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math.NA2026
Data-Consistent Learning of Inverse Problems
Markus Haltmeier, Gyeongha Hwang
Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring s…
math.NA2024
Data-driven Morozov regularization of inverse problems
Markus Haltmeier, Richard Kowar, Markus Tiefenthaler
The solution of inverse problems is crucial in various fields such as medicine, biology, and engineering, where one seeks to find a solution from noisy observations. These problems…
math.NA2024
Full Field Inversion of the Attenuated Wave Equation: Theory and Numerical Inversion
Ngoc Do, Markus Haltmeier, Richard Kowar +2
Standard photoacoustic tomography (PAT) provides data that consist of time-dependent signals governed by the wave equation, which are measured on an observation surface. In contras…