Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing

Abstract

We present a statistically principled sinogram smoothing approach for X-ray computed tomography (CT) with the intent of reducing noise-induced streak artifacts. These artifacts arise in CT when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines. Attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements. While these approaches involve loose consideration of the measurement statistics to determine smoothing levels, they do not explicitly model the statistical distributions of the measurement data. In this paper, we present an explicitly statistical approach to sinogram smoothing in the presence of photon-starved measurements. It is an extension of a nonparametric sinogram smoothing approach using penalized Poisson-likelihood functions that we have previously developed for emission tomography. Because the approach explicitly models the data statistics, it is naturally adaptive--it will smooth more variable measurements more heavily than it does less variable measurements. We find that it significantly reduces streak artifacts and noise levels without comprising image resolution.

Variance analysis of x-ray CT sinograms in the presence of electronic noise background

“…Another parameter in the mean-variance model (15), i.e., the mean m e of the electronic noise, arising from the detector dark current, can be determined immediately before each scan by sampling the signals in those unexposed detectors over some time interval. 6,7,12 From Figs. 4 and 5, it can be observed that another parameter, i.e., the variance σ 2 e of the electronic noise, reduces slightly as the mAs value increases, and can be determined by the exponential relationship of Fig.…”

“…In practice, the variance σ 2 e of the electronic noise may be estimated from the sample variance of a series of dark current measurements. 6,7 Given the above four physical quantities, Eq. (15) provides a theoretical means to estimate the variance, which reflects the relative importance of each measurement for various data processing tasks, for example, a statistical image reconstruction task in the sinogram domain.…”

“…1,2 However, the quality of low-dose CT images would be severely degraded due to excessive xray quanta fluctuation and system inherent electronic noise background in the acquired data, 3,4 if there is no adequate noise treatment in processing the data for image reconstruction. Accurate statistical modeling of the data is a fundamental issue for low-dose CT imaging via either statisticsbased sinogram restoration 2,[5][6][7] or statistical iterative image reconstruction. [8][9][10] For a clinical x-ray CT detection system, the quanta noise is introduced as x-ray flux being generated from the x-ray source and propagates along as the x-ray flux traversing the patient, while the electronic noise is intrinsic to the detection system.…”

“…To consider the electronic noise background, the x-ray source is usually assumed approximately as monochromatic and the signal statistics is then described by the Poisson distribution. 5,6,9 For a clinical x-ray CT detection system, the electronic noise background follows a normal distribution, 4,6,12 where the mean and variance reflect the dark current and readout noise of electronics, respectively. For low-dose CT imaging, the electronic noise background has been conjectured as an important factor affecting the image quality.…”

“…4,15 This work extends the previous study 16 to consider explicitly the electronic noise background. Because the variance of data measurements is an important factor and determines the relative weight for each measurement in either statistics-based sinogram restoration or statistical iterative image reconstruction, [5][6][7][8][9][10] this work focuses on the variance analysis, where a mean-variance relationship with inclusion of the electronic noise background is derived and validated and the contribution of the electronic noise to the data variance is measured. The remaining sections of this paper are organized as follows.…”