Higher Order Statistical Signal and Image Processing and Analysis

本研究涉及信号/图像处理算法的开发，分析和评估，除了通常的二阶统计之外，或代替二阶统计。正在考虑时间序列（仅观察系统输出）和系统识别（同时观察输入和输出）公式；一维和多维信号和系统都在研究中。信号的二阶统计量仅是底层系统传递函数大小的函数，而数据的高阶统计量（HOS）携带有关底层信号/系统相位特征的有用信息，这在反褶积问题中至关重要，如数字通信信道均衡、地震小波处理和图像恢复、分析和合成中出现的问题。在时域和频域分别采用高阶累积函数和高阶累积谱（或高阶积分累积谱）的方法。正在研究的应用包括：(i)图像纹理合成和分类，（ii）未知空间相关高斯噪声中的微分时滞和多普勒估计，（iii）未知的，可能是非最小相位的盲反卷积，信道包括图像恢复，以及（iv）噪声输入的系统识别。

This research is concerned with development, analysis and evaluation of algorithms for signal/image processing in addition to, or in lieu of, the usual second order statistics. Both time series (only system output is observed) and system identification (both input and output are observed) formulations are being considered; and both one-dimensional and multidimensional signals and systems are being investigated. Whereas the second order statistics of signals are a function of only the underlying system transfer function magnitude, higher order Statistics (HOS) of the data carry useful information about the phase characteristics of the underlying signal/system which is crucial in deconvolution problems such as those arising in digital communication channel equalization, seismic wavelet processing, and image restoration, analysis and synthesis. Time domain as well as frequency domain methods using higher order cumulant functions and higher order cumulant spectra (or higher order integrated cumulant spectra), respectively, are being pursued. Among the applications being investigated are: (i) image texture synthesis and classification, (ii) differential time-delay and doppler estimation in unknown spatially correlated Gaussian noise, (iii) blind deconvolution with unknown, possibly nonminimum phase, channels including image restoration, and (iv) system identification with noise inputs.