Daun Kyle J, Waslander Steven L, Tulloch Brandon B
Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada.
Appl Opt. 2011 Feb 20;50(6):891-900. doi: 10.1364/AO.50.000891.
In infrared species tomography, the unknown concentration distribution of a species is inferred from the attenuation of multiple collimated light beams shone through the measurement field. The resulting set of linear equations is rank-deficient, so prior assumptions about the smoothness and nonnegativity of the distribution must be imposed to recover a solution. This paper describes how the Kalman filter can be used to incorporate additional information about the time evolution of the distribution into the reconstruction. Results show that, although performing a series of static reconstructions is more accurate at low levels of measurement noise, the Kalman filter becomes advantageous when the measurements are corrupted with high levels of noise. The Kalman filter also enables signal multiplexing, which can help achieve the high sampling rates needed to resolve turbulent flow phenomena.
在红外物质层析成像中，通过测量穿过测量场的多束准直光束的衰减来推断物质未知的浓度分布。由此产生的线性方程组是秩亏的，因此必须对分布的平滑性和非负性施加先验假设才能得到解。本文描述了如何使用卡尔曼滤波器将关于分布随时间演变的额外信息纳入重建过程。结果表明，虽然在低测量噪声水平下进行一系列静态重建更准确，但当测量受到高水平噪声干扰时，卡尔曼滤波器就变得具有优势。卡尔曼滤波器还能实现信号复用，这有助于实现解析湍流现象所需的高采样率。
