Blind Noise Estimation Using Signal Statistics in Random Band-Pass Domains

噪声是信号处理中一个普遍存在的问题，它影响着信号处理中许多任务的性能。即使现代采集设备的质量和复杂性不断提高，由于许多不可控因素，数字信号仍然携带噪声。本研究的重点是直接从噪声污染的信号中估计随机噪声模型的参数的基本问题。作为一个直接的结果，这项调查的结果将适用于广泛的领域，包括数字图像的法医分析，医学图像的自动处理，无线通信中的频谱传感和感觉神经科学中的数据处理。本研究采用的技术方法利用了原始信号在多种信号表示中的常规统计特性及其与噪声参数的关系。具体而言，我们将调查使用的域构造的随机带通滤波器，更有效地揭示？典型的？信号的统计特性，特别是与确定性表示（如傅立叶、DCT和小波）相比时。同时，我们将研究噪声信号的观测统计量与噪声参数之间的数学关系。利用这些理论研究成果，本研究有望导致更有效和更高效的算法盲噪声估计。更一般地说，所提出的工作还将探索有效的算法，在非平稳噪声统计的存在下，盲局部噪声估计。

Noise, which corresponds to random variations extrinsic to the signals of interest, is an ubiquitous aspect that affects the performance of many tasks in signal processing. Even with the improving quality and sophistication of the modern acquisition devices, digital signals still carry noise due to many incontrollable factors. This research focuses on the fundamental problem of estimating parameters of the random noise model directly from a noise corrupted signal. As an immediate consequence, the results of this investigation will be applicable in a wide range of fields, including the forensic analysis of digital images, automatic processing of medical images, spectrum sensing in wireless communications and data processing in sensory neuroscience. The technical approach taken in this research exploits the regular statistical properties of the original signals in multiple signal representations and their relationship with the noise parameters. Specifically, we will investigate the use of domains constructed from random band-pass filters that are more effective in revealing ?typical? statistical properties of the signals, especially when compared with deterministic representations such as Fourier, DCT, and wavelet. Concurrently, we will investigate the mathematical relationship between the observed statistics of noisy signal and the noise parameters. Drawing on these theoretical findings, this research is expected to lead to more effective and efficient algorithms for blind noise estimation. More generally, the proposed work will also explore efficient algorithms for blind local noise estimation in the presence of non-stationary noise statistics.