Generalized Tree-Based Wavelet Transform and Applications to Patch-Based Image Processing
August 2nd, 2012
Hebrew University of Jerusalem (HUJI)

What if we take all the overlapping patches from a given image and organize them to create the shortest path by using their mutual distances? This suggests a reordering of the image pixels in a way that creates a maximal 1D regularity Could we repeat this process in several “scales” ? What could we do with such a construction? In this talk we consider a wider perspective of the above line of questions: We introduce a wavelet transform that is meant for data organized as a connected-graph or as a cloud of high dimensional points. The proposed transform constructs a tree that applies a 1D wavelet decomposition filters, coupled with a pre-reordering of the input, so as to best sparsify the given data. We adopt this transform to image processing tasks by considering the image as a graph, where every patch is a node, and vertices are obtained by Euclidean distances between corresponding patches. State of- the-art image denoising results are obtained with the proposed scheme.

It was also presented in the SIAM Imaging Science Conference, in the Session "Recent Advances in Patch-based Image Processing", organized by Peyman Milanfar, Gabriel Peyre and myself, Philadelphia May 2012. Joint work with Idan Ram (PhD student) and Israel Cohen, both from the Electrical Engiuneering Department at the Technion.