A comparison of the amplitude spectra of the “atypical” output part of RPCA, the whitened input and the whitened ideal input.

<p>This plot demonstrates that the particular whitening filter as used in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002372#pcbi.1002372-Olshausen1" target="_blank">[5]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002372#pcbi.1002372-Rehn1" target="_blank">[40]</a> can be seen as a linear approximation of the filtering properties of RPCA when only the atypical output is considered. The thick (red) line is the amplitude spectrum of the RPCA output. The dashed (blue) line with square markers is the amplitude spectrum of the training images filtered with the whitening filter. The thin (green) line serves as a reference: this is the amplitude spectrum of whitened ideal input which has an amplitude spectrum proportional to 1/frequency. Due to the limited input size, there is a natural cutoff at higher frequencies. (Since the size of the images is 16×16, the largest frequency is .) The whitening filter: , where the cutoff frequency is . The variances of the plots are due the artifacts caused by the rectangular sampling lattice. For comparison purposes the plots are rescaled onto .