Overview

Wavelets, the "little waves" of signal processing, came to the fore in the early 1990s as an attractive alternative to classical Fourier Transform based signal and image processing. While the underlying concepts behind wavelets have been known for close to a century (Haar described his multiresolution analysis in 1910), the pioneering work of many applied mathematicians have brought new insights into the field and wavelet theory and applications have found use in diverse areas like geophysical signal processing, medical imaging, and information theory. In this chapter, we look at wavelets from the image processing perspective, and develop wavelet-based algorithms for two operations previously studied in this book. The topic of edge detection was covered in 5.1, and in the first part of this chapter we develop a wavelet-based edge detection algorithm, and of course implement it on the DSP. The enhancement of images through various filtering schemes was the focus of Chapter 4, where we utilized linear, non-linear, and adaptive filters to denoise images. In the second part of this chapter, the topic of wavelet denoising is introduced and a fixed-point implementation tested on the C6416 is discussed.

Prior to embarking on this abbreviated tour of wavelet-based image processing, we must introduce at least a bare minimum of theory so that the algorithms and code make some sense to the reader. If the following discussion in 6.1 feels too abstract or mathematical in nature, I urge the reader to not get discouraged...