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The Bioimaging and Signals track is geared towards students with interests in any of the following areas:
1. Development and application of imaging devices;
2. Signal and image processing methods;
3. Biological/biomedical signal acquisition and analysis;
4. Computational modeling of biomedical signals and systems;
5. Biological/biomedical control systems; and/or
6. Biologically inspired signal and image processing.
This track may be particularly attractive to students with undergraduate degrees in bioengineering/biomedical engineering; electrical engineering; computer science and engineering; math; and/or physics, but it is open to all bioengineering graduate students.
Students who have not had “signals and systems” and/or “linear systems” courses at the undergraduate level, similar to BIOENG 1320 or MEMS 1014 offered at Pitt, may find that they lack the prerequisites for many of the track courses. Moreover, knowledge of the fundamentals of signals and systems provided in these courses will be required to pass the Preliminary Exam in the Bioimaging and Signals Track. Accordingly, students lacking this background are strongly encouraged to audit or take one of these three courses prior to taking the prelim exam in the late Spring of the first year. (Note that undergraduate courses do not fulfill graduate degree requirements.)
Students in the Bioimaging and Signals Track must complete 12 credits (4 different graduate level courses) in order to satisfy track requirements. At least one of these courses must be in the “bio-imaging” area, and at least one must be in the “signals and systems” area, as follows:
Signals and systems course requirements (choose at least one):
BIOENG 2005 - RADIOFREQUENCY MEDICAL DEVICES AND APPLICATIONS OF ELECTROMAGNETICS IN MEDICINE
BIOENG 2340 - INTRODUCTION TO MEDICAL IMAGING AND IMAGE ANALYSIS
ECE 2523 - DIGITAL SIGNAL PROCESSING
ECE 2646 - LINEAR SYSTEM THEORY
CMU 16-725 - (BIO)MEDICAL IMAGE ANALYSIS
Bioimaging course requirements (choose at least one):
BIOENG 2330 - BIOMEDICAL IMAGING
BIOENG 2340 - INTRODUCTION TO MEDICAL IMAGING AND IMAGE ANALYSIS
BIOENG 2505 - MULTI MODAL BIOMEDICAL IMAGING TECHNOLOGIES: FUNCTIONAL, MOLECULAR AND HYBRID IMAGING TECHNIQUES
BIOENG 3195 - ADVANCED TOPICS IN BIOENGINEERING
CMU 16-725 - (BIO)MEDICAL IMAGE ANALYSIS
The remaining two track courses may be selected from the lists above, or from the list below of the variety of bioimaging and signals courses available through Pitt and CMU that fulfill track requirements. However, the list is by no means comprehensive, and students are free and encouraged to explore course offerings from other science and engineering departments, at Pitt and CMU, including Electrical and Computer Engineering; Computer Science; Physics; and Neuroscience. Coupled with one additional open elective, the track requirements provide flexibility for students, in consultation with their research mentor, to design an appropriate curriculum of graduate study to complement their research.
Possible courses for the 3rd and 4th required track courses:
Note: courses not listed here require pre-approval by the Track Coordinators in order to fulfill track requirements:
BIOENG 2005 - RADIOFREQUENCY MEDICAL DEVICES AND APPLICATIONS OF ELECTROMAGNETICS IN MEDICINE
BIOENG 2045 - COMPUTATIONAL CASE STUDIES IN BIOMEDICAL ENGINEERING
BIOENG 2330 - BIOMEDICAL IMAGING
BIOENG 2340 - INTRODUCTION TO MEDICAL IMAGING AND IMAGE ANALYSIS
BIOENG 2383 - BIOMEDICAL OPTICAL MICROSCOPY
BIOENG 2390 - ARTIFICIAL INTELLIGENCE APPLICATIONS IN BIOENGINEERING
BIOENG 2505 - MULTI MODAL BIOMEDICAL IMAGING TECHNOLOGIES: FUNCTIONAL, MOLECULAR AND HYBRID IMAGING TECHNIQUES
BIOENG 2515 - CARDIO SYSTM DYNAMICS & MODELING
ECE 2372 - PATTERN RECOGNITION
ECE 2521 - ANALYSIS STOCHASTIC PROCESSES
ECE 2523 - DIGITAL SIGNAL PROCESSING
ECE 2556 - NEURO-SIGNAL MODELING AND ANALYSIS
ECE 2646 - LINEAR SYSTEM THEORY
ECE 2671 - OPTIMIZATION METHODS
ECE 3374 - APPLICATIONS OF WAVELET TRANSFORMS
ECE 3526 - MODERN SPECTRAL ESTIMATION
ECE 3650 - OPTIMAL CONTROL
CMU 8-792 - ADVANCED DIGITAL SIGNAL PROCESSING
CMU 10-601 - MACHINE LEARNING
CMU 16-725 - (BIO)MEDICAL IMAGE ANALYSIS
CMU 18-660 - NUMERICAL METHODS FOR ENGINEERING DESIGN AND OPTIMIZATION
CMU 18-790 - WAVELETS AND MULTIRESOLUTION TECHNIQUES
CMU 42-631 - NEURAL DATA ANALYSIS
CMU 42-632 - NEURAL SIGNAL PROCESSING
The “core” knowledge for first-year graduate students in the BioImaging & Signals track consists of a fundamental understanding of circuits, signals and systems that is commonly taught in the undergraduate curriculum in electrical, mechanical, or biomedical engineering. A partial listing of relevant topics includes, but is not limited to:
- Current-voltage relationships of common electric devices, such as resistors, capacitors and inductors, and/or their mechanical analogues (springs, masses and dashpots). Characteristics and solutions of 1st- and 2nd-order circuits / constant-coefficient differential equations.
- Linear, time-invariant (LTI) systems: properties (i.e. linearity, time-invariance, stability, causality); input-output relations; impulse response; step response; transfer function; frequency response; inverse systems; feedback (closed-loop control) systems; superposition theory
- Transforms: Fourier, Laplace.
- LTI filters: low-pass, high-pass, band-pass; time and frequency domain responses. Basic circuit configurations for RC, RL and RLC analog filters. Signal-to-noise ratio (SNR). Bode plots. Polezero plots.
- Discrete-time vs. continuous-time signals and systems: Sampling and aliasing, Shannon sampling theorem, Nyquist rate, Nyquist frequency; s-domain vs. z-domain representations; discrete Fourier vs. continuous Fourier.
In addition, graduate students are expected to have mastered the material covered in their first-year graduate courses.
Students should have a deeper understanding of those areas that are closely related to, or used in, their research; the more closely related to the student’s research, the deeper the knowledge is expected to be. Finally, the student should have an understanding of those areas of his/her research that may fall outside of the core Track knowledge.
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