In fact, the subband dyadic tree structure conceptualizes the wavelet multiresolution decomposition of a signal. Eventually, the signal can be represented by a low-pass or coarse signal at a certain scale (corresponding to the level of the tree), plus a sum of detail signals at different resolutions. Each coarse approximation in turn can be decomposed further into yet a coarser signal and a detail signal at that resolution. Simply stated, the wavelet transform permits a decomposition of a signal into the sum of a lower resolution (or coarser) signal plus a detail, much like the dyadic subband tree in the discrete-time case. The discrete wavelet transform (DWT) employs discretized dilation and translation parameters. The kernel of the wavelet transform is obtained by dilation and translation of a prototype bandpass function. Wavelet transforms recently have been proposed as a new multiresolution decomposition tool for continuous-time signals.
These topics are explained in detail and the reference is given in Chapter 3. Multiresolution dyadic tree: L and H represent low-pass and high-pass filters, respectively.Īn oversampled version of this tree, called the Laplacian pyramid, was first introduced for image coding by Burt and Adelson (1983).
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