CIF: Small: Integrating Imaging Detectors

集成探测器在科学和工程应用中的普遍存在表明，各种真实世界的测量都是高维计数数据。然而，计数数据通常是测量感兴趣的基本矢量值信号的间接手段--无论是像素传感器中的光强度、带电气体粒子中的能量，还是扫描电子显微镜检测到的非弹性散射中的能量--这些都不能直接测量。积分探测器中异方差噪声的两个主要来源是描述光子到达的随机性的泊松过程和粒子到电子转换产生的Fano噪声。因此，从观察到的计数数据估计该信号在不同的应用中起着突出的作用。本研究由四项调查组成。首先是从泊松计数数据中估计原始信号值的经典任务，为此提出了一种基于小波变换的最优去噪方法。其次，将噪声模型从经典的泊松破坏扩展到Fano噪声，这是一项具有挑战性的任务，因为Fano噪声的分布并不确切。三是针对噪声图像传感器数据中的视觉信息损失进行客观评价的研究，对图像信号恢复和视觉图像质量两方面的问题进行了讨论。第四是努力在集成探测器分辨率和噪声之间进行精确的权衡，目标是量化信号中信息的可识别性，而不是原始信号值。

The ubiquity of integrating detectors in scientific and engineering applications suggests that a variety of real-world measurements are high-dimensional count data. Count data, however, is usually an indirect means of measuring the underlying vector-valued signal of interest - whether it be light intensity in a pixel sensor, energy in charged gas particles, or energy in inelastic scattering detected by scanning electron microscope - that cannot be measured directly. The two dominating sources of heteroskedastic noise in an integrating detector are the Poisson process that describes the stochasticity in photon arrival and the Fano noise stemming from particle-to-electron conversion. As such, the estimation of this signal from the observed count data therefore plays a prominent role across diverse applications. This research is comprised of four investigations. First is the classical task of estimating the raw signal value from the Poisson count data, for which an optimal wavelet transform-based denoising method is being developed. Second, the noise model is extended from the cannonical Poisson corruption to Fano noise - a challenging task since the distribution of Fano noise is not known exactly. Third is a study aimed at objectively valuating the visual information loss in noisy image sensor data, where the problems of image signal recovery and visual image quality are reasoned jointly. Fourth is an effort to make precise the trade offs between integrating detector resolution and noise, where the goal is to quantify the discernibility of information in signal rather than the raw signal values.