About

Norbert Pelc is Professor of Radiology, Emeritus, at Stanford University. His primary research interests are in the physics, engineering, and mathematics of diagnostic imaging and the development of applications of this imaging technology. His current work focuses on computed tomography, specifically in methods to improve the information content and image quality and to reduce the radiation dose from these examinations. He holds a doctorate and master degrees in Medical Radiological Physics from Harvard University and a BS from the University of Wisconsin in Madison. Pelc has served on the first National Advisory Council of the National Institute of Biomedical Imaging and Bioengineering of the NIH. He is a member of the National Academy of Engineering and a Fellow of the American Association of Physicists in Medicine, the International Society for Magnetic Resonance in Medicine, the American Institute of Medical and Biological Engineering, and SPIE. He was recognized with the 2026 SPIE Harrison H. Barrett Award in Medical Imaging for his career’s work defining the fields of X-ray, CT, and MR imaging for clinical care and for educating generations of clinicians and scientists.

Research topics

• Computer Science
• Radiology
• Medicine
• Artificial Intelligence
• Physics
• Optics
• Biomedical engineering
• Medical physics
• Telecommunications
• Materials science
• Algorithm

Selected publications

• A virtual trial evaluation of patient motion in arc and linear system designs in body digital tomosynthesis

  Biomedical Physics & Engineering Express · 2025-07-25

  articleSenior author

  Abstract Background . Patient movement is an ever-present reality in any clinical imaging scenario. In the context of digital tomosynthesis, thoracic motion can profoundly impact the resulting image quality. Design of the system, based on either linear or multi-directional source positions, can influence this impact. The purpose of this study was to assess this influence through a virtual imaging trial. Methods . We utilized computational human models from the 4D extended cardiac-torso (XCAT) series, incorporating specific pathologies in the chest and abdomen, as well as four types of patient motions: cardiac, respiratory, bowel gas, and incidental movements. The models were imaged using representative simulators of digital tomosynthesis (DTS), with both a conventional linear motion system and a multi-source dome system (also known as an arc) featuring multi-directional source positions. The images were analyzed quantitatively and visually through an observer study to assess the relative impact of motions in the resulting images. Results . The multi-source arc system demonstrated an overall advantage over the conventional linear tomosynthesis system in terms of reduced susceptibility to motion artifacts. Observer scores indicated better image quality (by 35%) and lesion conspicuity (by 54%) with the arc system. Quantitative metrics indicated up to a two-fold increase in contrast, CNR, and SSIM for the arc system. Conclusions . The findings suggest that the arc geometry may offer improved robustness against patient motion compared to linear tomosynthesis. This advantage is attributed to the arc system’s ability to capture images from multiple angles in rapid sequence, thereby minimizing the impact of motion artifacts and enhancing overall image quality.

  PublisherDOI

• Analytical model for pulse pileup spectra and count statistics in photon counting detectors with seminonparalyzable behavior

  Medical Physics · 2025-03-17 · 1 citations

  articleOpen access

  Abstract Background Photon counting detectors (PCDs) with energy discriminating capabilities enable quantitative imaging of materials. However, the accuracy of estimates may be substantially degraded due to pulse pileup effects (PPEs) at high count rates. Accurate description of the output spectrum and count rate behavior of a PCD subject to pulse pileup is crucial to the development of photon counting computed tomography (PCCT). Purpose This study presents a fully analytical model to accurately predict the pulse pileup spectrum and count statistics (mean and covariance of energy‐binned counts) for a non‐paralyzable detector with nonzero pulse length and, therefore, seminonparalyzable behavior, that is, retriggering of dead time by pulses incident during the previous dead time. Methods We recursively computed the probability density function (PDF) of pulse pileup spectra at different pulse pileup orders. To do this, we considered the following factors: the unipolar pulse shape, the incident pulse spectrum, the distribution of time intervals between incident pulses, and the trigger threshold. We then derived the count rate and spectrum‐dependent expression of total count statistics (mean and variance of total counts) based on renewal theory. We simulated a non‐paralyzable PCD using Monte Carlo simulation to separately validate the spectrum and count statistics model outputs. Finally, we investigated the model accuracy in predicting material decomposition noise using the Cramér–Rao lower bound (CRLB) and a multibin system model. A comparison between predictions of the proposed model and Monte Carlo simulation is presented. Results The results show excellent agreement between the proposed model prediction of pulse pileup spectrum and count statistics and Monte Carlo simulation for relative count rates (the average number of counts detected during one dead time, ) of up to . The coefficient of variation (CV) values between the spectra from model prediction and Monte Carlo simulation are less than , and the coefficient of determination values, , between the count statistics from model prediction and Monte Carlo simulation are greater than . The proposed model also accurately predicts material decomposition noise for a non‐paralyzable PCD for relative count rates of up to , with relative error (RE) less than . Conclusions We developed a fully analytical model of the pulse pileup spectrum and count statistics for a non‐paralyzable detector model with nonzero pulse length. The model predictions agree with the Monte Carlo simulation outputs. This model could be used to correct and compensate for pulse pileup when imaging with PCDs.

  PublisherOA PDFDOI

• The effects of intra‐detector Compton scatter on low‐frequency DQE for photon‐counting CT using edge‐on‐irradiated silicon detectors

  Medical Physics · 2024-05-16 · 9 citations

  articleOpen access

  BACKGROUND: Edge-on-irradiated silicon detectors are currently being investigated for use in full-body photon-counting computed tomography (CT) applications. The low atomic number of silicon leads to a significant number of incident photons being Compton scattered in the detector, depositing a part of their energy and potentially being counted multiple times. Even though the physics of Compton scatter is well established, the effects of Compton interactions in the detector on image quality for an edge-on-irradiated silicon detector have still not been thoroughly investigated. PURPOSE: To investigate and explain effects of Compton scatter on low-frequency detective quantum efficiency (DQE) for photon-counting CT using edge-on-irradiated silicon detectors. METHODS: We extend an existing Monte Carlo model of an edge-on-irradiated silicon detector with 60 mm active absorption depth, previously used to evaluate spatial-frequency-based performance, to develop projection and image domain performance metrics for pure density and pure spectral imaging tasks with 30 and 40 cm water backgrounds. We show that the lowest energy threshold of the detector can be used as an effective discriminator of primary counts and cross-talk caused by Compton scatter. We study the developed metrics as functions of the lowest threshold energy for root-mean-square electronic noise levels of 0.8, 1.6, and 3.2 keV, where the intermediate level 1.6 keV corresponds to the noise level previously measured on a single sensor element in isolation. We also compare the performance of a modeled detector with 8, 4, and 2 optimized energy bins to a detector with 1-keV-wide bins. RESULTS: In terms of low-frequency DQE for density imaging, there is a tradeoff between using a threshold low enough to capture Compton interactions and avoiding electronic noise counts. For 30 cm water phantom, 4 energy bins, and a root-mean-square electronic noise of 0.8, 1.6, and 3.2 keV, it is optimal to put the lowest energy threshold at 3, 6, and 1 keV, which gives optimal projection-domain DQEs of 0.64, 0.59, and 0.52, respectively. Low-frequency DQE for spectral imaging also benefits from measuring Compton interactions with respective optimal thresholds of 12, 12, and 13 keV. No large dependence on background thickness was observed. For the intermediate noise level (1.6 keV), increasing the lowest threshold from 5 to 35 keV increases the variance in a iodine basis image by 60%-62% (30 cm phantom) and 67%-69% (40 cm phantom), with 8 bins. Both spectral and density DQE are adversely affected by increasing the electronic noise level. Image-domain DQE exhibits similar qualitative behavior as projection-domain DQE. CONCLUSIONS: Compton interactions contribute significantly to the density imaging performance of edge-on-irradiated silicon detectors. With the studied detector topology, the benefit of counting primary Compton interactions outweighs the penalty of multiple counting at all lowest threshold energies. Compton interactions also contribute significantly to the spectral imaging performance for measured energies above 10 keV.

  PublisherOA PDFDOI

• Spectral optimization using fast kV switching and filtration for photon counting CT with realistic detector responses: a simulation study

  Journal of Medical Imaging · 2024-07-25 · 2 citations

  articleOpen access

  Purpose: Photon counting CT (PCCT) provides spectral measurements for material decomposition. However, the image noise (at a fixed dose) depends on the source spectrum. Our study investigates the potential benefits from spectral optimization using fast kV switching and filtration to reduce noise in material decomposition. Approach: The effect of the input spectra on noise performance in both two-basis material decomposition and three-basis material decomposition was compared using Cramer-Rao lower bound analysis in the projection domain and in a digital phantom study in the image domain. The fluences of different spectra were normalized using the CT dose index to maintain constant dose levels. Four detector response models based on Si or CdTe were included in the analysis. Results: . For three-material decomposition, greater noise reduction in material images was found with fast kV switching (26.2% for calcium and 25.8% for iodine, in terms of SD), which suggests that challenging tasks benefit more from the richer spectral information provided by fast kV switching. Conclusions: The performance of PCCT in material decomposition can be improved by optimizing source spectrum settings. Task-specific tube voltages can be selected for single kV scans. Also, our results demonstrate that utilizing fast kV switching can substantially reduce the noise in material decomposition for both two- and three-material decompositions, and a fixed Gd filter can further enhance such improvements for two-material decomposition.

  PublisherOA PDFDOI

• Empirical optimization of energy bin weights for compressing measurements with realistic photon counting x‐ray detectors

  Medical Physics · 2023-07-03 · 4 citations

  articleOpen access

  Abstract Background Photon counting detectors (PCDs) provide higher spatial resolution, improved contrast‐to‐noise ratio (CNR), and energy discriminating capabilities. However, the greatly increased amount of projection data in photon counting computed tomography (PCCT) systems becomes challenging to transmit through the slip ring, process, and store. Purpose This study proposes and evaluates an empirical optimization algorithm to obtain optimal energy weights for energy bin data compression. This algorithm is universally applicable to spectral imaging tasks including 2 and 3 material decomposition (MD) tasks and virtual monoenergetic images (VMIs). This method is simple to implement while preserving spectral information for the full range of object thicknesses and is applicable to different PCDs, for example, silicon detectors and CdTe detectors. Methods We used realistic detector energy response models to simulate the spectral response of different PCDs and an empirical calibration method to fit a semi‐empirical forward model for each PCD. We numerically optimized the optimal energy weights by minimizing the average relative Cramér–Rao lower bound (CRLB) due to the energy‐weighted bin compression, for MD and VMI tasks over a range of material area density (0–40 g/cm 2 water, 0–2.16 g/cm 2 calcium). We used Monte Carlo simulation of a step wedge phantom and an anthropomorphic head phantom to evaluate the performance of this energy bin compression method in the projection domain and image domain, respectively. Results The results show that for 2 MD, the energy bin compression method can reduce PCCT data size by 75% and 60%, with an average variance penalty of less than 17% and 3% for silicon and CdTe detectors, respectively. For 3 MD tasks with a K‐edge material (iodine), this method can reduce the data size by 62.5% and 40% with an average variance penalty of less than 12% and 13% for silicon and CdTe detectors, respectively. Conclusions We proposed an energy bin compression method that is broadly applicable to different PCCT systems and object sizes, with high data compression ratio and little loss of spectral information.

  PublisherOA PDFDOI

• Early CT physics research at Massachusetts General Hospital

  Medical Physics · 2023-01-22

  reviewOpen access1st authorCorresponding

  Although CT imaging was introduced at Massachusetts General Hospital (MGH) quite early, with its first CT scanner installed in 1973, CT research at MGH started years earlier. The goal of this paper is to describe some of this innovative work and related accomplishments.

  PublisherOA PDFDOI

• Fast kV switching for improved material decomposition with photon counting x-ray detectors

  Medical Imaging 2022: Physics of Medical Imaging · 2022-03-31 · 6 citations

  article

  Photon counting x-ray detectors enable spectral imaging, which can be utilized for material decomposition and quantitative imaging tasks. This study investigates potential benefits of tube voltage optimization, including fast kV switching, on material decomposition noise. In simulation studies, single kV scans including 80/100/120/140 kV were tested as well as an 80/140 fast kV switching pair. Fluences of spectra were normalized with respect to CTDI to keep dose neutral. An open-source spectral response model of a realistic Si detector was used in the Cramér–Rao lower bound calculation, which estimates the lower bound of the noise in material decomposition. A simulated CT scan of an anthropomorphic head phantom was performed for noise analysis in the image domain. Simulation results showed that a single kV can be optimized for specific imaging tasks depending on the object size, while fast kV switching can substantially reduce the noise in material decomposition compared to single kV scan. Additionally, noise can be further reduced with a fixed Kedge (Gd) filter during fast kV switching acquisitions.

  PublisherDOI

• Empirical optimization of energy bin weights for compressing measurements with photon counting x-ray detectors

  Medical Imaging 2022: Physics of Medical Imaging · 2022-03-31 · 4 citations

  article

  Photon counting detectors (PCDs) with energy discrimination capabilities provide spectral information through energy binning and higher spatial resolution than conventional energy integrating detectors (EIDs). However, the projection data transmission from the detector across the slip ring to the processing computer becomes more challenging due to the increased amount of data, including multiple (e.g., 8) energy bins. In this work, we propose a projection-domain energy bin weighting method that produces two energy-weighted measurements to provide comparable spectral information as the original binned counts for material decomposition and virtual monoenergetic imaging tasks. We obtain the optimal energy bin weights by minimizing the Cramér–Rao lower bound (CRLB) ratio between the weighted measurements and that of the original binned counts and evaluate their respective material decomposition performance using Monte Carlo simulation. The experiments were conducted with realistic photon counting detector energy responses, which were not assumed to be known. Instead, only an empirical calibration using a step-wedge phantom is required, making this process extensible to any photon counting detector without prior knowledge of its energy response or the incident spectrum. The results show that the two energy-weighted measurements generated with our method can provide comparable material decomposition results with low bias and less than 20% variance penalty to that of the original binned counts for a large range of patient size, with a data reduction of 75% for a silicon detector with 8 energy bins and 60% for a CdTe detector with 5 energy bins.

  PublisherDOI

• Comparison of energy bin compression strategies for photon counting detectors

  7th International Conference on Image Formation in X-Ray Computed Tomography · 2022-10-18 · 5 citations

  articleOpen access

  Photon counting detectors (PCDs) with energy discrimination capabilities allow us to perform quantitative material decomposition with high spatial resolution. Although PCDs provide more spectral information than conventional energy integrating detectors (EIDs), it is more challenging for the system to transmit projection data from the detectors across the slip ring to the processing computer and store the data, due to the increased amount of data with increasing number of energy bins. To address this problem, many approaches have been proposed to compress the bin data while maintaining the image quality. In this work, we compare the performance of strategies to reduce projection data and determine the optimal choice of bin compression strategies and the number of measurements for multiple tasks. We first obtain the optimal thresholds for conventional energy bins, as determined by minimizing the Cramér–Rao lower bound (CRLB) for material decomposition tasks with a realistic silicon detector energy response. We then consider the case of reducing data from eight native energy bins by forming weighted sums, either with binary weights or continuous weights, by minimizing the relative CRLB between the compressed measurements and the original eight bins. We then evaluate their respective performance using Monte Carlo simulation for a head phantom. The results show that the continuous weights strategy is superior to others, with low bias and less than 10% variance penalty for two weighted sums, with a data reduction of 75% within a large material thickness space. The other strategies have up to 50% variance penalty compared with the original eight bins and are less robust when there is photon starvation. With additional weighted measurements, the continuous weights method can achieve less than 1% variance penalty when reducing the eight native energy bins to half the number of measurements. Overall, combining energy bins by forming weighted sums with continuous weights is an effective strategy for reducing data while preserving spectral information.

  PublisherOA PDFDOI

• The effects of intra-detector Compton scatter on zero-frequency DQE for photon-counting CT using edge-on-irradiated silicon detectors

  arXiv (Cornell University) · 2022-06-08 · 7 citations

  preprintOpen access

  Background: Edge-on-irradiated silicon detectors are currently being investigated for use in photon-counting CT applications. The low atomic number of silicon leads to a significant number of incident photons being Compton scattered in the detector, depositing a part of their energy and potentially being counted multiple times. Although the physics of Compton scatter is well established, the effects of Compton interactions in the detector on image quality for an edge-on-irradiated silicon detector have still not been thoroughly investigated. Purpose: To investigate and explain effects of Compton scatter on zero-frequency DQE for photon-counting CT using edge-on-irradiated silicon detectors. Methods: We extend an existing Monte Carlo model of an edge-on-irradiated silicon detector to develop projection and image domain performance metrics for pure density and pure spectral imaging tasks. We show that the lowest energy threshold of the detector can be used as an effective discriminator of primary counts and cross-talk caused by Compton scatter. We study the developed metrics as functions of the lowest threshold energy. Results: Density imaging performance decreases monotonically as a function of the lowest threshold in both projection and image domains. Spectral imaging performance has a plateau between 0 and 10 keV and decreases monotonically thereafter, in both projection and image domain. Conclusions: Compton interactions contribute significantly to the density imaging performance of edge-on-irradiated silicon detectors. With the studied detector topology, the benefit of counting primary Compton interactions outweighs the penalty of multiple counting at all lower threshold energies. Compton interactions also contribute significantly to the spectral imaging performance for measured energies above 10 keV.

  PublisherOA PDFDOI

Recent grants

• Dynamic bowtie attenuator for CT dose reduction and dynamic range control

  NIH · $426k · 2013–2016

• NIH Grant R01EB000198

  NIH · $1.3M · 2006

• NIH Grant R01EB006837

  NIH · $4.3M · 2012

• High dose efficiency CT System

  NIH · $1.5M · 2014–2018

• NIH Grant R01HL046347

  NIH · $2.6M · 2002

Frequent coauthors

• Gary H. Glover

  Stanford University

  44 shared

• Rebecca Fahrig

  Siemens Healthcare (Germany)

  35 shared

• Robert J. Herfkens

  Stanford University

  32 shared

• Dieter R. Enzmann

  31 shared

• Adam Wang

  Stanford University

  30 shared

• Jongduk Baek

  Yonsei University

  26 shared

• Scott S. Hsieh

  Mayo Clinic in Arizona

  25 shared

• Marcus T. Alley

  25 shared

Education

• Ph.D., Biomedical Engineering

  Stanford University

  1970

• M.S., Electrical Engineering

  University of California, Berkeley

  1966

• B.S., Electrical Engineering

  University of California, Berkeley

  1964

Awards & honors

• 2026 SPIE Harrison H. Barrett Award in Medical Imaging