Measurements and operators: Reworking the essential imaging elements

We solve imaging problems by recovering, transforming, and modifying what we have---the measurements and the operator. In the first parts of this thesis, we formulate techniques for imaging problems where the phase of the measurements is lost. We begin by showing how to use distance geometry to recover the missing phase of these measurements. This enables us to rapidly perform matrix-vector optically. Knowing the measurement phase is also useful because it transforms the cumbersome quadratic problem of optical imaging operator calibration into a simple linear problem which, for typical sized operators, can be solved in minutes rather than hours. However, unfortunately calibrated operators have errors which can result in poor reconstructions when used for imaging. This motivates us to next create a total least squares framework to account of operator errors when imaging with phaseless measurements. The effectiveness of all these phase problem techniques is verified by experiments on optical hardware. We then use deep learning for scenarios where measurements are scarce and training data is not available. Instead of learning a map from measurements to target reconstructions, we learn a map from measurements to low-dimensional projections of the target. The projections are viewed as measurements from a imaging operator built of multiple projection operators. Solving this new inverse problem gives reconstructions that are more robust to measurement noise. Next, we solve imaging problems when the measurement coordinates such as sensor locations or projection angles are uncertain. Using implicit neural networks and differentiable splines, we learn a representation of the measurements which can be evaluated at any measurement coordinate. By optimizing the inputs at the same time as the measurement representation parameters, we learn the unknown measurement coordinates. To ensure consistency we also jointly reconstruct the final image during the optimization.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Gupta, Sidharth

Contributors dc:contributor

• Dokmanic, Ivan
• Bresler, Yoram
• Singer, Andrew C
• Zhao, Zhizhen

• Signal Processing
• Machine Learning
• Imaging
• Phase Retrieval
• Inverse Problems
• Operator Error
• Measurements
• Random Scattering

Statement dc:rights

• Copyright 2023 Sidharth Gupta

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120272

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120272