Efficient computational tools for inverse imaging problems

用目前最先进的数码相机拍摄的照片像素在1000万到2000万之间。一些摄像头的传感器像素高达4100万。尽管传感器和光学技术取得了进步，但在苛刻的条件下，技术上完美的照片仍然很难拍到。在光线较弱的情况下，即使是最好的相机也会产生嘈杂的图像。休闲摄影师不能总是拿着相机不动，尽管有先进的减震技术，照片还是变得模糊了。因此，我们面临着在后期处理中改进照片的挑战。这将是一个理想的自动化过程，基于可以依赖的数学上很好理解的模型。数千万像素的真实照片的困难在于由此产生的优化问题--根据模型找到最佳增强图像的任务--是巨大的，并且计算非常密集。此外，成像问题的计算量通常非常大。基于数学原理的最先进的图像处理技术只能实时处理小图像。此外，为模型选择正确的参数可能很困难。参数选择可以方便，但同样是以计算非常密集的方式。现在的问题是，我们能否设计出更快的优化算法，使这项任务和其他图像处理任务易于处理，以处理真实的高分辨率照片？拟议中的项目的目标是开发能够完成这项任务的优化算法。该项目的重点是研究适用于各种图像处理任务和一般大数据问题的通用方法。除了摄影，我们还将把开发的工具应用到生物学和医学的问题上，涉及磁共振成像和显微镜。

A photograph taken with current state-of-the-art digital cameras has between 10 to 20 million pixels. Some cameras have up to 41 million sensor pixels. Despite advances in sensor and optical technology, technically perfect photographs are still elusive in demanding conditions. In low light even the best cameras produce noisy images. Casual photographers cannot always hold the camera steady, and the photograph becomes blurry despite advanced shake reduction technologies. We are thus presented with the challenge of improving the photographs in post-processing. This would desirably be an automated process, based on mathematically well understood models that can be relied upon.The difficulty with real photographs of tens of millions of pixels is that the resulting optimisation problems -- the task of finding the best enhanced image according to a model -- are huge, and computationally very intensive. Moreover, imaging problems generally computationally very intensive. State-of-the-art image processing techniques based on mathematical principles are only up to processing small images in real time. Further, choosing the right parameters for the models can be difficult. Parameter choice can be facilitated, but again in computationally very intensive ways. The question now is, can we design faster optimisation algorithms that would make this and other image processing tasks tractable for real high-resolution photographs?The objective of the proposed project is to develop optimisation algorithms that are up to this task. The focus of the project is on general methods that will be applicable to a wide variety of image processing tasks and general big data problems. Besides photography, we will apply the developed tools to problems from biology and medicine, involving magnetic resonance imaging and microscopy.