New proximal algorithms for computational imaging: From optimisation theory to enhanced deep learning

计算成像的新近端算法：从优化理论到增强型深度学习

• 批准号: EP/X028860/1
• 负责人: Audrey Repetti
• 金额: $ 36.23万
• 依托单位: Heriot-Watt University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX028860%2F1
• 关键词: New; proximal; algorithms; computational; imaging

Reliable data-driven decision-making processes depend on the robustness of the methods used to interpret the data. For many applications, ranging from healthcare to astronomy, defence and finance, data interpretation consists of solving an inverse problem, by estimating an unknown object from degraded measurements (e.g., a brain image from an MR scan), that becomes even more challenging for high dimensional data. A classical approach is to define the unknown object as a solution to a minimisation problem. Such problems can be solved efficiently using optimisation algorithms, most of them having well established theoretical guarantees. Their theoretical analysis are often complex, involving tools as convex, nonconvex, stochastic optimisation theories, and monotone operator theory. Recently, growing interest has been given to optimisation methods involving NNs. Two main classes can be distinguished: PnP algorithms injecting NNs in iterative algorithms, and unfolded NNs unrolling finite number of iterations of an algorithm. Although these approaches have been shown to produce high quality results, their theoretical behavior is still not fully understood.This project will provide new hybrid optimisation methods involving NNs, with theoretical results, to accurately solve high dimensional inverse problems. To this aim, averaging properties of unfolded NNs will be investigated, and the resulting NNs will be plugged into proximal algorithms leading to convergent PnP methods. Characterisation of the resulting method outputs will be investigated. The new algorithms will be used for computational imaging. We will particularly focus on two photon imaging applications in medicine.

可靠的数据驱动决策过程取决于用于解释数据的方法的鲁棒性。对于许多应用，从医疗保健到天文学，国防和金融，数据解释包括解决反问题，通过估算从降解测量值的未知物体（例如，MR SCAN的大脑图像）估算一个未知物体，对于高维数据而言，这变得更具挑战性。一种经典的方法是将未知对象定义为解决最小化问题的解决方案。可以使用优化算法有效地解决此类问题，其中大多数具有很好的理论保证。他们的理论分析通常很复杂，涉及凸，非凸，随机优化理论和单调操作者理论的工具。最近，人们对涉及NNS的优化方法的兴趣日益增长。可以区分两个主要类：PNP算法在迭代算法中注入NN，以及展开的NNS展开算法的有限数量。尽管这些方法已被证明会产生高质量的结果，但其理论行为仍未得到充分理解。该项目将提供涉及NNS的新混合优化方法以及理论上的结果，以准确解决高维逆问题。为此，将研究展开的NNS的平均属性，并将所得的NNS插入近端算法中，从而导致趋同的PNP方法。将研究结果方法输出的表征。新算法将用于计算成像。我们将特别关注医学中的两个光子成像应用。