Undecimated Wavelet Transform
The stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of Translation invariance, translation-invariance of the discrete wavelet transform (DWT). Translation-invariance is achieved by removing the Downsampling (signal processing), downsamplers and Upsampling, upsamplers in the DWT and upsampling the filter coefficients by a factor of 2^ in the jth level of the algorithm. The SWT is an inherently redundant scheme as the output of each level of SWT contains the same number of samples as the input – so for a decomposition of N levels there is a redundancy of N in the wavelet coefficients. This algorithm is more famously known by the French expression , meaning “with holes”, which refers to inserting zeros in the filters. It was introduced by Holschneider et al. Definition The basic discrete wavelet transform (DWT) algorithm is adapted to yield a stationary wavelet transform (SWT) which is independent of the origin. The approach of ...
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