Higher Order Statistical Signal and Image Processing and Analysis

这项研究关注于信号/图像处理算法的开发、分析和评估，以补充或取代通常的二阶统计量。正在考虑时间序列(仅观察到系统输出)和系统辨识(同时观察到输入和输出)公式；正在研究一维和多维信号和系统。虽然信号的二阶统计量仅是基础系统传递函数大小的函数，但数据的高阶统计量(HOS)携带关于基础信号/系统的相位特征的有用信息，这在诸如数字通信信道均衡、地震子波处理以及图像恢复、分析和合成中出现的去卷积问题中是至关重要的。分别使用高阶累积量函数和高阶累积量谱(或高阶积分累积量谱)的时间域和频域方法正在被追求。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延和多普勒估计，(Iii)未知的、可能非最小相位的盲反卷积，包括图像恢复的信道，以及(Iv)具有噪声输入的系统辨识。

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.