Bayesian computation for low-photon imaging

图像包含大量具有重大经济和社会价值的数据，在过去十年中，它们已成为许多学科(如医学、生物学、农业、国防、地球科学和无损检测)的基本信息来源。这些学科现在推动了尖端和专业成像设备的发展。这类设备将两种形式的创新紧密结合在一起，以提供最先进的性能：1)将技术和物理推向极限的复杂仪器和传感器，以及2)高度先进的计算成像(CI)方法，它仔细分析生成的原始数据，以产生精细细节的锐利图像。这项建议侧重于用于量子增强成像的CI方法，这是一种新的成像范式，试图利用光的量子本质，在空间和时间分辨率和动态范围方面远远超过经典光学的可能。这一变革性的方法将极大地推动成像技术的发展，并产生巨大的社会和经济影响。为了确保英国走在这一战略技术发展的前沿，英国政府于2014年创建了量子增强成像中心(QUANTIC)，作为英国国家量子技术计划的一部分，该计划于今年更新。量子公司已经开发出适用于极端成像条件的令人印象深刻的新型传感器。然而，传感器技术的这些进步并没有与CI方法的进步相匹配，严重危害了这些有前途的技术的影响。该提议的目的是开发专门为解决量子增强成像问题而设计的CI方法，在这些问题中，很少观察到光子(即低光子和单光子成像问题)。我们的方法将在贝叶斯统计框架下制定，这特别适合于解决这些具有挑战性的成像问题，因为：1)它允许使用复杂的统计模型来准确描述潜在的物理；2)它允许自动校准模型；3)它提供工具来量化提供的解的不确定性。目前，贝叶斯统计CI方法的好处和优越的性能是以高昂的计算成本为代价获得的。我们计划通过开发专门的计算方法来显著加快量子增强成像问题的贝叶斯解决方案，这些方法结合并扩展了应用数学、计算统计和人工智能的不同领域的想法。我们相信，快速贝叶斯计算方法的可获得性将释放这些有前途的量子增强成像技术的潜力，并导致它们在科学和工程中的广泛应用，产生巨大的社会效益和经济效益，对医学、生物学、农业、国防、地球科学和无损检测产生影响。为了保证这一影响，在项目期间，我们将把所提出的方法应用于三个重要的量子增强成像问题(低光子多光谱单像素成像、高分辨率PGET和带有阵列传感器的单光子3D LIDAR)。这些应用程序将与世界领先的专家合作进行调查，这些专家将提供数据和培训，并帮助传播研究成果。为了最大限度地发挥我们工作的影响，我们还将开发开源软件--包括文档和演示--我们将在网上分享这些软件，并在旨在向公众介绍STEM研究和激励年轻人追求STEM职业生涯的外联活动中使用这些软件。该项目还将有助于培养下一代人工智能和量子技术方面的顶级人才。

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.