Conference paper
Dynamical Functional Theory for Compressed Sensing
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix ensemble. By design, the fixed points of the algorithm obey the Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble.
Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way that the resulting fields become Gaussian random variables allowing for an explicit analysis.
The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem.
| Language: | English |
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| Publisher: | IEEE |
| Year: | 2017 |
| Pages: | 2143-2147 |
| Proceedings: | 2017 IEEE International Symposium on Information Theory |
| ISBN: | 150904096X , 150904096x , 1509040978 , 9781509040964 and 9781509040971 |
| ISSN: | 21578117 and 21578095 |
| Types: | Conference paper |
| DOI: | 10.1109/ISIT.2017.8006908 |
| ORCIDs: | Winther, Ole |
AMP algorithm Algorithm design and analysis Discrete Fourier transforms Gaussian processes Gaussian random variables Heuristic algorithms Information theory Mathematical model Signal processing algorithms Sparse matrices TAP equations Thouless-Anderson-Palmer equations approximate message passing approximation theory compressed sensing designing generalizations dynamical functional approach dynamical functional theory effective stochastic process invariant random matrix matrix algebra observation matrices
