Stationary wavelet transform
The stationary wavelet transform (SWT ) is a wavelet transform algorithm to eliminate the shift variance of the discrete wavelet transform (DWT). This results in minimally shifted signals substantially different wavelet coefficients and not minimally displaced, but otherwise identical coefficients.
The stationary wavelet transformation represents the signal analysis with respect to time or location axis represents an alternative to the continuous wavelet transformation, but is discrete scales. For example, it is used for edge detection.
The shift-invariance is achieved on the ten scale of the algorithm by removing up-and down-sampling steps of DWT and adding upsampling the filter coefficients by a factor of. SWT is inherently redundant scheme, since the output on each scale SWT the same number of samples as the input provides. Thus, in a decomposition upon the scale creates a fold redundancy of the wavelet coefficients.
The algorithm is also known as " à trous algorithme " in French ( trous: holes ), which refers to the inserted zeros in the filter coefficients. He was of Holschneider et al. introduced.
Implementation
The following block diagram represents a digital implementation of the SWT
In the above diagram, the filter of the previous grading scale used for each scale, in which the sampling rate was increased ( up-sampling ) ( see figure below).
Areas of application
The SWT is applied in various fields, for example in
- Pattern Recognition
- Signal noise suppression
Synonyms
The idea to omit the sub-sampling of the discrete wavelet transform is sufficiently intuitive that this variant was "invented" several times, each with different names.
- Stationary wavelet transform ( stationary wavelet transform)
- Redundant wavelet transform (redundant wavelet transform)
- Algorithme à trous
- Quasi- continuous wavelet transform ( continuous wavelet transform quasi- )
- Shift-invariant wavelet transform (shift - invariant wavelet transform)
- Translation-invariant wavelet transform (translation - invariant wavelet transform)
- Wavelet transform with maximum overlap (maximum overlap wavelet transform, MODWT )
- Undecimated wavelet transform ( UWT )
- Cycle spinning