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An Introduction to Wavelet-Based Image Processing and its Applications
Abstract
This chapter gives a brief introduction of wavelets and multi-resolution analysis. Wavelets overcome the limitations of Discrete Cosine Transform and hence found its application in JPEG 2000. In wavelet transform, the scaling functions provide approximations or low-pass filtering of the signal and the wavelet functions add the details at multiple resolutions or perform high-pass filtering of the signal. Applying Discrete Wavelet Transform to an image decomposes it into LL, LH, HL, and HH subbands. The low frequency LL band carries most of the significant information in the image. Wavlet transform allows us to analyse the local properties of a signal or image by shifting and scaling operations. The inherent properties of wavelets makes it useful in image denoising, edge detection, image compression, compressed sensing and illumination normalization. The wavelet coefficients at various levels of decomposition follows a parent-child relationship.
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