Statistical characterization of noise for spatial standardization of CT scans: Enabling comparison with multiple kernels and doses

Abstract

Computerized tomography (CT) is a widely adopted modality for analyzing directly or indirectly functional, biological and morphological processes by means of the image characteristics. However, the potential utilization of the information obtained from CT images is often limited when considering the analysis of quantitative information involving different devices, acquisition protocols or reconstruction algorithms. Although CT scanners are calibrated as a part of the imaging workflow, the calibration is circumscribed to global reference values and does not circumvent problems that are inherent to the imaging modality. One of them is the lack of noise stationarity, which makes quantitative biomarkers extracted from the images less robust and stable. Some methodologies have been proposed for the assessment of non-stationary noise in reconstructed CT scans. However, those methods focused on the non-stationarity only due to the reconstruction geometry and are mainly based on the propagation of the variance of noise throughout the whole reconstruction process. Additionally, the philosophy followed in the state-of-the-art methods is based on the reduction of noise, but not in the standardization of it. This means that, even if the noise is reduced, the statistics of the signal remain non-stationary, which is insufficient to enable comparisons between different acquisitions with different statistical characteristics. In this work, we propose a statistical characterization of noise in reconstructed CT scans that leads to a versatile statistical model that effectively characterizes different doses, reconstruction kernels, and devices. The statistical model is generalized to deal with the partial volume effect via a localized mixture model that also describes the non-stationarity of noise. Finally, we propose a stabilization scheme to achieve stationary variance. The validation of the proposed methodology was performed with a physical phantom and clinical CT scans acquired with different configurations (kernels, doses, algorithms including iterative reconstruction). The results confirmed its suitability to enable comparisons with different doses, and acquisition protocols.

Autocalibration method for non-stationary CT bias correction

“…Obviously, this constraint on the lower attenuation level enforces a positive skewness in the distribution of noise. The positive skewness was confirmed in Vegas-Sánchez-Ferrero et al (2017), where the statistical response of noise was studied for different doses, reconstruction kernels, and devices. In Fig.…”

“…(5), the bias correction will require the calculation of accurate estimates of local variance and local mean. This is achieved by considering the statistical characterization of noise proposed in Vegas-Sánchez-Ferrero et al (2017), which adopts a non-central Gamma (nc-Γ) model as a suitable distribution that models the stochastic behavior of homogeneous tissues in CT scans with different reconstruction kernels, doses or devices. This model is a three-parameter distribution whose density function (PDF) is defined as: $$f_X(x|\alpha ,\beta ,\delta )=\frac{{(x-\delta )}^{\alpha -1}}{{\beta }^{\alpha }\Gamma (\alpha )}{e}^{-\frac{x-\delta }{\beta }},x\ge \delta \text{and}\alpha \text{,}\beta \text{,}>0,$$ where Γ ( x ) is the Euler Gamma function, α is the shape parameter, β is the scale parameter, and δ is defined as the least attenuation level (typically around −1000 HU, in our case 1024 HU).…”

“…As in Vegas-Sánchez-Ferrero et al (2017), the mixture model parameters are estimated by Expectation-Maximization.…”

“…In our previous work Vegas-Sánchez-Ferrero et al (2017), we proposed a statistical framework to describe the non-stationary behavior of noise and proposed a stabilization scheme to transform it into a stationary Gaussian process, enabling the local comparison of histograms between different doses and reconstruction kernels. This methodology would suffice to standardize scanners under the same calibration assuming the reconstruction methods do not introduce any bias.…”

“…The local variance has to be carefully estimated to remove the spatial dependence between bias and noise. We propose a robust methodology to estimate the local variance that avoids artifacts due to tissue boundaries and non-homogeneities based on the statistical characterization and variance stabilization methods recently proposed in Vegas-Sánchez-Ferrero et al (2017). Then, an autocalibration scheme is proposed to establish a common framework for comparison of studies.…”