Wavelet Transform

This chapter presents the multi-resolution analysis theory by formally introducing the contemporary wavelet theories. It starts with formulating a wavelet transform as a transform similar to windowed FT but at multiple resolutions or scales. It then uses the simplest wavelet i.e. Haar wavelet to demonstrate step-by-step how both 1D and 2D discrete wavelet transforms (DWT) work. A 2D wavelet decomposition tree is used to help readers understanding 2D DWT. Readers are then demonstrated with a DWT application on image analysis. By finishing this chapter, readers will have a full understanding how DWT works, what types of features a wavelet can capture and how they can be used for image data mining.