Handling data redundancy in helical cone beam reconstruction with a cone-angle-based window function and its asymptotic approximation

• Published in: Medical physics (Lancaster) Vol. 34; no. 6; pp. 1989 - 1998
• Main Authors: Tang, Xiangyang, Hsieh, Jiang
• Format: Journal Article
• Language: English
• Published: United States American Association of Physicists in Medicine 01.06.2007
• Subjects: 3D reconstruction; ALGORITHMS; Algorithms for functional approximation; approximation theory; APPROXIMATIONS; Brain - diagnostic imaging; Computed radiography; Computed tomography; Computer simulation; computerised tomography; COMPUTERIZED SIMULATION; COMPUTERIZED TOMOGRAPHY; Cone beam computed tomography; cone-beam volume CT; CT reconstruction; Data acquisition; data handling; DATA PROCESSING; EVALUATION; helical CT; Humans; Image analysis; IMAGE PROCESSING; image reconstruction; Image sensors; Imaging, Three-Dimensional - methods; Information Storage and Retrieval - methods; medical image processing; Medical image quality; Medical image reconstruction; Medical imaging; Particle beam detectors; PHANTOMS; Phantoms, Imaging; Radiographic Image Enhancement - methods; Radiographic Image Interpretation, Computer-Assisted - methods; RADIOLOGY AND NUCLEAR MEDICINE; reconstruction algorithms; Reproducibility of Results; Sensitivity and Specificity; TAMOXIFEN; Tomography, Spiral Computed - instrumentation; Tomography, Spiral Computed - methods; window function; reconstruction algorithms; window function; 3D reconstruction; cone-beam volume CT; helical CT; CT reconstruction
• ISSN: 0094-2405; 2473-4209
• DOI: 10.1118/1.2736789

A cone-angle-based window function is defined in this manuscript for image reconstruction using helical cone beam filtered backprojection (CB-FBP) algorithms. Rather than defining the window boundaries in a two-dimensional detector acquiring projection data for computed tomographic imaging, the cone-angle-based window function deals with data redundancy by selecting rays with the smallest cone angle relative to the reconstruction plane. To be computationally efficient, an asymptotic approximation of the cone-angle-based window function is also given and analyzed in this paper. The benefit of using such an asymptotic approximation also includes the avoidance of functional discontinuities that cause artifacts in reconstructed tomographic images. The cone-angle-based window function and its asymptotic approximation provide a way, equivalent to the Tam-Danielsson-window, for helical CB-FBP reconstruction algorithms to deal with data redundancy, regardless of where the helical pitch is constant or dynamically variable during a scan. By taking the cone-parallel geometry as an example, a computer simulation study is conducted to evaluate the proposed window function and its asymptotic approximation for helical CB-FBP reconstruction algorithm to handle data redundancy. The computer simulated Forbild head and thorax phantoms are utilized in the performance evaluation, showing that the proposed cone-angle-based window function and its asymptotic approximation can deal with data redundancy very well in cone beam image reconstruction from projection data acquired along helical source trajectories. Moreover, a numerical study carried out in this paper reveals that the proposed cone-angle-based window function is actually equivalent to the Tam-Danielsson-window, and rigorous mathematical proofs are being investigated.