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Julia Dobrosotskaya (Case Western Reserve University)


Data adaptive multiscale bases inducing joint compressibility and their applications


Given a set of vectors sharing a fair amount of structural similarities, we recover a multiscale basis, in which, if possible, the given dataset is jointly compressible. This is achieved by minimizing a weighted l1-norm based energy functional over all unitary matrices, for which we describe an efficient iterative strategy. As the recovered basis stores the most important features of the dataset ierarchically, it may be utilized to enforce the regularity with respect to the given dataset in a variational framework of signa recovery. We illustrate the efficiency of this approach with examples in image recovery and explain the advantages and limitations of the associated methods.