**Mathematics of Image Science (BME 470/570 and ESE 5931)**

Department of Biomedical Engineering

2:30-4 pm, Whitaker 218

Fall 2018 – Fall 2020

**Course description**: The course will expose students to a unified treatment of the mathematical properties of images and imaging. This will include an introduction to linear vector space theory, operator theory on Hilbert spaces, and concepts from applied functional analysis. Further, concepts from Fourier analysis and integral transforms (e.g. Radon transform) will be discussed. These tools will be applied to conduct deterministic analyses of imaging systems that are described as continuous-to-continuous, continuous-to-discrete, and discrete-to-discrete mappings from object properties to image data.

**Course outcomes**: By the end of this course, the student would have learned to describe the process of imaging within a rigorous unified mathematical framework. Further, the student would also learn tools to analyze the deterministic and stochastic properties of imaging systems. The course would serve as a foundation for future courses on computational imaging, image science, image reconstruction, and imaging technologies.

**Credit hours**: 3 units

**Learning management system**: Canvas (https://mycanvas.wustl.edu/)

**Pre-requisites:**

- Familiarity with Matlab (Please see Instructor if not familiar with Matlab)

**Required textbook: **

- Foundations of Image Science, Harrison H. Barrett and Kyle J. Myers (https://www.amazon.com/Foundations-Image-Science-Harrison-Barrett/dp/0471153001). Soft copy of the book is available from the library. A hard copy of the book is available for reserve at Olin Library (Call number: TK8315 .B37)
- Lecture notes and material will be available on Canvas.

**Class Participation: **Active learning will be used in class. Thus, participation in class activities by students is highly encouraged.