Quantitative recovery conditions for tree-based compressed sensing

As shown in [Blumensath and Davies 2009, Baraniuk et al. 2010], signals whose wavelet coefficients exhibit a rooted tree structure can be recovered using specially-adapted compressed sensing algorithms from just n=O(k) measurements, where k is the sparsity of the signal. Motivated by these results, we introduce a simplified proportional-dimensional asymptotic framework which enables the quantitative evaluation of recovery guarantees for tree-based compressed sensing. In the context of Gaussian m...