NPRE 435: Radiological Imaging
Fall, 2026
Course
Description
This course introduces the
physical, mathematical, and experimental foundations of radiological imaging
techniques and their applications in diagnostic radiology and nuclear security.
During the first half of the course, we will discuss linear system theory and
tomographic image processing techniques; radiation sources for diagnostic
imaging and radiation therapy; the interaction of ionizing radiation with imaging
sensor technologies; and image formation techniques. The second half of the
course will focus on the standard radiological imaging modalities, including
X-ray computed tomography (CT), single-photon emission computed tomography
(SPECT), positron emission tomography (PET), and their applications in clinical
radiology and radiation therapy. We will also discuss several emerging
radiological imaging techniques that explore complex nuclear physics phenomena,
such as the temporal and angular correlation of X-ray and gamma-ray emissions,
positronium lifetime, and quantum entanglement of annihilation photons.
Teaching
Staff and Office Hours
Instructor: Ling-Jian Meng, Ph.D. E-mail: ljmeng@illinois.edu;
Office: 111E Talbot Lab; Tel: 217-3337710.
Office hours: 3-5 pm on Friday. Please feel free to come to my office
during regular hours or email me to schedule an appointment.
Lecture Time and Place
MWF 2:00 pm -
2:50 pm; 111K Talbot Lab.
Prerequisites
Unofficially: radiation interactions, basic principles of
radiation detectors, probability and random variables, complex numbers, linear
algebra, MATLAB.
Textbook
Required textbooks
[1] Medical Imaging Signals and Systems (2nd Edition), J. Prince and J. M. Links, Pearson Prentice Hall, 2012.
Chapters 1-3, Chapters 4-6.
Reference
[1] Foundations
of Medical Imaging, Z. H. Cho, John Wiley & Sons, 1993.
[2] Radiation
Detection and Measurements, Third Edition, G. F. Knoll, John Wiley & Sons,
1999.
Course Website
Course website:
https://courses.engr.illinois.edu/npre435/
Lecture Notes (will be
posted after each lecture)
Introduction to Radiological Imaging.
Chapter 1: Mathematical Preliminaries for Radiological
Imaging
§ Signals and systems:
Reading Material: Chapter 2 in Ref. book [1].
§ Fourier transform basics and sampling
theory: Reading Material: Chapter 2 in Ref. book [1] and Chapter 2
in Ref. book [2].
§ Analytical Image Reconstruction
Methods (1): Radon Transform & Central Slice Theorem: Reading:
Chapter 3 in Ref. book [1]. Chapter 6 (Pages 192-207) in Ref. book [2]
§ Analytical Image Reconstruction
Methods (2): Back-projection-based reconstruction methods
§ Iterative Image Reconstruction Methods:
please also see the attached paper by Shepp and Vardi on the MLEM algorithm.
§ Image Quality: Reading
Material: Chapter 3 in Ref. book [2].
Chapter 2: Introduction to Physical Principles in
Radiological Imaging
§ Typical radiation sources for radiological imaging and
radiation therapy. Reading Material: Chapter 1 in Ref. book [3].
§ Spatial, spectral, and temporal
characteristics of X-ray and gamma-ray emissions. Reading Material: Chapter 2
in Ref. book [3].
§ Interactions of ionizing radiation with matter.
Chapter 3: X-ray Radiography and Computed Tomography
§
Basic principles, current implementations,
and future trends of X-ray generators. Reading Material: Chapters 4 & 5 in
Ref. book [2]
§
X-ray imaging sensors. Reading Material:
Chapters 4 & 5 in Ref. book [2]
§
Planar radiography and X-Ray computed
tomography (CT). Reading Material: Chapters 4 & 5 in Ref. book [2]
§
Neutron and charged-particle transmission CT.
Reading Material: Chapter 6 in Ref. book [2].
Chapter 4: Emission Tomography I: Standard
Modalities for Diagnostic Radiology
§ Gamma-ray imaging sensor technologies
§ Single-photon emission computed tomography (SPECT)
§ Positron emission tomography (PET)
Chapter 5: Emission Tomography II: Emerging
Imaging Technologies
§ Positronium lifetime tomography
§ Imaging techniques exploring the
spatial-spectral-temporal correlations of gamma-ray emissions
§ Imaging techniques exploring the quantum entanglement of
annihilation gamma-rays
Homework (will be posted
after each Monday’s lecture)
Homework
1. Due date: 5 pm on Wednesday, September 16th, 2026. Please email your
solutions to me at ljmeng@illinois.edu.
Homework
2. Due date: 5 pm on Monday, September 28th, 2026.
Homework
3. Due date: 5 pm on Monday, October 12, 2026. Please see here for the
MATLAB code used in the homework.
Term Project
TP1: Paper review
and presentation: Please find the instructions here.
The presentations are scheduled for
Friday, Oct. 23, during the lecture.
Mid-term Exam
Information
TBA.
Final Exam Information
TBA.
Grading
Homework 40%
Term Project: 20%
Midterm and Final exams: 40%