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

噪声对应于感兴趣信号外部的随机变化，是一个普遍存在的方面，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精确度不断提高，由于许多不可控因素，数字信号仍然带有噪声。本文主要研究了直接从被噪声污染的信号中估计随机噪声模型参数的基本问题。因此，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、无线通信中的频谱感知和感觉神经科学中的数据处理。研究中采用的技术方法是利用原始信号在多种信号表示下的规律性统计特性及其与噪声参数的关系。具体地说，我们将调查由随机带通滤波器构造的域的使用，这些域在揭示典型的？信号的统计特性，特别是与傅立叶、DCT和小波等确定性表示法相比较时。同时，我们将研究观测到的噪声信号的统计量与噪声参数之间的数学关系。基于这些理论发现，这项研究有望带来更有效和高效的噪声盲估计算法。更广泛地说，这项工作还将探索在非平稳噪声统计存在的情况下进行局部噪声盲估计的有效算法。

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.