With emphasis on medical Computed Tomography, this course included Radon Transforms and an implementation of the FDK (Feldcamp, Davis & Kress) filtered backprojection algorithm, including a parallel GPU version in MATLAB.

Introduction to metric spaces, Lipschitz maps, isometries, group of isometries of the Euclidean plane, surfaces as metric spaces, geodesics, topological spaces, continuity, compactness, connectedness, identification spaces.

Imaging modalities for biomedical research. Microscopy optical physics for confocal microscopy, super resolution microscopy, electron microscopy. Image formation in Ultrasound, X-Ray, Computed Tomography, and Magnetic Resonance Imaging.

Existence, uniqueness and characterization of solutions to finite dimensional unconstrained and constrained optimization problems. Solution methods for finite dimensional unconstrained and constrained optimization problems. Newton and quasi-Newton methods. Globalization strategies, Linear Programming. Least Squares. Quadratic Programming. Convex Programming.

Electrophysiology and bioelectricity at the tissue and whole-organ level for heart and brain.

C/C++ for scientific/engineering computing, including using third-party libraries (openCV) and interfacing with real-world robots (iRobot Create).

Noninvasive visualization of anatomy and/or physiology for detection, diagnosis, and monitoring in therapy. Covers physics, image formation theory, and applications for x-ray, computed tomography, ultrasound, nuclear medicine, and magnetic resonance imaging. Includes implementation of core image formation algorithms.

Acoustic wave physics in biological materials. Practical medical instrumentation. Diagnostic and theraputic applications.

Mathematical foundations of imaging, inluding linear systems, probability and random variables, and detection and estimation theory. Topics in linear systems include convolution, Fourier series and transformations, sampling and discrete-time processing.

Sampling theory, transforms, and filtering for digital images. Implementation of algorithms for enhancement, reconstruction, segmentation, feature detection, and compression on real images.

Survey of technologies and equipment available on campus for biomedical research. Hands-on interactive demonstration and experience of applying the techniques to achieve research goals. Cell Imaging (light sheet, confocal, widefield microscopy), DNA sequencing (Sanger and Next-Gen), high-throughput screening, flow cytometry.