Matlab code for adapting a wavelet pyramid to natural images

Phil Sallee and Bruno Olshausen

The following files provide the Matlab code necessary for adapting wavelet bases to natural images (or any other image ensemble), as described in:

Olshausen BA, Sallee P, Lewicki MS  (2001).  Learning Sparse Image Codes using a Wavelet Pyramid Architecture.  Advances in Neural Information Processing Systems, 13,  (in press)  (ps)

Note: To use these files, you must first download the matlabPyrTools library provided by Eero Simoncelli. His package is available as a gnu-zipped UNIX "tar" file, via anonymous ftp from (IP number in the file pub/eero/matlabPyrTools.tar.gz. You may also access it from his home page Shown below are the results we obtained running the algorithm on these training images.

Learned basis functions ('learned') and corresponding power spectra for M=3, 4 and 6 bands, along with a standard 9/7 biorthogonal wavelet ('standard').  Each column shows a different band, while each row shows a different level.  The lone basis function in the last row is the scaling function (twice convolved with itself).  The power spectra are plotted in the 2D-Fourier plane (vertical vs. horizontal spatial-frequency) with the maximum spatial-frequency at the Nyquist rate.