Abstract
Recent studies in linear inverse problems have recognized the sparse representation of unknown signal in a certain basis as an useful and effective prior information to solve those problems. In many multiscale bases (e.g. wavelets), signals of interest (e.g. piecewise-smooth signals) not only have few significant coefficients, but also <i>those significant coefficients are well-organized in trees</i>. We propose to exploit the <i>tree-structured sparse representation</i> as additional prior information for linear inverse problems with limited numbers of measurements. We present numerical results showing that exploiting the sparse <i>tree</i> representations lead to better reconstruction while requiring less time compared to methods that only assume sparse representations.
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