RIA: Optimum Multiresolution Analysis in Statistical Signal Processing

这个项目的目标是：(1)研究非平稳随机过程的多分辨逼近；(2)建立一个研究非平稳信号的新框架；(3)开发新的分析工具来解决相关的挑战性问题，如时变滤波、估计和编码。对于给定过程的“最佳”(均方意义下)低分辨率近似，提出了一种最优尺度函数。这种近似有望改善用于子带编码以有效传输图像或语音数据的滤波器组的性能。它还将导致模式识别问题中的最优特征提取过程，出现在水下和遥感应用中。

The goals of this project are to: (1) study multiresolution approximations of nonstationary stochastic processes; (2) establish a novel framework for studying nonstationary signals, and (3) develop new analytic tools for addressing the related challenging problems of time-varying filtering, estimation, and coding. An optimal scaling function is proposed for "best" (in the mean- square sense) low-resolution approximation of a given process. Such an approximation is expected to improve the performance of filter banks used in subband coding for the efficient transmission of image or voice data. It will also lead to optimal feature extraction procedures in pattern recognition problems, appearing in underwater and remote sensing applications.