Journal article
Noise properties of CT images reconstructed by use of constrained total-variation, data-discrepancy minimization : Noise properties of CT images
Purpose: The authors develop and investigate iterative image reconstruction algorithms based on data-discrepancy minimization with a total-variation (TV) constraint. The various algorithms are derived with different data-discrepancy measures reflecting the maximum likelihood (ML) principle. Simulations demonstrate the iterative algorithms and the resulting image statistical properties for low-dose CT data acquired with sparse projection view angle sampling.
Of particular interest is to quantify improvement of image statistical properties by use of the ML data fidelity term. Methods: An incremental algorithm framework is developed for this purpose. The instances of the incremental algorithms are derived for solving optimization problems including a data fidelity objective function combined with a constraint on the image TV.
For the data fidelity term the authors, compare application of the maximum likelihood principle, in the form of weighted least-squares (WLSQ) and Poisson-likelihood (PL), with the use of unweighted least-squares (LSQ). Results: The incremental algorithms are applied to projection data generated by a simulation modeling the breast computed tomography (bCT) imaging application.
The only source of data inconsistency in the bCT projections is due to noise, and a Poisson distribution is assumed for the transmitted x-ray photon intensity. In the simulations involving the incremental algorithms an ensemble of images, reconstructed from 1000 noise realizations of the x-ray transmission data, is used to estimate the image statistical properties.
The WLSQ and PL incremental algorithms are seen to reduce image variance as compared to that of LSQ without sacrificing image bias. The difference is also seen at few iterations-short of numerical convergence of the corresponding optimization problems. Conclusions: The proposed incremental algorithms prove effective and efficient for iterative image reconstruction in low-dose CT applications particularly with sparse-view projection data.
| Language: | English |
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| Publisher: | American Association of Physicists in Medicine |
| Year: | 2015 |
| Pages: | 2690-2698 |
| ISSN: | 24734209 and 00942405 |
| Types: | Journal article |
| DOI: | 10.1118/1.4914148 |
| ORCIDs: | Andersen, Martin S. |
computed tomography incremental algorithms iterative image reconstruction noise properties total variation
Algorithms Biological material, e.g. blood, urine; Haemocytometers Computed tomography Computer Simulation Computerised tomographs Digital computing or data processing equipment or methods, specially adapted for specific applications Humans Image data processing or generation, in general Image enhancement or restoration, e.g. from bit‐mapped to bit‐mapped creating a similar image Image reconstruction Least-Squares Analysis Likelihood Functions Mammography Medical X‐ray imaging Medical image noise Medical image reconstruction Numerical optimization Photons Poisson Distribution Poisson's equation Probability theory, stochastic processes, and statistics Reconstruction Statistical properties Tomography, X-Ray Computed X-Rays X‐ray imaging computerised tomography image denoising image reconstruction iterative methods least squares approximations maximum likelihood estimation medical image processing minimisation
