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

Abstract

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.

Keywords: gel dosimetry; iterative image reconstruction; optical CT; polar coordinate discretization; system matrix.