A Hierarchical Likelihood Model for Non-linear Inverse Problems under Additive and Multiplicative Noise
Recovering hidden information when measurements are noisy and incomplete
When scientists try to reconstruct hidden information from messy, real-world measurements, they face a thorny problem: the data contains multiple types of noise and gaps. This paper presents a mathematical framework and efficient algorithm that handles all these complications at once, without requiring tedious manual tuning. Tests on astronomical data show it outperforms existing methods in both accuracy and speed.
Inverse problems appear everywhere—from medical imaging to geophysics to astronomy—where researchers must infer what they can't directly observe from imperfect measurements. Previous approaches required researchers to either ignore some noise sources or manually calibrate workaround models, both of which degrade results. This method automates the process and handles realistic conditions more faithfully, letting scientists spend time on science rather than fitting their tools.