Title: Multidimensional wavelets with adaptive random partitioning and its application to probabilistic image process
Authors: Meng Li - Rice University (United States) [presenting]
Li Ma - Duke University (United States)
Abstract: The aim is to introduce a probabilistic model-based technique called WARP, or wavelets with adaptive random partitioning, with which multidimensional signals can be represented by a mixture of one-dimensional (1D) wavelet decompositions. A probability model, in the form of randomized recursive partitioning, is constructed on the space of wavelet coefficient trees, allowing the decomposition to adapt to the geometric features of the signal. In particular, when combined with the Haar basis, we show that fully probabilistic function estimation can be carried out in closed form using exact recursive belief propagation. We demonstrate that with WARP, even simple 1D Haar wavelets can achieve excellent performance in image denoising via numerical experiments, outperforming state-of-the-art multidimensional wavelet-based methods especially in low signal-to-noise ratio settings.