Wavelet transform of a spatial convolution

1. Is wavelet transform a convolution?
2. What does the wavelet transform do?
3. What is wavelet transform in DSP?
4. How wavelet transform is used in image processing?

Is wavelet transform a convolution?

A wavelet transform is essentially a convolution with a bunch of functions chosen to be “compact” in frequency and time. Here compact means that the functions are nonzero only over a limited range of frequency and time.

What does the wavelet transform do?

Wavelet transforms are mathematical tools for analyzing data where features vary over different scales. For signals, features can be frequencies varying over time, transients, or slowly varying trends. For images, features include edges and textures.

What is wavelet transform in DSP?

The short duration wavelet is superimposed to the signal under consideration for a short duration of time and decompose them to useful form. This process is called wavelet transform. The method of transforming the decomposed signal to original wave is called inverse wavelet transform.

How wavelet transform is used in image processing?

Using wavelet transform, image can be decomposed at different levels of resolution as wavelet decomposition has varying window size and can also be processed from low resolution to high resolution as wavelet transformation is localized both in time and frequency domains.