Quantifying Dual Energy Signal Hidden within Single Energy Noise
Abstract
Purpose
Neural networks have recently been demonstrated that convert single-energy CT images into dual-energy CT images. It seems at first that this “dual-energy conversion” is only possible using image priors: one might assert that if a neural network is shown a phantom containing some new insert, it has no ability to perform dual energy conversion of this insert because of the fundamental ambiguity between electron density and atomic number. We challenge this assertion by demonstrating that dual energy information can still be extracted in this scenario by analyzing sinogram noise.
Methods
If the mean attenuation is known or can be accurately estimated, then the variance in the sinogram is related to atomic number: greater photoelectric effect leads to fewer, higher-energy quanta, and hence higher variance. This effect is small. To determine possible clinical utility, consider the task of kidney stone classification, modeled as a uniform cylindrical lesion, composed of either uric acid or calcium, placed at the center of a 30 cm water phantom. It is +500 HU, 10 mm in diameter, 10 mm in height, and imaged with a CT scanner with 120 kVp, 1000 views, z-FFS, and a detector pixel size of 0.5 mm at isocenter. We construct an estimator that sums the variance through all rays passing through the lesion, and threshold this value to classify the lesion as uric acid or calcium-based.
Results
The proposed variance estimator can be approximated as following a chi-squared distribution with many degrees of freedom. Using this distribution, we estimate that the method has an area under the receiver operating curve of 0.97 for discriminating 10 mm uric acid from calcium kidney stones.
Conclusion
Some dual energy information is available in the noise of single energy CT. Whether existing neural networks actually exploit this information remains unknown.