Statistical Image Reconstruction for Polyenergetic X-Ray Computed Tomography

This paper describes a statistical image reconstruction method for X-ray computed tomography (CT) that is based on a physical model that accounts for the polyenergetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. We assume that the object consists of a given number of nonoverlapping materials, such as soft tissue and bone. The attenuation coefficient of each voxel is the product of its unknown density and a known energy-dependent mass attenuation coefficient. We formulate a penalized-likelihood function for this polyenergetic model and develop an ordered-subsets iterative algorithm for estimating the unknown densities in each voxel. The algorithm monotonically decreases the cost function at each iteration when one subset is used. Applying this method to simulated X-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artifacts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85895/1/Fessler74.pd

A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data

The proposed spectral CT method solves the constrained one-step spectral CT reconstruction (cOSSCIR) optimization problem to estimate basis material maps while modeling the nonlinear X-ray detection process and enforcing convex constraints on the basis map images. In order to apply the optimization-based reconstruction approach to experimental data, the presented method empirically estimates the effective energy-window spectra using a calibration procedure. The amplitudes of the estimated spectra were further optimized as part of the reconstruction process to reduce ring artifacts. A validation approach was developed to select constraint parameters. The proposed spectral CT method was evaluated through simulations and experiments with a photon-counting detector. Basis material map images were successfully reconstructed using the presented empirical spectral modeling and cOSSCIR optimization approach. In simulations, the cOSSCIR approach accurately reconstructed the basis map images

Segmentation-Free Statistical Image Reconstruction for Polyenergetic X-Ray Computed Tomography with Experimental Validation

This paper describes a statistical image reconstruction method for x-ray CT that is based on a physical model that accounts for the polyenergetic x-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. Unlike our earlier work, the proposed algorithm does not require pre-segmentation of the object into the various tissue classes (e.g., bone and soft tissue) and allows mixed pixels. The attenuation coefficient of each voxel is modelled as the product of its unknown density and a weighted sum of energy-dependent mass attenuation coefficients. We formulate a penalized-likelihood function for this polyenergetic model and develop an iterative algorithm for estimating the unknown density of each voxel. Applying this method to simulated x-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artefacts relative to conventional beam hardening correction methods. We also apply the method to real data acquired from a phantom containing various concentrations of potassium phosphate solution. The algorithm reconstructs an image with accurate density values for the different concentrations, demonstrating its potential for quantitative CT applications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85911/1/Fessler66.pd

Segmentation-Free Statistical Image Reconstruction for Polyenergetic X-Ray Computed Tomography

This paper describes a statistical iterative reconstruction method for X-ray CT based on a physical model that accounts for the polyenergetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. The algorithm accommodates mixtures of tissues with known mass attenuation coefficients but unknown densities. We formulate a penalized-likelihood approach for this polyenergetic model based on Poisson statistics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85881/1/Fessler173.pd

Superiorization and Perturbation Resilience of Algorithms: A Continuously Updated Bibliography

This document presents a, (mostly) chronologically ordered, bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms which is compiled and continuously updated by us at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html. Since the beginings of this topic we try to trace the work that has been published about it since its inception. To the best of our knowledge this bibliography represents all available publications on this topic to date, and while the URL is continuously updated we will revise this document and bring it up to date on arXiv approximately once a year. Abstracts of the cited works, and some links and downloadable files of preprints or reprints are available on the above mentioned Internet page. If you know of a related scientific work in any form that should be included here kindly write to me on: [email protected] with full bibliographic details, a DOI if available, and a PDF copy of the work if possible. The Internet page was initiated on March 7, 2015, and has been last updated on March 12, 2020.Comment: Original report: June 13, 2015 contained 41 items. First revision: March 9, 2017 contained 64 items. Second revision: March 8, 2018 contained 76 items. Third revision: March 11, 2019 contains 90 items. Fourth revision: March 16, 2020 contains 112 item

Maximum-Likelihood Dual-Energy TomographicImage Reconstruction

Dual-energy (DE) X-ray computed tomography (CT) has shown promise for material characterization and for providing quantitatively accurate CT values in a variety of applications. However, DE-CT has not been used routinely in medicine to date, primarily due to dose considerations. Most methods for DE-CT have used the filtered backprojection method for image reconstruction, leading to suboptimal noise/dose properties. This paper describes a statistical (maximum-likelihood) method for dual-energy X-ray CT that accommodates a wide variety of potential system configurations and measurement noise models. Regularized methods (such as penalized-likelihood or Bayesian estimation) are straightforward extensions. One version of the algorithm monotonically decreases the negative log-likelihood cost function each iteration. An ordered-subsets variation of the algorithm provides a fast and practical version.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85934/1/Fessler172.pd

Simplified statistical image reconstruction for X-ray CT with beam-hardening artifact compensation

CT images are often affected by beam-hardening artifacts due to the polychromatic nature of the X-ray spectra. These artifacts appear in the image as cupping in homogeneous areas and as dark bands between dense regions, such as bones. This paper proposes a simplified statistical reconstruction method for X-ray CT based on Poisson statistics that accounts for the non-linearities caused by beam hardening. The main advantages of the proposed method over previous algorithms is that it avoids the preliminary segmentation step, which can be tricky, especially for low-dose scans, and it does not require knowledge of the whole source spectrum, which is often unknown. Each voxel attenuation is modeled as a mixture of bone and soft tissue by defining density-dependent tissue fractions, maintaining one unknown per voxel. We approximate the energy-dependent attenuation corresponding to different combinations of bone and soft tissue, so called beam-hardening function, with the 1D function corresponding to water plus two parameters that can be tuned empirically. Results on both simulated data with Poisson sinogram noise and two rodent studies acquired with the ARGUSCT system showed a beam hardening reduction (both cupping and dark bands) similar to analytical reconstruction followed by post-processing techniques, but with reduced noise and streaks in cases with low number of projections, as expected for statistical image reconstruction.This work was partially funded by NIH grants R01-HL-098686 and U01 EB018753, by Spanish Ministerio de Economia y Competitividad (projects TEC2013-47270-R and RTC-2014-3028-1) and the Spanish Ministerio de Economia, Industria y Competitividad (projects DPI2016-79075-R AEI/FEDER, UE - Agencia Estatal de Investigación and DTS17/00122 Instituto de Salud Carlos III - FIS), and co-financed by ERDF (FEDER) Funds from the European Commission, “A way of making Europe”. The CNIC is supported by the Spanish Ministerio de Economia, Industria y Competitividad and the Pro CNIC Foundation, and is a Severo Ochoa Center of Excellence (SEV-2015-0505).En prens

Efficient and Accurate Llikelihood for Iterative Image Reconstruction in X-Ray Computed Tomography

We report a novel approach for statistical image reconstruction in X-ray CT. Statistical image reconstruction depends on maximizing a likelihood derived from a statistical model for the measurements. Traditionally, the measurements are assumed to be statistically Poisson, but more recent work has argued that CT measurements actually follow a compound Poisson distribution due to the polyenergetic nature of the X-ray source. Unlike the Poisson distribution, compound Poisson statistics have a complicated likelihood that impedes direct use of statistical reconstruction. Using a generalization of the saddle-point integration method, we derive an approximate likelihood for use with iterative algorithms. In its most realistic form, the approximate likelihood we derive accounts for polyenergetic X-rays and Poisson light statistics in the detector scintillator, and can be extended to account for electronic additive noise. The approximate likelihood is closer to the exact likelihood than is the conventional Poisson likelihood, and carries the promise of more accurate reconstruction, especially in low X-ray dose situations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85924/1/Fessler182.pd