Statistical distributions of ultra-low dose CT sinograms and their fundamental limits

Lee, Tzu-Cheng; Zhang, Ruoqiao; Alessio, Adam M.; Fu, Lin; Man, Bruno De; Kinahan, Paul E.

doi:10.1117/12.2254375

Cited by 5 publications

(10 citation statements)

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“…Such an ultra-low-dose setting is not currently used in routine diagnostic CT applications but is nevertheless a stress test to exemplify the difference between different statistical options in MBIR. There are also increasing interests in ultra-low-dose CT imaging in specific non-diagnostic applications, including image registration across multi-frame CT images and attenuation correction for PET/CT imaging [37][85], virtual CT colonoscopy screening [86], and chest CT using dose similar to chest x-ray dose [5]. A standard-dose reference scan was also acquired with 120 kVp, 310 mA, with other settings kept the same.…”

Section: Methodsmentioning

confidence: 99%

“…Assuming both noise sources are independent and additive, we have a ‘Poisson+ Gaussian’ model [66]

y_{i} ~ Poisson false{α ŷ_{i} false} / α + Normal false{0, σ^{2} false},

where y i and ŷ i are both in units of current-integrating DAS output, α is a scaling factor that converts the DAS output values to equivalent numbers of x-ray photons depending on the effective x-ray energy and the DAS gain, and σ 2 is the variance of the DAS electronic noise. σ 2 in modern CT DAS is typically equivalent to the counting statistics corresponding to from a handful [77][17][17][67][78] to a few hundred x-ray photons [65][37][13]. The parameters α and σ 2 can be measured by standard detector calibration processes [6].…”

Section: Statistical Modelsmentioning

confidence: 99%

“…Ideally the weights should equal the inverse variance of the log-transformed data. Estimation of the weights is challenging due to the correction of non-positive values and the non-linearity of the logarithm [37]. Examples of existing variance estimation techniques include noisy-data based weights [14], [21], [24], [38], denoised-data based weights [31], [32], [36], [38], model-based weights using certain mean-variance relationship [39][10][40], and iteratively re-weighted least-squares [17], [29], [41].…”

Section: Introductionmentioning

confidence: 99%

“…Here we define the ultra-low-dose (ULD) CT as a dose regime where the exposure level is a factor of 10 lower than current low-dose CT technique levels [37]. At this dose level, the mean number of x-ray photons received per detector cell exposure is commonly in the range of tens [17][10], and photon starvation is common in highly attenuated projections.…”

Section: Introductionmentioning

confidence: 99%

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Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

Lee

Kim

et al. 2017

IEEE Trans. Med. Imaging

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X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.

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Section: Methodsmentioning

confidence: 99%

“…Assuming both noise sources are independent and additive, we have a ‘Poisson+ Gaussian’ model [66]

y_{i} ~ Poisson false{α ŷ_{i} false} / α + Normal false{0, σ^{2} false},

Section: Statistical Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

Lee

Kim

et al. 2017

IEEE Trans. Med. Imaging

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“…Thus, approximation the noise simply as a Gaussian for the post-log sinogram data can hardly capture the actual statistical properties of data concealed by logarithm transform. In addition, estimation of the weights in the PWLS method is generally a challenging task due to the correction of non-positive values and the non-linearity of the logarithm [20]. Statistical correlation between the estimated weights and the noisy data can further cause negative bias in the reconstructed image.…”

Section: Introductionmentioning

confidence: 99%

Robust Low-Dose CT Sinogram Preprocessing via Exploiting Noise-Generating Mechanism

Xie

Zeng

Zhao

et al. 2017

IEEE Trans. Med. Imaging

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Computed tomography (CT) image recovery from low-mAs acquisitions without adequate treatment is always severely degraded due to a number of physical factors. In this paper, we formulate the low-dose CT sinogram preprocessing as a standard maximum a posteriori (MAP) estimation, which takes full consideration of the statistical properties of the two intrinsic noise sources in low-dose CT, i.e., the X-ray photon statistics and the electronic noise background. In addition, instead of using a general image prior as found in traditional sinogram recovery models, we design a new prior formulation to more rationally encode the piecewise-linear configurations underlying a sinogram than previously used ones, like the total variation prior term. As compared with the previous methods, especially the MAP-based ones, both the likelihood/loss and prior/regularization terms in the proposed model are ameliorated in a more accurate manner and better comply with the statistical essence of the generation mechanism of a practical sinogram. We further construct an efficient alternating direction method of multipliers (ADMM) algorithm to solve the proposed MAP solution. Experiments on simulated and real low-dose CT data demonstrate the superiority of the proposed method according to both visual inspection and comprehensive quantitative performance evaluation.

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Unbiased zero-count correction method in low-dose high-resolution photon counting detector CT

et al. 2023

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Objective: To address the zero-count problem in low-dose, high-spatial-resolution photon counting detector CT (PCD-CT) without introducing statistical biases and without degrading spatial resolution.Approach: The classical approach to generate the sinogram projection data for estimating the line integrals of the linear attenuation coefficients of the image object is to take a log transform of detector counts, which requires zero counts to be replaced by positive numbers. Both the log transform and the zero-count replacement introduce biases. After analyzing the statistical properties of the zero-count replaced pre-log and post-log data, a formula for the statistical sinogram bias was derived, based on which a new sinogram estimator was empirically constructed to cancel the statistical biases. Dose- and object-independent free parameters in the proposed estimator were learned from simulated data, and then the estimator was applied to experimental low-dose PCD-CT data of physical phantoms for validation and generalizability testing. Both bias and noise performances of the proposed method were evaluated and compared with those of previous zero-count correction methods, including zero-weighting, zero-replacement, and adaptive filtration-based methods. The impact of these correction methods on spatial resolution was also quantified using line-pair patterns. Main Results: For all objects and reduced-dose levels, the proposed method reduces the statistical CT number biases to be within $\pm10$ HU, which is significantly lower than the biases given by the classical zero-count correction methods. The Bland-Altman analysis demonstrated that the proposed led to negligible sinogram biases at all attenuation levels, whereas the other correction methods did not. Additionally, the proposed method was found to have no discernible impact on image noise and spatial resolution.Significance: The proposed zero-count correction scheme allows the CT numbers of low-dose, high-spatial-resolution PCD-CT images to match those of standard-dose and standard-resolution PCD-CT images.

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Statistical distributions of ultra-low dose CT sinograms and their fundamental limits

Cited by 5 publications

References 0 publications

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

Robust Low-Dose CT Sinogram Preprocessing via Exploiting Noise-Generating Mechanism

Unbiased zero-count correction method in low-dose high-resolution photon counting detector CT

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