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Introduction to Image Science, Spring 2024

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Computed Tomography Angiogram [Image Source]

Course Description

The course covers the basics of image science. This includes the theoretical and mathematical foundations of image science, as well as their application to the analysis of modern (computational) imaging systems. Concrete examples from medical imaging, industrial inspection, remote sensing, virtual reality, or microscopy will be introduced and discussed.

Course Goals: By taking the course, students are expected to gather a broad “toolbox” of basic optical, mathematical, and computational principles used in imaging science. The goal is that students can apply these tools to concrete future tasks they might face in industry or their future research.

Students will be able to identify the measured object properties and how the respective imaging system collects and processes the captured data to extract the desired information. Moreover, students will learn about the analysis of imaging systems and the concept of task-based assessment of image quality.

Prerequisites: This course is intended for graduate students in optical sciences or engineering with an appropriate mathematical background at the level of advanced calculus.

Program: The four key parts of the course include (tentative outline):

Part I: Mathematical formalism of image science

Image formation
Objects as vectors in a vector space, image formation as a continuous to continuous or continuous to discrete mapping from an object vector space to an image vector space
Eigenfunctions, linear systems, Fourier transforms

Part II: The role of optics and computation in modern imaging science

Indirect imaging, inverse problems, iterative algorithms
Radiometry
Geometrical optics description of imaging
Coherent and incoherent imaging, diffraction
Physical optics description and fundamental limits
Digital imaging, sampling, image detectors, displays
Image processing

Part III: Modern (computational) imaging systems

X-ray imaging, computed tomography
Microscopy
Time-of-Flight cameras, Non-Line-of-Sight imaging
(Multi-wavelength) Interferometry, optical coherence tomography
Remote sensing
Coded apertures
Triangulation (structured light)
Deflectometry and Photometric Stereo
Neuromorphic Imaging / Event Cameras

Part IV: Observers and task-based image quality assessment

Noise in imaging systems
Classification and estimation tasks, ideal observer
Image quality, task-performance evaluation

Course Logistics

Class: M, W 2:00 – 3:15 in Meinel Building West Wing 307
Material made available: http://d2l.arizona.edu
Instructors: Florian Willomitzer (after spring break), Lars Furenlid (before spring break)
TA: Micaehla May

Contact Information Prof. Willomitzer (after spring break):
Room: Meinel 629
Email: fwillomitzer@arizona.edu
Office hours: In person or via zoom. Send email to reserve a 15min slot.

Contact Information Prof. Furenlid (before spring break):
Room: Meinel 433
Email: furen@radiology.arizona.edu
Office hours: tba

Contact Information Micaehla May:
Email: mmay@optics.arizona.edu
Office hours: tba

Grading

Grading will based on homework assignments (6 in total), a midterm exam, and a final exam. Each of these three components will be weighted equally (Homework = 1/3, Midterm Exam = 1/3, Final = 1/3). Opportunities for bonus points may occur at select times during the semester.

Policy: Late homework will not be accepted without prior instructor approval. Students may study and work together, but homework must be completed and turned in independently. Direct plagiarism on homework assignments is not acceptable. The University’s Student Code of Academic Integrity applies to this class and should be reviewed by each student. Cases of suspected academic dishonesty including plagiarism, cheating on tests or altering graded homework will be referred to the appropriate College Dean. The academic penalty for academic dishonesty is an “F” grade. Homework will only be re-graded when there is evidence of a grading error. The instructors reserve the right to re-grade an entire homework or test.

Lecture and Homework Schedule

Scheduled lecture topics are tentative and might change while the course is ongoing. Possible changes in homework out/due dates will be announced at least several days in advance.

Day	Lec #	Topic	Homework
1/10/2023	1	Introduction (course description and overview)
1/15/2023		MLK DAY – No class
1/17/2023	2	Image formation, CC and CD mappings, object basis functions
1/22/2023	3	Vector spaces, eigenfunctions, linear systems, Fourier transforms	HW 1 out
1/24/2023	4	Forward and inverse problems
1/29/2023	5	Pseudoinverses, regularization
1/31/2023	6	Waves, free-space propagation, transfer function
2/5/2023	7	Diffraction and wave propagation	HW 1 due / HW 2 out
2/7/2023	8	Coherent imaging
2/12/2023	9	Incoherent Imaging, Geometrical optics imaging
2/14/2023	10	Forward Radon transform
2/19/2023	11	Inverse Radon transform	HW 2 due / HW 3 out
2/21/2023	12	X-ray imaging and x-ray computed tomography
2/26/2023	13	SPECT and PET
2/28/2023	14	Iterative reconstructions
3/4/2023		SPRING RECESS – no class	HW 3 due
3/6/2023		SPRING RECESS – no class
3/11/2023	15	Image Processing I – Spatial domain
3/13/2023	16	Image Processing II – Fourier domain
3/18/2023		MIDTERM EXAM (2pm-3:15pm @ Meinel 307)	HW 4 out
3/20/2023	17	Radiometry
3/25/2023	18	Photometric Stereo
3/27/2023	19	Triangulation
4/1/2023	20	Deflectometry	HW 4 due / HW 5 out
4/3/2023	21	Event Sensing
4/8/2023	22	Noise in Imaging Systems
4/10/2023	23	Image Quality
4/15/2023	24	Optical Systems I	HW 5 due / HW 6 out
4/17/2023	25	Optical Systems II
4/22/2023	26	Interferometry and Holography
4/24/2023	27	Speckle and Optical Coherence Tomography
4/29/2023	28	Time-of-Flight and Light-in-Flight	HW 6 due
5/1/2023	29	Non-Line-of-Sight imaging and Imaging through scattering media
Fri 5/3/2023		FINAL EXAM (1pm – 3pm @ Meinel 307)