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

噪声对应于感兴趣的信号外部的随机变化，是影响信号处理中许多任务性能的普遍方面。尽管现代采集设备的质量和精密程度不断提高，但由于许多不可控因素的影响，数字信号仍然带有噪声。本文研究了直接从噪声干扰信号中估计随机噪声模型参数的基本问题。直接的结果是，这项研究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个信号表示中的规则统计特性及其与噪声参数的关系。具体来说，我们将研究由随机带通滤波器构建的域的使用，它可以更有效地揭示“典型”信号。信号的统计特性，特别是与确定性表征如傅里叶、DCT和小波相比较时。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。利用这些理论发现，本研究有望导致更有效和高效的盲噪声估计算法。更一般地说，提出的工作还将探索在存在非平稳噪声统计的情况下盲局部噪声估计的有效算法。

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.