Abstract
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.
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Zhang, D. (2019). Wavelet Transform. In: Fundamentals of Image Data Mining. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-17989-2_3
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DOI: https://doi.org/10.1007/978-3-030-17989-2_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-17988-5
Online ISBN: 978-3-030-17989-2
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