Wavelets provide an amazing set of tools for handling all sorts of fundamental problems in science, and engineering, such as audio de-noising, signal compression, object detection, fingerprint compression, image de-noising, image enhancement, diagnostic heart trouble, speech recognition, and video compression to name a few. Here, we are going to concentrate on the foundations of approximation and detail operators which are created by the coefficients associated with their scaling function and wavelet function counterparts. Since there are various wavelets out there this paper has a focus on the Haar system to help develop a concrete understanding of the approximation and detail operators. Then we will continue to use these operators in a more general sense to allowing us to formally write the definition of the 3D-DWT.
|Commitee:||Jarosz, Krzysztof, Pelekanos, George|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mathematics and Statistics|
|School Location:||United States -- Illinois|
|Source:||MAI 54/05M(E), Masters Abstracts International|
|Keywords:||3d-dwt, Approximation operator, Benjamin schulte, Detail operator, Discrete wavelet transform, Wavelets|
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