Iterative image reconstruction algorithm analysis for optical CT radiochromic gel dosimetry.

Background.Modern radiation therapy technologies aim to enhance radiation dose precision to the tumor and utilize hypofractionated treatment regimens. Verifying the dose distributions associated with these advanced radiation therapy treatments remains an active research area due to the complexity of delivery systems and the lack of suitable three-dimensional dosimetry tools. Gel dosimeters are a potential tool for measuring these complex dose distributions. A prototype tabletop solid-tank fan-beam optical CT scanner for readout of gel dosimeters was recently developed. This scanner does not have a straight raypath from source to detector, thus images cannot be reconstructed using filtered backprojection (FBP) and iterative techniques are required.Purpose.To compare a subset of the top performing algorithms in terms of image quality and quantitatively determine the optimal algorithm while accounting for refraction within the optical CT system. The following algorithms were compared: Landweber, superiorized Landweber with the fast gradient projection perturbation routine (S-LAND-FGP), the fast iterative shrinkage/thresholding algorithm with total variation penalty term (FISTA-TV), a monotone version of FISTA-TV (MFISTA-TV), superiorized conjugate gradient with the nonascending perturbation routine (S-CG-NA), superiorized conjugate gradient with the fast gradient projection perturbation routine (S-CG-FGP), superiorized conjugate gradient with with two iterations of CG performed on the current iterate and the nonascending perturbation routine (S-CG-2-NA).Methods.A ray tracing simulator was developed to track the path of light rays as they traverse the different mediums of the optical CT scanner. Two clinical phantoms and several synthetic phantoms were produced and used to evaluate the reconstruction techniques under known conditions. Reconstructed images were analyzed in terms of spatial resolution, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), signal non-uniformity (SNU), mean relative difference (MRD) and reconstruction time. We developed an image quality based method to find the optimal stopping iteration window for each algorithm. Imaging data from the prototype optical CT scanner was reconstructed and analysed to determine the optimal algorithm for this application.Results.The optimal algorithms found through the quantitative scoring metric were FISTA-TV and S-CG-2-NA. MFISTA-TV was found to behave almost identically to FISTA-TV however MFISTA-TV was unable to resolve some of the synthetic phantoms. S-CG-NA showed extreme fluctuations in the SNR and CNR values. S-CG-FGP had large fluctuations in the SNR and CNR values and the algorithm has less noise reduction than FISTA-TV and worse spatial resolution than S-CG-2-NA. S-LAND-FGP had many of the same characteristics as FISTA-TV; high noise reduction and stability from over iterating. However, S-LAND-FGP has worse SNR, CNR and SNU values as well as longer reconstruction time. S-CG-2-NA has superior spatial resolution to all algorithms while still maintaining good noise reduction and is uniquely stable from over iterating.Conclusions.Both optimal algorithms (FISTA-TV and S-CG-2-NA) are stable from over iterating and have excellent edge detection with ESF MTF 50% values of 1.266 mm-1and 0.992 mm-1. FISTA-TV had the greatest noise reduction with SNR, CNR and SNU values of 424, 434 and 0.91 × 10-4, respectively. However, low spatial resolution makes FISTA-TV only viable for large field dosimetry. S-CG-2-NA has better spatial resolution than FISTA-TV with PSF and LSF MTF 50% values of 1.581 mm-1and 0.738 mm-1, but less noise reduction. S-CG-2-NA still maintains good SNR, CNR, and SNU values of 168, 158 and 1.13 × 10-4, respectively. Thus, S-CG-2-NA is a well rounded reconstruction algorithm that would be the preferable choice for small field dosimetry.

Iterative image reconstruction with polar coordinate discretized system matrix for optical CT radiochromic gel dosimetry.

BACKGROUND: Gel dosimeters are a potential tool for measuring the complex dose distributions that characterize modern radiotherapy. A prototype tabletop solid-tank fan-beam optical CT scanner for readout of gel dosimeters was recently developed. This scanner does not have a straight raypath from source to detector, thus images cannot be reconstructed using filtered backprojection (FBP) and iterative techniques are required. Iterative image reconstruction requires a system matrix that describes the geometry of the imaging system. Stored system matrices can become immensely large, making them impractical for storage on a typical desktop computer. PURPOSE: Here we develop a method to reduce the storage size of optical CT system matrices through use of polar coordinate discretization while accounting for the refraction in optical CT systems. METHODS: A ray tracing simulator was developed to track the path of light rays as they traverse the different mediums of the optical CT scanner. Cartesian coordinate discretized system matrices (CCDSMs) and polar coordinate discretized system matrices (PCDSMs) were generated by discretizing the reconstruction area of the optical CT scanner into a Cartesian pixel grid and a polar coordinate pixel grid, respectively. The length of each ray through each pixel was calculated and used to populate the system matrices. To ensure equal weighting during iterative reconstruction, the radial rings of PCDSMs were asymmetrically spaced such that the area of each polar pixel was constant. Two clinical phantoms and several synthetic phantoms were produced and used to evaluate the reconstruction techniques under known conditions. Reconstructed images were analyzed in terms of spatial resolution, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), signal nonuniformity (SNU), and Gamma map pass percentage. RESULTS: A storage size reduction of 99.72% was found when comparing a PCDSM to a CCDSM with the same total number of pixels. Images reconstructed with a PCDSM were found to have superior SNR, CNR, SNU, and Gamma (1 mm, 1%) pass percentage compared to those reconstructed with a CCDSM. Increasing spatial resolution in the radial direction with increasing radial distance was found in both PCDSM and CCDSM reconstructions due to the outer regions refracting light more severely. Images reconstructed with a PCDSM showed a decrease in spatial resolution in the azimuthal directions as radial distance increases, due to the widening of the polar pixels. However, this can be mitigated with only a slight increase in storage size by increasing the number of projections. A loss of spatial resolution in the radial direction within 5 mm radially from center was found when reconstructing with a PCDSM, due to the large innermost pixels. However, this was remedied by increasing the number of radial rings within the PCDSM, yielding radial spatial resolution on par with images reconstructed with a CCDSM and a storage size reduction of 99.26%. CONCLUSIONS: Discretizing the image pixel elements in polar coordinates achieved a system matrix storage size reduction of 99.26% with only minimal reduction in the image quality.

Superiorization versus regularization: A comparison of algorithms for solving image reconstruction problems with applications in computed tomography.

PURPOSE: A system matrix can be built in order to account for the refractions in an optical computed tomography (CT) system. In order to utilize this system matrix, iterative methods are employed to solve the image reconstruction problem. The purpose of this study is to compare potential iterative algorithms to solve this image reconstruction problem. Comparisons examine both solution time and the quality of the reconstructed image. While our work is motivated by optical CT, the results can be extended more generally to CT. METHODS: A collection of 21 algorithms for solving the image reconstruction problem were evaluated. Specifically, algorithms using (i) superiorization techniques and (ii) regularization to avoid overfitting were compared. Multiple test problems are investigated using 18 different image phantoms, parallel-beam and fan-beam system matrices, and varying noise levels. Comparison of the algorithms is done using performance profiles on three different performance measures. RESULTS: The results for both the synthetic and clinical test problems show that there is not one single algorithm outperforming all others, but instead a set of top algorithms that give the best values on the performance profiles. When qualitative analyses such as reliance on stopping conditions, number of input parameters, and run time are also considered, FISTA-TV shows slight advantages over the other top algorithms. CONCLUSIONS: There is a set of top algorithms that all show good results in the performance profiles with a mix of superiorized and regularized model algorithms. As to which of these top algorithms outperforms the rest is undetermined and further research needs to be investigated.

Dichotomization: 2 x 2 (x2 x 2 x 2...) categories: infinite possibilities.

BACKGROUND: Consumers of epidemiology may prefer to have one measure of risk arising from analysis of a 2-by-2 table. However, reporting a single measure of association, such as one odds ratio (OR) and 95% confidence interval, from a continuous exposure variable that was dichotomized withholds much potentially useful information. Results of this type of analysis are often reported for one such dichotomization, as if no other cutoffs were investigated or even possible. METHODS: This analysis demonstrates the effect of using different theory and data driven cutoffs on the relationship between body mass index and high cholesterol using National Health and Nutrition Examination Survey data. The recommended analytic approach, presentation of a graph of ORs for a range of cutoffs, is the focus of most of the results and discussion. RESULTS: These cutoff variations resulted in ORs between 1.1 and 1.9. This allows investigators to select a result that either strongly supports or provides negligible support for an association; a choice that is invisible to readers. The OR curve presents readers with more information about the exposure disease relationship than a single OR and 95% confidence interval. CONCLUSION: As well as offering results for additional cutoffs that may be of interest to readers, the OR curve provides an indication of whether the study focuses on a reasonable representation of the data or outlier results. It offers more information about trends in the association as the cutoff changes and the implications of random fluctuations than a single OR and 95% confidence interval.