Researchers have developed a new statistical inverse learning method that utilizes \(\\ell^1\)-regularization to recover sparse functions from indirect and noisy observations. The proposed method is analyzed theoretically, establishing its consistency and deriving convergence rates in prediction and \(\\ell^1\) reconstruction norms. These rates are shown to be optimal through matching minimax lower bounds. The framework is applied to problems such as identifying reaction coefficients in elliptic PDEs and sparse computed tomography, with explicit convergence rates derived for filtered Radon transforms. AI
RANK_REASON The item is an academic paper published on arXiv detailing a new statistical method. [lever_c_demoted from research: ic=1 ai=1.0]
- arXiv
- computed tomography
- \(\ell^1\)
- Elliptic PDEs
- Radon transform
- reproducing kernel Hilbert space
- stat.ML
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