# EE C261. Medical Imaging Signals and Systems

Catalog Description: Biomedical imaging is a clinically important application of engineering, applied mathematics, physics, and medicine. In this course, we apply linear systems theory and basic physics to analyze X-ray imaging, computerized tomography, nuclear medicine, and MRI. We cover the basic physics and instrumentation that characterizes medical image as an ideal perfect-resolution image blurred by an impulse response. This material could prepare the student for a career in designing new medical imaging systems that reliably detect small tumors or infarcts.

Units: 4

Course Objectives: • understand how 2D impulse response or 2D spatial frequency transfer function (or Modulation Transfer Function) allow one to quantify the spatial resolution of an imaging system. • understand 2D sampling requirements to avoid aliasing • understand 2D filtered backprojection reconstruction from projections based on the projection-slice theorem of Fourier Transforms • understand the concept of image reconstruction as solving a mathematical inverse problem. • understand the limitations of poorly conditioned inverse problems and noise amplification • understand how diffraction can limit resolution---but not for the imaging systems in this class • understand the hardware components of an X-ray imaging scanner •, • understand the physics and hardware limits to spatial resolution of an X-ray imaging system • understand tradeoffs between depth, contrast, and dose for X-ray sources • understand resolution limits for CT scanners • understand how to reconstruct a 2D CT image from projection data using the filtered backprojection algorithm • understand the hardware and physics of Nuclear Medicine scanners • understand how PET and SPECT images are created using filtered backprojection • understand resolution limits of nuclear medicine scanners • understand MRI hardware components, resolution limits and image reconstruction via a 2D FFT • understand how to construct a medical imaging scanner that will achieve a desired spatial resolution specification.

Student Learning Outcomes: • students will be tested for their understanding of the key concepts above • undergraduate students will apply to graduate programs and be admitted • students will apply this knowledge to their research at Berkeley, UCSF, the national labs or elsewhere • students will be hired by companies that create, sell, operate or consult in biomedical imaging

Prerequisites: Undergraduate level course work covering integral and differential calculus, two classes in engineering-level physics, introductory level linear algebra, introductory level statistics, at least 1 course in LTI system theory including (analog convolution, Fourier transforms, and Nyquist sampling theory). The recommended undergrad course prerequisites are introductory level skills in Python or Matlab and either EECS 16A, EECS 16B and EL ENG 120, or MATH 54, BIO ENG 101, and BIO ENG 105.

Formats:
Spring: 3.0 hours of lecture and 1.0 hours of discussion per week
Fall: 3.0 hours of lecture and 1.0 hours of discussion per week