Wavelet-based multiscale filtering is a model-free filtering technique that utilizes multiscale representation of data. Multiscale representation is a mathematical representation of a data set as a weighted sum of basis functions called wavelets and scaling functions. The advantage of this multiscale representation is that it separates features occurring at different frequencies. This allows effective removal of noise from important features in the data. Wavelet-based multiscale filtering is a three step procedure: decompose the data at multiple scales, threshold the wavelet coefficients smaller than a threshold value, and finally reconstruct the thresholded coefficients back to the time domain.
Published in Chapter:
Multiscale Filtering and Applications to Chemical and Biological Systems
Mohamed N. Nounou (Texas A&M University at Qatar,Qatar), Hazem N. Nounou (Texas A&M University at Qatar, Qatar), and Muddu Madakyaru (Texas A&M University at Qatar, Qatar)
Copyright: © 2014
|Pages: 38
DOI: 10.4018/978-1-4666-4450-2.ch025
Abstract
Measured process data are a valuable source of information about the processes they are collected from. Unfortunately, measurements are usually contaminated with errors that mask the important features in the data and degrade the quality of any related operation. Wavelet-based multiscale filtering is known to provide effective noise-feature separation. Here, the effectiveness of multiscale filtering over conventional low pass filters is illustrated though their application to chemical and biological systems. For biological systems, various online and batch multiscale filtering techniques are used to enhance the quality of metabolic and copy number data. Dynamic metabolic data are usually used to develop genetic regulatory network models that can describe the interactions among different genes inside the cell in order to design intervention techniques to cure/manage certain diseases. Copy number data, however, are usually used in the diagnosis of diseases by determining the locations and extent of variations in DNA sequences. Two case studies are presented, one involving simulated metabolic data and the other using real copy number data. For chemical processes it is shown that multiscale filtering can greatly enhance the prediction accuracy of inferential models, which are commonly used to estimate key process variables that are hard to measure. In this chapter, we present a multiscale inferential modeling technique that integrates the advantages of latent variable regression methods with the advantages of multiscale filtering, and is called Integrated Multiscale Latent Variable Regression (IMSLVR). IMSLVR performance is illustrated via a case study using synthetic data and another using simulated distillation column data.