Physics-based computational imaging for positron emission tomography and lensless endoscopy

Unraveling the mysteries of life has fascinated humans for millenniums. The emergence of digital computers paved the way to new imaging modalities able to measure properties and signals coming from the inside of the body, without opening it. Computational imaging (CI) was born. CI acquires digital observations that are often not readily understandable (e.g., returning echoes in ultrasound scans). A recovery step is thus necessary to extract useful information. To solve the so-called inverse problem, we resort to an optimization including knowledge about the acquisition process (emission and collection processes, noise corruption, etc.) and the expected properties of the final estimate (e.g., piecewise-smoothness). In this thesis, we focus on two modalities designed to image cellular processes in living organisms: positron emission tomography (PET) and lensless endoscopy (LE). PET imaging is widely used to get information about patient physiological activity. It suffers from blurring and high level of noise. LE exploits fluorescence phenomenon to capture biological information at a micrometer scale. A challenging task is to avoid tissue photobleaching. The dissertation addresses two inverse problems related to PET and LE. First, we study the deblurring of reconstructed PET images polluted by a high level of noise in non-blind and blind contexts. Then, we explore acquisition and reconstruction strategies for LE that exploits nice properties of the sensing operator to collect far less observations as in a traditional scheme. This approach leads to both reduced acquisition time and light exposure.