Bayesian computation for low-photon imaging

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Images are rich in data of significant economic and social value, and over the past decade, they have become fundamental sources of information in many disciplines (e.g., medicine, biology, agriculture, defence, earth sciences, and non-destructive testing). These disciplines now drive the development of sophisticated and specialised imaging devices. Such devices tightly combine two forms of innovation to deliver state-of-the-art performance: 1) sophisticated instrumentation and sensors that push technology and physics to the limits, and 2) highly advanced computational imaging (CI) methods that carefully analyse the generated raw data to produce sharp images with fine detail.This proposal focuses on CI methodology for quantum-enhanced imaging, a new imaging paradigm that seeks to exploit the quantum nature of light to go far beyond what is possible in classical optics in terms of spatial and temporal resolution and dynamic range. This transformative approach is poised to dramatically advance imaging technologies and generate great social and economic impact. To make sure that the UK is at the forefront of this strategic technological developments, the UK government created the Quantum Enhanced Imaging Hub (QUANTIC) in 2014 as part of the UK National Quantum Technology Programme, which was renewed this year. QUANTIC has developed impressive new sensors for extreme imaging conditions. However, these advances in sensor technology have not been matched by progress in CI methodology, gravely jeopardizing the impact of these promising technologies.The aim of this proposal is to develop CI methodology specifically designed for solving quantum-enhanced imaging problems in which very few photons are observed (i.e., low-photon and single-photon imaging problems). Our methods will be formulated in the Bayesian statistical framework, which is particularly appropriate for solving these challenging imaging problems because: 1) it enables the use of sophisticated statistical models to accurately describe the underlying physics, 2) it allows the automatic calibration of models, and 3) it provides tools to quantify the uncertainty in the solutions delivered.At present, the benefits and superior performance of Bayesian statistical CI methods is obtained at the expense of a prohibitively high computational cost. We plan to significantly accelerate Bayesian solutions for quantum-enhanced imaging problems by developing specialised computation methods that combine and extend ideas from different areas of applied mathematics, computational statistics, and artificial intelligence. We believe that the availability of fast Bayesian computation methods will unlock the potential of these promising quantum-enhanced imaging technologies and lead to their wide adoption in science and engineering, generating generate great social and economic benefit through an impact on medicine, biology, agriculture, defence, earth sciences, and non-destructive testing. In order to guarantee this impact, during the project, we will apply the proposed methods to three important quantum-enhanced imaging problems (low-photon multispectral single-pixel imaging, high-resolution PGET, and single-photon 3D LIDAR with array sensors). These applications will be investigated in collaboration with world-leading experts who will provide data and training, and help disseminate the research outputs. To maximise the impact of our work, we will also develop open-source software - with documentation and demonstrations - that we will share online and use in outreach activities aimed at informing the public about STEM research and inspiring young people to pursue STEM careers. This project will also help train the next generation of top-tier talent in AI and quantum technology.