Publisher's Synopsis
Wavelet Toolbox software contains graphical tools and command line functions that let you examine and explore characteristics of individual wavelet packets, perform wavelet packet analysis of 1-D and 2-D data, use wavelet packets to compress and remove noise from signals and images. This book takes you step-by-step through examples that teach you how to use the Wavelet Packet 1-D and Wavelet Packet 2-D graphical tools. One section discusses how to transfer information from the graphical tools into your disk, and back again. The choice of wavelet is dictated by the signal or image characteristics and the nature of the application. If you understand the properties of the analysis and synthesis wavelet, you can choose a wavelet that is optimized for your application. The Wavelet Toolbox provides a number of functions for the estimation of an unknown function (signal or image) in noise. You can use these functions to denoise signals and as a method for nonparametric function estimation. Use wavelets to denoise signals and images. Because wavelets localize features in your data to different scales, you can preserve important signal or image features while removing noise. The basic idea behind wavelet denoising, or wavelet thresholding, is that the wavelet transform leads to a sparse representation for many real-world signals and images. What this means is that the wavelet transform concentrates signal and image features in a few large-magnitude wavelet coefficients. Wavelet coefficients which are small in value are typically noise and you can "shrink" those coefficients or remove them without affecting the signal or image quality. After you threshold the coefficients, you reconstruct the data using the inverse wavelet transform. The compression features of a given wavelet basis are primarily linked to the relative scarceness of the wavelet domain representation for the signal. The notion behind compression is based on the concept that the regular signal component can be accurately approximated using the following elements: a small number of approximation coefficients (at a suitably chosen level) and some of the detail coefficients.
