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An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizingExpand
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The Stability of Inverse Problems
TLDR
Many inverse problems arising in optics and other fields like geophysics, medical diagnostics and remote sensing, present numerical instability: the noise affecting the data may produce arbitrarily large errors in the solutions. Expand
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Elastic-net regularization in learning theory
TLDR
We prove that there exists a particular ''elastic-net representation'' of the regression function such that, if the number of data increases, the elastic-net estimator is consistent not only for prediction but also for variable/feature selection. Expand
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Linear inverse problems with discrete data: II. Stability and regularisation
For pt.I. see ibid., vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems hasExpand
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Linear inverse problems with discrete data. I. General formulation and singular system analysis
The authors discuss linear methods for the solution of linear inverse problems with discrete data. Such problems occur frequently in instrumental science, e.g. tomography, radar, sonar, opticalExpand
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Feature selection for high-dimensional data
This paper focuses on feature selection for problems dealing with high-dimensional data. We discuss the benefits of adopting a regularized approach with L1 or L1–L2 penalties in two differentExpand
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A Regularized Framework for Feature Selection in Face Detection and Authentication
TLDR
We propose a general framework for selecting features in the computer vision domain—i.e., learning descriptions from data—where the prior knowledge related to the application is confined in the early stages. Expand
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A Regularized Method for Selecting Nested Groups of Relevant Genes from Microarray Data
TLDR
We propose a two-stage regularization method able to learn linear models characterized by a high prediction performance and its potential as a starting point for further biological investigations. Expand
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A Sparsity-Enforcing Method for Learning Face Features
TLDR
In this paper, we propose a new trainable system for selecting face features from over-complete dictionaries of image measurements. Expand
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