Abstract | ||
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In this paper, we address the question of information preservation in ill-posed, non-linear inverse problems, assuming that the measured data is close to a low-dimensional model set. We provide necessary and sufficient conditions for the existence of a so-called instance optimal decoder, i.e., that is robust to noise and modelling error. Inspired by existing results in compressive sensing, our analysis is based on a (Lower) Restricted Isometry Property (LRIP), formulated in a non-linear fashion. We also provide sufficient conditions for non-uniform recovery with random measurement operators, with a new formulation of the LRIP. We finish by describing typical strategies to prove the LRIP in both linear and non-linear cases, and illustrate our results by studying the invertibility of a one-layer neural net with random weights. |
Year | DOI | Venue |
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2018 | 10.1088/1742-6596/1131/1/012002 | arXiv: Information Theory |
Field | DocType | Volume |
Mathematical optimization,Algorithm,Inverse problem,Operator (computer programming),Decoding methods,Artificial neural network,Compressed sensing,Mathematics,Restricted isometry property | Journal | abs/1802.09905 |
Issue | Citations | PageRank |
1 | 1 | 0.36 |
References | Authors | |
11 | 2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Nicolas Keriven | 1 | 21 | 3.74 |
Rémi Gribonval | 2 | 1207 | 83.59 |