基于信号不变量的非线性盲声源分离
Performing Nonlinear Blind Source Separation with Signal Invariants
摘要：
给定多分量测量值x（t）的时间序列，非线性盲声源分离（BSS）的通常目标是找到“源”时间序列s（t），该“源”时间序列由测量值的统计独立组合组成。本文要求源时间序列在（s，ds/dt）空间中的密度函数等于各分量密度函数的乘积。BSS问题的这种公式化具有唯一的解决方案，直到排列和分量变换。可分离性施加限制的某些局部不变（标量）的功能x，这是来自本地高阶相关的数据的速度dx/dt。数据是可分离的，当且仅当它们满足这些约束，并且如果满足这些约束，则可以从数据显式地构造源。该方法说明了使用它来分离两个语音类似的声音记录与一个麦克风。
英文摘要：
Given a time series of multicomponent measurements x(t), the usual objective of nonlinear blind source separation (BSS) is to find a "source" time series s(t), comprised of statistically independent combinations of the measured components. In this paper, the source time series is required to have a density function in (s,ds/dt)-space that is equal to the product of density functions of individual components. This formulation of the BSS problem has a solution that is unique, up to permutations and component-wise transformations. Separability is shown to impose constraints on certain locally invariant (scalar) functions of x, which are derived from local higher-order correlations of the data's velocity dx/dt. The data are separable if and only if they satisfy these constraints, and, if the constraints are satisfied, the sources can be explicitly constructed from the data. The method is illustrated by using it to separate two speech-like sounds recorded with a single microphone.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
