To Joe:
I don't know much about denoising, what I said about classical denoising methods is about using filters, most likely are adaptive filter, to reduce the effects of noise. (Soemtimes maybe only mean-filter or median-filter. For example, I think median-filter can get good result to the USPS data which are contaminated by grain noise. It is much easier than KPCA. But anyway, as explained by Belongie, the comparison appeared in the paper is just to show the advantage of KPCA to PCA, so maybe what I said before is just irrelevant to the paper, :)) I know people have done much work on using wavelet tranform in denoising, such as thresholding the wavelet coefficients to get a denoised image.