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Off-the-grid prediction and testing for mixtures of translated features
It turns out that, in this framework, our upper bound on the minimax separation rate matches (up to a logarithmic factor) the lower bound on the minimax separation rate for signal detection in the high dimensional linear model associated to a fixed dictionary of features.
MS-PS: A Multi-Scale Network for Photometric Stereo With a New Comprehensive Training Dataset
The photometric stereo (PS) problem consists in reconstructing the 3D-surface of an object, thanks to a set of photographs taken under different lighting directions.
Simultaneous off-the-grid learning of mixtures issued from a continuous dictionary
Following recent works on the geometry of off-the-grid methods, we show that such functions can be constructed provided the parameters of the active features are pairwise separated by a constant with respect to a Riemannian metric. When the number of signals is finite and the noise is assumed Gaussian, we give refinements of our results for $p=1$ and $p=2$ using tail bounds on suprema of Gaussian and $\chi^2$ random processes.
Off-the-grid learning of sparse mixtures from a continuous dictionary
We propose an off-the-grid optimization method, that is, a method which does not use any discretization scheme on the parameter space, to estimate both the non-linear parameters of the features and the linear parameters of the mixture.
