Theory for learning blind inverse problems with finite samples
Researchers establish sample complexity bounds and optimal estimators for blind inverse problems using linear minimum mean square estimation framework.
Source: arxiv/cs.LG · Nathan Buskulic, Luca Calatroni, Lorenzo Rosasco, Silvia Villa · open original ↗
New theoretical framework quantifies how many samples are needed to learn blind inverse problems where both signal and operator are unknown.
- — Blind inverse problems lack ground truth for the forward operator, creating identifiability and symmetry challenges absent in standard settings.
- — Data-driven methods show empirical promise but offer no theoretical guarantees, limiting adoption in calibration-critical imaging applications.
- — Linear minimum mean square estimators (LMMSEs) provide closed-form optimal solutions with explicit dependence on signal, noise, and operator distributions.
- — Finite-sample error bounds connect convergence rates directly to noise level, problem conditioning, operator randomness, and training sample count.
- — Tikhonov regularization structure adapts automatically based on unknown signal and operator statistics, improving interpretability over black-box approaches.
- — Reconstruction error decreases predictably as noise and operator randomness diminish, validated by numerical experiments matching theoretical predictions.
- — Source condition assumptions enable explicit convergence rate analysis, bridging classical recovery theory with the blind setting.
Astrobobo tool mapping
- Knowledge Capture Record the closed-form LMMSE solution and the three key factors affecting convergence (noise, conditioning, operator randomness) as a reference card for your imaging pipeline.
- Focus Brief Summarize the Tikhonov regularization structure and how it depends on unknown distributions; use this to design a validation experiment comparing learned vs. classical regularization.
- Reading Queue Queue the paper's references on identifiability and source conditions to deepen understanding of when the LMMSE framework applies to your specific problem.
Frequently asked
- A blind inverse problem requires recovering a signal when both the signal and the forward operator (measurement process) are unknown. This is harder than standard inverse problems because you cannot use known operator properties to guide recovery, and multiple different signal-operator pairs may produce identical measurements, creating ambiguity. The paper addresses this by deriving theoretical bounds on how many samples are needed to resolve this ambiguity.
cite ▸
APA
Nathan Buskulic, Luca Calatroni, Lorenzo Rosasco, Silvia Villa. (2026, April 21). Theory for learning blind inverse problems with finite samples. Astrobobo Content Engine (rewrite of arxiv/cs.LG). https://astrobobo-content-engine.vercel.app/article/theory-for-learning-blind-inverse-problems-with-finite-samples-5e2d83
MLA
Nathan Buskulic, Luca Calatroni, Lorenzo Rosasco, Silvia Villa. "Theory for learning blind inverse problems with finite samples." Astrobobo Content Engine, 21 Apr 2026, https://astrobobo-content-engine.vercel.app/article/theory-for-learning-blind-inverse-problems-with-finite-samples-5e2d83. Based on "arxiv/cs.LG", https://arxiv.org/abs/2512.23405.
BibTeX
@misc{astrobobo_theory-for-learning-blind-inverse-problems-with-finite-samples-5e2d83_2026,
author = {Nathan Buskulic, Luca Calatroni, Lorenzo Rosasco, Silvia Villa},
title = {Theory for learning blind inverse problems with finite samples},
year = {2026},
url = {https://astrobobo-content-engine.vercel.app/article/theory-for-learning-blind-inverse-problems-with-finite-samples-5e2d83},
note = {Astrobobo rewrite of arxiv/cs.LG, https://arxiv.org/abs/2512.23405},
}