Phil Sallee and Bruno Olshausen
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 ftp.cis.upenn.edu (IP number 220.127.116.11) in the file pub/eero/matlabPyrTools.tar.gz. You may also access it from his home page http://www.cns.nyu.edu/~eero
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)
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.