Multiscale Methods for Denoising and Compression

Multiscale methods for denoising and compression are discussed in this chapter. Denoising of an individual signal is usually performed by various filtering methods based on assumptions about the nature of the errors and the smoothness of the underlying signal. These methods are the primary emphasis of this chapter. For denoising multivariate data, fundamental or empirical models relating the variables may be used. Denoising with fundamental process models is referred to as “data reconciliation,” and requires solution of a constrained optimization problem. If an accurate fundamental model is not available, multivariate data may be denoised by empirical modeling methods, such as principal component analysis. Because accurate process models relating the hundreds of measured variables are not easily obtained, the simplest and most widely used denoising methods do not rely on a fundamental or empirical process model. The chapter reviews multiscale wavelet-based representation of data and its advantages. Then, various filtering and compression techniques are described, which include linear filtering such as finite impulse response (FIR) and infinite impulse response (IIR) filtering, and nonlinear filtering and compression such as median hybrid filters (FMH) filtering and multiscale filtering. Finally, an online multiscale filtering technique is presented.