How Students and Algorithms Learn to Filter: Investigating Students' Understanding of Signal Processing Concepts and Bilevel Methods for Learning Filters for Image Reconstruction
Crockett, Caroline
2022
Abstract
Signals and systems (S&S) concepts are the theoretical foundation of machine learning and signal processing, cutting-edge fields with real-world applications in many domains. This dissertation combines two projects on S&S in the fields of engineering education research and image reconstruction. Within the field of engineering education research, this dissertation discusses which S&S concepts students understand and what factors—such as motivation, choice of upper-level electives, or use of evidence-based instructional practices like active learning—influence their understanding. This research project involved three phases. The first phase used quantitative methods to measure CU and investigated factors that predict CU of students at the end of their S&S course. This phase found that measures of ability and motivation are significantly predictive of CU. Phase one also served as a pilot project for the following two phases that concentrate on CU of senior undergraduate students. The second phase used think-aloud interviews and a concept inventory to measure CU of S&S. The results show that many seniors understand some topics, such as filtering and time invariance, but struggle with other S&S concepts, such as linearity and convolution. The third phase used interviews and qualitative data analysis methods to investigate what factors impact CU over the course of an undergraduate degree. The results provide recommendations for how instructors and curriculum designers can improve students’ CU of S&S, such as emphasizing the purpose of concepts, using contrasting examples in lectures, translating mathematics, and repeating concepts across multiple courses. The second part of this dissertation applies concepts from S&S to image reconstruction. Image reconstruction is the process of taking input data from one signal space and producing an interpretable image. In medical image reconstruction, state-of-the-art methods use advances in machine learning and training datasets to learn parameters that can be used to reconstruct high-quality images with fewer measurements, thus decreasing radiation exposure for patients while providing doctors with high-quality images to properly diagnose and treat many diseases. The image reconstruction project in this dissertation motivates and reviews bilevel methods for learning image reconstruction parameters. Bilevel methods are task-based, so that learned parameters are expected to perform best at reconstructing; are explainable and interpretable, thus improving the likelihood that doctors will trust and adopt them; and allow for different measures of image quality, including traditional mean square error metrics that are easy to use and metrics that more accurately capture human perception. The results demonstrate that parameters learned in a common non-bilevel formulation under-perform handcrafted parameters due to the structure of the learning problem and that bilevel methods help to address this gap.Deep Blue DOI
Subjects
conceptual understanding image reconstruction signals and systems bilevel methods
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