applications, dual-SGCT scan whose detector segments are placed perpendicular to each other, is of particular interest and is proposed. Two segments of SGCT together can make sure that the passing rays cover at least 180 degrees for each and every point if carefully designed. In general, however, there exists a data redundancy problem for a dual-SGCT. So a weighting strategy is developed to maximize the use of projection data collected while avoid image artifacts. In addition, we further extend the fan-beam SGCT to cone beam and obtain a Feldkamp-Davis-Kress (FDK)-type reconstruction algorithm. Finally, we conduct a set of experimental studies both in simulation and on a prototype SGCT system and validate our proposed methods. Results A simulation study using the Shepp-Logan head phantom confirms that CT images can be exactly reconstructed from dual-SGCT scan and that our proposed weighting strategy is able to handle the data redundancy properly. Compared with the rebinning-to-parallel-beam method using the forward projection of an abdominal CT dataset, our proposed method is seen to be less sensitive to data truncation. Our algorithm can achieve 10.64 lp/cm of spatial resolution at 50% modulation transfer functions point, higher than that of the rebinning method which can only reach at 9.42 lp/cm even with extremely fine interpolation. Real experiments of a cylindrical object on a prototype SGCT further prove the effectiveness and practicability of the direct FBP method proposed, with similar level of noise performance to rebinning algorithm. Conclusions A new concept of SGCT with linearly distributed source and detector is investigated in this work, in which spinning of sources and detectors is no longer needed during data acquisition, simplifying its system design, development, and manufacturing. A direct FBP-type algorithm is developed for analytical reconstruction from SGCT projection data. Numerical and real experiments validate our method and show that exact CT image can be reconstructed from dual-SGCT scan, where data redundancy problem can be solved by our proposed weighting function.