Compressed Representations of Signals and Models
Ashbrock, Jonathan
0000-0002-1889-7253
:
2021-02-22
Abstract
In modern digital systems, the efficient representation of data becomes an important consideration.
The encoding and decoding process of digital signals can be computationally expensive
and can often induce significant errors. This dissertation studies three new methods in efficient
data compression and recovery. The first, Stochastic Markov Gradient Descent, is a technique for
training neural networks with small memory footprints. The second, Dynamical Quantization, exploits
rigid structure available in frame theory to produce exponentially accurate quantized redundant
frame expansions. The third and final method introduced in this dissertation is Look Ahead
Thresholding which employs gradient-informed projections to enhance standard compressed sensing
algorithms. Each of these methods is supported by rigorous mathematical theory explaining
their function as well as practical experiments showcasing applicability to real problems.