We propose a new smoothing algorithm for noisy images as well as for higher dimensional data. The algorithm is closely related to the easy path wavelet transform (EPWT) introduced by Plonka (2009) for image approximation and to the generalized tree-based wavelet transform (GTBWT), a special wavelet transform for high dimensional data or data on graphs, introduced by Ram et al (2011).
We consider noisy function values of a real piecewise smooth function sampled at D-dimensional possibly scattered points. The proposed denoising scheme works as follows: At each level of transform, we construct a suitable path vector through the point set resembling similarities of the points in terms of their spatial distance and difference of their corresponding function values. Subsequently, we apply a one-dimensional wavelet shrinkage procedure along the constructed path vector. We repeat the whole procedure for different path vectors and average the outputs to improve the denoising result by exploiting redundancy.
This talk presents the denoising scheme in detail and also features numerical results for images.