I am working with wavelets for my thesis, and I would like to know if there is an intuitive dependency between the levels of a DWT.
To make it clear: The DWT performs a convolution, and then the result is downsampled, right?
- Can we say that 2 adjacent values in the original are projected onto 1 value in the transform?
For example, the first value in the first level of the DWT would then be "responsible" for values 1 and 2 in the original. So that we would know where e.g. a pattern in a high DWT level actually comes from.
- Does this kind of projection exist?
- If it does not work, why not?
- Is the convolution/downsampling performed differently than I imagined?