Multi-directional context sets with applications to universal denoising and compression

The classical framework of context-tree models used in sequential decision problems such as compression and prediction is generalized to a setting in which the observations are multi-tracked or multi-directional, and for which it may be beneficial to consider contexts comprised of possibly differing numbers of symbols from each track or direction. Context set definitions, tree representations, and pruning algorithms are all extended from the classical uni-directional setting to the m-directional setting, with an emphasis on the case of m = 2. We provide a simple example suggesting that determining (pruning) the best m-directional context set for m >= 3 is substantially more complex than in the case of m = 2. After briefly describing how the multi-directional framework can be applied to universal data compression, we focus on its application to universal denoising, where we pair the proposed framework with a new technique for estimating the loss of a denoising algorithm based only on noisy observations.