2017/02/03 by Robert Alvarez, Alvarez, Robert
Engineering · Medicine · #Advanced X-ray and CT Imaging #FOS: Physical sciences #Medical Imaging Techniques and Applications #Medical Physics (physics.med-ph) #Radiation Dose and Imaging
paper · pdf · doi:10.48550/arxiv.1702.01006
openalex publication_date 2017/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
-Purpose: A neural network estimator to process x-ray spectral measurements\nfrom photon counting detectors with pileup. The estimator is used with an\nexpansion of the attenuation coefficient as a linear combination of functions\nof energy multiplied by coefficients that depend on the material composition at\npoints within the object [R.E. Alvarez and A. Macovski, Phys. Med. Biol., 1976,\n733-744]. The estimator computes the line integrals of the coefficients from\nmeasurements with different spectra. Neural network estimators are trained with\nmeasurements of a calibration phantom with the clinical x-ray system. One\nestimator uses low noise training data and another network is trained with data\ncomputed by adding random noise to the low noise data. The performance of the\nestimators is compared to each other and to the Cramer-Rao lower bound (CRLB).\nMethods: The estimator performance is measured using a Monte Carlo simulation\nwith an idealized model of a photon counting detector that includes only pileup\nand quantum noise. Transmitted x-ray spectra are computed for a calibration\nphantom. The transmitted spectra are used to compute random data for photon\ncounting detectors with pileup. Detectors with small and large dead times are\nconsidered. Neural network training data with extremely low noise are computed\nby averaging the random detected data with pileup for a large numbers of\nexposures of the phantom. Each exposure is equivalent to a projection image or\none projection of a computed tomography scan. Training data with high noise are\ncomputed by using data from one exposure. Finally, training data are computed\nby adding random data to the low noise data. The added random data are\nmultivariate normal with zero mean and covariance equal to the sample\ncovariance of data for an object with properly chosen attenuation. To test the\nestimators, random data are computed for different thicknesses of three test\nobjects with different compositions. These are used as inputs to the neural\nnetwork estimators. The mean squared errors (MSE), variance and square of the\nbias of the neural networks' outputs with the random object data are each\ncompared to the CRLB. Results: The MSE for a network trained with low noise\ndata and added noise is close to the CRLB for both the low and high pileup\ncases. Networks trained with very low noise data have low bias but large\nvariance for both pileup cases. [email protected] Networks trained with\nhigh noise data have both large bias and large variance. Conclusion: With a\nproperly chosen level of added training data noise, a neural network estimator\nfor photon counting data with pileup can have variance close to the CRLB with\nnegligible bias.\n