| Compressed sensing is the method of compactly acquiring a signal at the sampling stage and later recovering the signal based on the assumption that signal is sparse when represented in some basis. In fact, most naturally occurring signals do satisfy this sparsity assumption. We apply graphical models to the problem of compressed sensing and also exploit the close relationship between compressed sensing and error-correcting codes. Our structure and algorithm mimic the decoding structure and algorithm for low-density parity-check codes. We use a hierarchical model to encode the sparsity prior. We also utilize methods from existing compressed sensing algorithms. The resulting algorithm has running time linear in the problem size and is therefore scalable. We show through computer simulations that our algorithm has performance that surpass those of other current algorithms in many interesting settings. |
