Stationary wavelet transform

The Stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT). Translation-invariance is achieved by removing the downsamplers and upsamplers 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. The Stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT). Translation-invariance is achieved by removing the downsamplers and upsamplers 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.