Discrete Wavelet Transform (DWT)

Discrete Wavelet Transform (DWT) is a wavelet transform, using discrete wavelet functions, which operate with discrete signals. In comparison to Fourier transform, DWT is able to present space and time information.
Different types of wavelet transforms:

1. Haar wavelets transform
2. Daubechies wavelets transform
3. Complex wavelet transform

Wavelet transformations are used to represent an approximation of a signal with a cluster of functions - wavelets. Wavelets from a specific cluster are related to a mother wavelet by translation and stretching^[1].
Wavelets can be used to denoise an image distorted by Gaussian noise.

Definition and layering

DWT can be defined by passing a signal through a series of filters. The original signal x is filtered by a high-pass filter, returning 1st level detail coefficients.
The same original signal x is filtered with a low-pass filter, which returns signal of the second layer x2. This signal (x2) can be filtered again with a high-pass filter, returning 2nd level detail coefficients. Filtering x2 with a low-pass filter gives us 3rd level signal x3 and the process can be repeated multiple times.

References

Wikipedia. (n.d.). Discrete wavelet transform Wikipedia. Retrieved 01.09.2023 from URL