@article {24843,
	title = {A machine learning approach to optimal Tikhonov regularization I: Affine manifolds},
	journal = {Analysis and Applications},
	year = {2020},
	publisher = {MIT Press},
	abstract = {Inspired by several real-life applications in audio processing and medical image analysis, where the quantity of interest is generated by several sources to be accurately modeled and separated, as well as by recent advances in \&nbsp;regularization theory and optimization, we study the conditions on optimal support recovery in inverse problems of unmixing type by means of multi-penalty regularization. \&nbsp;We consider and analyze a regularization functional composed of a data-fidelity term, where signal and noise are additively mixed, a non-smooth, convex, sparsity promoting term, and a quadratic penalty term to model the noise. We prove not only that \&nbsp;the well-established theory for sparse recovery in the single parameter case can be translated to the multi-penalty settings, but \&nbsp;we also demonstrate the enhanced properties of multi-penalty regularization in terms of support identification compared to sole $\ell^1$-minimization. \&nbsp;We additionally confirm and support the theoretical results by extensive numerical simulations, which give a statistics of robustness of the multi-penalty regularization scheme with respect to the single-parameter counterpart.\&nbsp;Eventually, we confirm a significant improvement in performance compared to standard $\ell^1$-regularization\&nbsp;for compressive sensing problems considered in our experiments.\&nbsp;},
	url = {http://arxiv.org/abs/1610.01952},
	author = {De Vito, Ernesto and Fornasier, Massimo and Naumova, Valeriya}
}
@misc {26836,
	title = {Automated parameter estimation for selected inverse problems},
	howpublished = {Grenoble, France},
	year = {2019},
	author = {Fornasier, Massimo and De Vito, Ernesto and Kereta, Zeljko and Naumova, Valeriya}
}
@inproceedings {26830,
	title = {Monte Carlo wavelets: a randomized approach to frame discretization},
	journal = {Sampling Theory and Applications},
	year = {2019},
	publisher = {IEEE},
	author = {De Vito, Ernesto and Kereta, Zeljko and Naumova, Valeriya and Rosasco, Lorenzo and Vigogna, Stefano}
}
@article {26832,
	title = {Unsupervised parameter selection for denoising with the elastic net},
	journal = {Machine Learning},
	year = {2019},
	publisher = {Springer},
	author = {De Vito, Ernesto and Kereta, Zeljko and Naumova, Valeriya}
}
@misc {26834,
	title = {Unsupervised Parameter Selection in Variational Regularization},
	year = {2019},
	address = {SPARS 2019, Toulouse, France},
	author = {De Vito, Ernesto and Kereta, Zeljko and Naumova, Valeriya}
}
@article {26315,
	title = {A Learning Theory Approach to a Computationally Efficient Parameter Selection for the Elastic Net},
	journal = {arXiv},
	year = {2018},
	month = {09/2018},
	publisher = {arXiv},
	author = {De Vito, Ernesto and Kereta, Zeljko and Naumova, Valeriya}
}
@misc {26838,
	title = {Nearly Optimal Parameter selection for the Elastic Net},
	howpublished = {Hangzhou, China},
	year = {2017},
	author = {De Vito, Ernesto and Kereta, Zeljko and Naumova, Valeriya}
}
