Doing better than L1 on signals that are not canonically sparse yet are undersampled and

*with noise*....another one of these things that make you mhhhh....We study the problem where an input is measured via a linear matrix multiplication under additive noise. In particular, we focus on compressed sensing (CS), where the matrixmultiplication also provides dimensionality reduction. While this setup usually assumes sparsity or compressibility in the observed signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. We provide initial theoretical, algorithmic, and experimental evidence based on maximum a posteriori (MAP) estimation that shows the promise of universality in CS, particularly for low-complexity sources that do not exhibit standard sparsity or compressibility.

The universal compressed sensing estimation software is here.

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