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<p>The emerging theory of compressed sensing has been nothing short of a revolution
in signal processing, challenging some of the longest-held ideas in signal processing
and leading to the development of exciting new ways to capture and reconstruct signals
and images. Although the theoretical promises of compressed sensing are manifold,
its implementation in many practical applications has lagged behind the associated
theoretical development. Our goal is to elevate compressed sensing from an interesting
theoretical discussion to a feasible alternative to conventional imaging, a significant
challenge and an exciting topic for research in signal processing. When applied to
imaging, compressed sensing can be thought of as a particular case of computational
imaging, which unites the design of both the sensing and reconstruction of images
under one design paradigm. Computational imaging tightly fuses modeling of scene content,
imaging hardware design, and the subsequent reconstruction algorithms used to recover
the images. </p><p>This thesis makes important contributions to each of these three
areas through two primary research directions. The first direction primarily attacks
the challenges associated with designing practical imaging systems that implement
incoherent measurements. Our proposed snapshot imaging architecture using compressive
coded aperture imaging devices can be practically implemented, and comes equipped
with theoretical recovery guarantees. It is also straightforward to extend these ideas
to a video setting where careful modeling of the scene can allow for joint spatio-temporal
compressive sensing. The second direction develops a host of new computational tools
for photon-limited inverse problems. These situations arise with increasing frequency
in modern imaging applications as we seek to drive down image acquisition times, limit
excitation powers, or deliver less radiation to a patient. By an accurate statistical
characterization of the measurement process in optical systems, including the inherent
Poisson noise associated with photon detection, our class of algorithms is able to
deliver high-fidelity images with a fraction of the required scan time, as well as
enable novel methods for tissue quantification from intraoperative microendoscopy
data. In short, the contributions of this dissertation are diverse, further the state-of-the-art
in computational imaging, elevate compressed sensing from an interesting theory to
a practical imaging methodology, and allow for effective image recovery in light-starved
applications.</p>
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