The MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Chemical and Physical Sciences, Victoria University of Wellington, PO Box 600 Wellington, New Zealand.
Appl Spectrosc. 2009 Dec;63(12):1370-6. doi: 10.1366/000370209790108905.
Wavelet transforms are an extremely powerful tool when it comes to processing signals that have very "low frequency" components or non-periodic events. Our particular interest here is in the ability of wavelet transforms to remove backgrounds of spectroscopic signals. We will discuss the case of surface-enhanced Raman spectroscopy (SERS) for illustration, but the situation it depicts is widespread throughout a myriad of different types of spectroscopies (IR, NMR, etc.). We outline a purpose-built algorithm that we have developed to perform an iterative wavelet transform. In this algorithm, the effect of the signal peaks above the background is reduced after each iteration until the fit converges close to the real background. Experimental examples of two different SERS applications are given: one involving broad backgrounds (that do not vary much among spectra), and another that involves single molecule SERS (SM-SERS) measurements with narrower (and varying) backgrounds. In both cases, we will show that wavelet transforms can be used to fit the background with a great deal of accuracy, thus providing the framework for automatic background removal of large sets of data (typically obtained in time-series or spatial mappings). A MATLAB((R)) based application that utilizes the iterative algorithm developed here is freely available to download from http://www.victoria.ac.nz/raman/publis/codes/cobra.aspx.
小波变换在处理具有非常“低频”成分或非周期性事件的信号时是一种极其强大的工具。我们特别感兴趣的是小波变换能够去除光谱信号背景的能力。我们将以表面增强拉曼光谱（SERS）为例进行讨论，但这种情况在各种不同类型的光谱学（IR、NMR 等）中都很普遍。我们概述了我们专门开发的一种用于执行迭代小波变换的算法。在这个算法中，在每次迭代后，都会减少信号峰高于背景的影响，直到拟合接近真实背景。我们给出了两个不同 SERS 应用的实验示例：一个涉及宽背景（在光谱之间变化不大），另一个涉及具有较窄（且变化）背景的单分子 SERS（SM-SERS）测量。在这两种情况下，我们将表明小波变换可以非常准确地拟合背景，从而为自动去除大量数据（通常在时间序列或空间映射中获得）的背景提供了框架。一个基于 MATLAB((R)) 的应用程序，利用这里开发的迭代算法，可以从 http://www.victoria.ac.nz/raman/publis/codes/cobra.aspx 自由下载。
