CIF: Small: Low-Light 3D Imaging: From Fundamental Limits to Practical Systems

由于越来越多地使用计算方法和各种各样的意义，形成图像的重点，空间分辨光是一个快速创新的领域？形象。？ 通过光学手段获得的图像除了具有类似于激光器的特性外，还可以显示距离、厚度、化学浓度、分子能量转移和许多其他特性，这取决于收集和分析的方法。 在许多情况下，希望从非常少的检测光形成图像;收集更多的光可能需要更多的能量、时间或空间，或者可能损坏正在研究的生物或分子样品。 该项目将开发新的方法，从非常少的检测光计算成像。 其目标既是理论上的，也是实践上的：了解准确性和检测到的光量之间的基本权衡，并接近最佳性能。 该项目有可能改善远程遥感以及各种形式的microscope.的半经典模型的光探测表明，光场强度转化为在单光子探测器输出观察到的泊松过程的速率。 在充分利用这一流行模式方面存在着重大的智力挑战。 虽然近年来已经取得了将分段平滑（例如，小波域稀疏性）和在自然信号中常见的其他结构，该进展很大程度上依赖于高斯的测量似然函数。 为泊松过程设计的信号处理方法并不常见，它们中的大多数都是逐点应用，而不是允许包含有用的信号先验。 凸信号先验与泊松似然的朴素组合可能导致难以处理的非凸优化。该项目将开发替代方法，特别是针对实时3D采集。

Forming images with focused, spatially resolved light is an area of rapid innovation due to the growing use of computational methods and the variety of meanings of ?image.? Aside from being photograph-like, an image acquired through optical means could show distances, thicknesses, chemical concentrations, molecular energy transfers and many other properties, depending on the methods of collection and analysis. In many settings, it is desirable to form images from very little detected light; collecting more light could take more energy, time, or space, or it could damage a biological or molecular sample under investigation. This project will develop new methods for computational image formation from very little detected light. The goals are both theoretical and practical: to understand the fundamental trade-offs between accuracy and amount of detected light, and to approach the best possible performance. The project has the potential to improve long-range remote sensing as well as various forms of microscopy.The semiclassical model of light detection dictates that light field intensity translates to the rate of a Poisson process observed at a single-photon detector output. There are significant intellectual challenges in fully exploiting this prevailing model. While progress has been made in recent years to incorporate piecewise smoothness (e.g., wavelet-domain sparsity) and other structure that is commonly found in natural signals, this progress has largely relied on measurement likelihood functions being Gaussian. Signal processing methods designed for Poisson processes are uncommon, and most of them apply pointwise rather than to allow the inclusion of useful signal priors. Naive combinations of convex signal priors with Poisson likelihoods can lead to intractable nonconvex optimizations. This project will develop alternative approaches, especially toward real-time 3D acquisition.