search

PyWavelets / pywt

PyWavelets - Wavelet Transforms in Python
http://pywavelets.readthedocs.org
MIT License
2.09k stars 487 forks source link

How to obtain transformation matrix directly? #304

Closed ghost closed 5 years ago

ghost commented 7 years ago

Is there a way to obtain the n^2 matrix itself rather than have the library perform the operation?

I want to implement it as simple matrix multiplication on the GPU, and the O(N^2) memory complexity is tolerable.

A function to construct such a matrix based on the desired number of levels and w*h input would be nice.

grlee77 commented 7 years ago

We do not currently have anything in PyWavelets to do this.

I will leave this open as a feature request. Is this something you might be interested in contributing? I think supporting all edge-modes and arbitraty number of dimensions would be a bit of work, but if you wanted to just support the 1D case and periodic boundary conditions it could be pretty straightforward.

As you indicate, since the DWT is implemented via (downsampled) convolutions, this could be done by using a matrix-representation of the operator. You can get the FIR filters from a Wavelet object as illustrated below, but we do not currently have a function that directly converts these into the corresponding (convolution + downsampling) matrices.

import pywt
w = pywt.Wavelet('db2')
print(w.dec_lo)  # decomposition lowpass
print(w.dec_hi)  # decomposition highpass
print(w.rec_lo)   # reconstruction lowpass
print(w.rec_hi)   # reconstruction highpass
grlee77 commented 7 years ago

As the matrix will be mostly zeros (at least in the typical case where the signal has many more samples than the FIR filters), the memory usage shouldn't be too high if sparse matrices are used.

ghost commented 7 years ago

What about lifting schemes?

https://en.wikipedia.org/wiki/Lifting_scheme

grlee77 commented 7 years ago

We do not currently have a lifting-based transform in PyWavelets.