费舍尔信息框架下弱信号随机共振问题的研究

The theory of noise enhanced signal processing is a hot research topic in the world which is widely concerned in the field of physics, biomedical engineering, image processing and neural dynamics and so on. This project studies that in the small-signal limit noise induced signal-to-noise ratio (SNR) gain of a parallel nonlinear array and the fisher information of asymptotic upper bounds of the nonlinearities can be given. For the given noisy weak signal, the relationship between the nonlinear array performance and the array size, the array structure, the array noise level will be deduced. The optimal type of array noise and array noise intensity for given array structure will be solved and the upper bounds of array, and the machining of stochastic resonance for weak signal will be set up. This project studies the SR effects in an array of static and dynamical nonlinearities in the condition of weak signal, the approximate range for the fisher information of the different nonlinearities and the approximate range for the fisher information of the SR effects and the high-frequency vibration resonance effects. The influence of the kurtosis of external noise for the performance is also studied in the project and the theory of weak signal stochastic resonance will be applied to the digital watermarking.

噪声增强信号处理理论是国际上一个研究热点，在物理、生物医学工程、图像处理、神经动力学等领域得到广泛关注。本项目研究在弱信号的情况下，噪声增强并联非线性阵列的信噪比增益，并给出弱信号处理中的非线性系统渐近性能上界的费舍尔信息条件；对给定的被噪声污染的弱信号，推导非线性阵列性能与阵列数目、阵列结构和阵列内部噪声强度的关系，求解给定阵列结构情况下最优阵列噪声的类型与强度范围，以及阵列性能的上界，建立弱信号随机共振机制；研究弱信号下的动态和静态非线性阵列随机共振效果以及不同系统性能对于费舍尔信息的逼近范围，随机共振和高频振动共振性能对于费舍尔信息的逼近范围，并研究外部噪声峰度对系统性能的影响。并将弱信号随机共振理论结合到数字水印应用中。

噪声增强信号处理理论是国际上一个研究热点，在物理、生物医学工程、图像处理、神经动力学等领域得到广泛关注。本项目研究了在弱信号的情况下，噪声增强并联非线性阵列的信噪比增益，并给出了弱信号处理中的非线性系统渐近性能上界的费舍尔信息条件；研究了弱信号下振荡共振机制，对比振荡共振和随机共振之间的效果，并研究了阵列内部高频正弦信号以及外部不同噪声对振荡共振结果的影响；研究了不同阶数动态非线性系统对随机共振结果的影响，主要对二阶非线性系统的随机共振机制进行研究，并与一阶动态非线性系统的随机共振效果进行了对比。利用极限学习机方法研究了动态非线性系统的智能信号处理算法，并将弱信号随机共振理论用于图像增强的应用研究中。