NPRE 435: Radiological Imaging
Fall, 2025
Course
Description
This course is designed to introduce
the physical, mathematical, and experimental foundation of radiological image
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, 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 emerging 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 to send me an email to make an appointment.
Lecture Time and Place
MWF 2:00pm-2:50pm;
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.
Chapter 1-3, Chapter 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: Chapters 2 in Ref. book [1].
§ Fourier transform basics
and sampling theory: Reading
Material: Chapters 2 in Ref. book [1] and Chapters 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: Chapters 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: Chapters
1 in Ref. book [3].
§ 
Spatial, spectral, and temporal
characteristics of X-ray and gamma-ray emissions. Reading Material:
Chapters 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: Chapters 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 on Monday,
September 15. Solutions.
Homework 2. Due on Monday,
September 29. Solutions.
Homework 3. Due on Monday,
October 6. Matlab code. Solutions.
Homework 4. Due on
Wednesday, October 22. Solutions.
Term Project
Date Assigned: Monday, October 20th.
Due Date: The term-project
presentation will take place on Wednesday, Nov. 12 and Friday, Nov. 14.
Please see the information sheet for
further details.
Mid-term Exam
Information
Date and Time: Friday, October 24th,
2-3 pm.
Location: 111 K Talbot Lab.
Content covered in the
exam: Chapter 1: Mathematical Preliminaries for Radiological
Imaging.
Format of the exam: Open
book. You may bring your textbook, printout of the
lecture slides, and your notes. No computer, cellphone, or tablet allowed.
Final Exam Information
Date and Time: Tuesday, December 16th,
1:30-4:30 pm.
Location: 111 K Talbot Lab.
Content covered in the
exam: Chapter 2-4 above.
Format: Open book. You may bring your
textbook, printout of the lecture slides, and your notes. No computer,
cellphone, or tablet allowed.
Review slides for Chapters 2, 3, and 4.
Grading
Homework 40%
Term Project: 20%
Midterm and Final exam: Exam 40%