Discrete denoising of heterogeneous two-dimensional data

We consider discrete denoising of two-dimensional data with characteristics that may be varying abruptly between regions. Using a quadtree decomposition technique and space-filling curves, we extend the recently developed S-DUDE (Shifting Discrete Universal DEnoiser), which was tailored to one-dimensional data, to the two-dimensional case. Our scheme competes with a genie that has access, in addition to the noisy data, also to the underlying noiseless data, and can employ m different two-dimensional sliding window denoisers along m distinct regions obtained by a quadtree decomposition with m leaves, in a way that minimizes the overall loss. We show that, regardless of what the underlying noiseless data may be, the two-dimensional S-DUDE performs essentially as well as this genie, provided that the number of distinct regions satisfies m = o(n), where n is the total size of the data. The resulting algorithm complexity is still linear in both n and m, as in the one-dimensional case. Our experimental results show that the two-dimensional S-DUDE can be effective when the characteristics of the underlying clean image vary across different regions in the data.