Expectation maximization (EM) algorithms using polar symmetries for computed tomography (CT) image reconstruction

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.

Effect of Reconstruction Algorithm on the Identification of 3D Printing Polymers Based on Hyperspectral CT Technology Combined with Artificial Neural Network

Hyperspectral X-ray CT (HXCT) technology provides not only structural imaging but also the information of material components therein. The main purpose of this study is to investigate the effect of various reconstruction algorithms on reconstructed X-ray absorption spectra (XAS) of components shown in the CT image by means of HXCT. In this paper, taking 3D printing polymer as an example, seven kinds of commonly used polymers such as thermoplastic elastomer (TPE), carbon fiber reinforced polyamide (PA-CF), acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), ultraviolet photosensitive resin (UV9400), polyethylene terephthalate glycol (PETG), and polyvinyl alcohol (PVA) were selected as samples for hyperspectral CT reconstruction experiments. Seven kinds of 3D printing polymer and two interfering samples were divided into a training set and test sets. First, structural images of specimens were reconstructed by Filtered Back-Projection (FBP), Algebra Reconstruction Technique (ART) and Maximum-Likelihood Expectation-Maximization (ML-EM). Secondly, reconstructed XAS were extracted from the pixels of region of interest (ROI) compartmentalized in the images. Thirdly, the results of principal component analysis (PCA) demonstrated that the first four principal components contain the main features of reconstructed XAS, so we adopted Artificial Neural Network (ANN) trained by the reconstructed XAS expressed by the first four principal components in the training set to identify that the XAS of corresponding polymers exist in both of test sets from the training set. The result of ANN displays that FBP has the best performance of classification, whose ten-fold cross-validation accuracy reached 99%. It suggests that hyperspectral CT reconstruction is a promising way of getting image features and material features at the same time, which can be used in medical imaging and nondestructive testing.