Compressed sensing recovery with unlearned neural networks

This report investigates methods for solving the problem of compressed sensing, in which the goal is to recover a signal from noisy, linear measurements. Compressed sensing techniques enable signal recovery with far fewer measurements than required by traditional methods such as Nyquist sampling. Signal recovery is an incredibly important area in application domains such as consumer electronics, medical imaging, and many others. While classical methods for compressed sensing recovery are well established, recent developments in machine learning have created wide opportunity for improvement. In this report I first discuss pre-existing approaches, both classical and modern. I then present my own contribution to this field: creating a method using untrained machine learning models. This approach has several advantages which enable its use in complex domains such as medical imaging