"A Unified Approach to Uniform Signal Recovery From Non-Linear Observations"Genzel, MartinRecent advances in quantized compressed sensing and high-dimensional estimation theory have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated guarantees is uniformity, i.e., recovery succeeds for an entire class of structured signals with a fixed measurement ensemble. However, despite significant results in various special cases, a general understanding of uniform recovery from non-linear observations is still missing. We will present a unified approach to this problem under the assumption of i.i.d. (sub-)Gaussian measurement vectors. It will turn out that a simple generalized Lasso estimator can serve as a universal recovery strategy, which is (outlier) robust and does not require explicit knowledge of the underlying non-linearity. A key technical ingredient is an approximative increment condition that can be implemented for many types of non-linear models. This flexibility allows us to apply our approach to a variety of problems in quantized compressed sensing and high-dimensional statistics. Each of these applications is accompanied by a conceptually simple and systematic proof, which does not rely on any deeper properties of the observation model. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Genzel_2021-06_bare_conf_ICCHA.pdf |
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