New statistical inverse learning method uses $\\ell^1$-regularization for sparse function recovery

By PulseAugur Editorial · [1 sources] · 2026-07-08 14:32

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

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$New statistical inverse learning method uses $\\ell^1$-regularization for sparse function recovery$

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arXiv stat.ML TIER_1 English(EN) · Luca Ratti · 2026-07-08 14:32

Statistical inverse learning and $\ell^1$-regularization

We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning. The unknown is modeled as an element of $\ell^1$, and observations are generated through a possibly nonlinear forward operator $A:\ell^1\to H$…

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Statistical inverse learning and $\ell^1$-regularization

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