Discrete Wavelet Transformations, 2nd Edition

CHAPTER 6WAVELET SHRINKAGE: AN APPLICATION TO DENOISING

We now consider the problem of denoising a digital signal. We present a method for denoising called wavelet shrinkage. This method was developed largely by Stanford statistician David Donoho and his collaborators. In a straightforward argument, Donoho [35] explains why wavelet shrinkage works well for denoising problems, and the advantages and disadvantages of wavelet shrinkage have been discussed by Taswell [93]. Vidakovic [98] has authored a nice book that discusses wavelet shrinkage in detail and also covers several other applications of wavelets in the area of statistics.

Note

The material developed in this section makes heavy use of ideas from statistics. If you are not familiar with concepts such as random variables, distributions, and expected values, you might first want to read Appendix A. You might also wish to work through the problems at the end of each section of the appendix. Two good sources for the material we use in this section are DeGroot and Schervish [33] and Wackerly et al. [99].

In the next section we present a basic overview of wavelet shrinkage and its application to signal denoising. In the final two sections of this chapter, we discuss two wavelet‐based methods used to denoise signals. The VisuShrink method [36] is described in Section 6.2 and the SureShrink method [37] is developed in Section 6.3. Section 6.2 contains an application of wavelets and denoising to the problem of image segmentation.

6.1 ...