Stationary wavelet transform

The stationary wavelet transform (SWT) is a <a href="/facts/Wavelet_transform/4vk3W5be">wavelet transform</a> algorithm designed to overcome the lack of <a href="/facts/Translation_invariance/PYVMaqWb">translation-invariance</a> of the <a href="/facts/Discrete_wavelet_transform/19DVnk4n">discrete wavelet transform</a> (DWT). Translation-invariance is achieved by removing the <a href="/facts/Downsampling_(signal_processing)/gN5Wwrhv">downsamplers</a> and <a href="/facts/Upsampling/ndAk3IxG">upsamplers</a> in the DWT and upsampling the filter coefficients by a factor of 
 
 
 
 
 2
 
 (
 j
 −
 1
 )
 
 
 
 
 {\displaystyle 2^{(j-1)}}
 
 in the 
 
 
 
 j
 
 
 {\displaystyle j}
 
th 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 as "algorithme à trous" in French (word trous means holes in English) which refers to inserting zeros in the filters. It was introduced by Holschneider et al.

Stationary wavelet transform open-in-new

Stationary wavelet transform