The Inverse Problems and Mathematical Imaging (IPMI) group at RICAM develops math-
ematical theory, computational methods, and data-driven approaches for extracting hidden
information from indirect, incomplete, or noisy observations. Such questions arise naturally
in modern imaging, wave propagation, tomography, machine learning, and the mathematical
analysis of complex physical systems.

Our research combines rigorous analysis with algorithmic design. We study inverse and ill-
posed problems from several complementary perspectives, including regularization theory,
mathematical imaging, inverse scattering, coupled-physics modalities, learning-based meth-
ods, and the analysis of wave phenomena across multiple scales. A common goal is to design
methods that are both mathematically reliable and effective in challenging applications.
The group’s work is strongly interdisciplinary. It connects analysis, partial differential equa-
tions, optimization, numerical mathematics, and scientific computing with applications in
medicine, materials science, physics, and engineering. Particular emphasis is placed on de-
veloping new imaging concepts, understanding the role of physical models in reconstruction,
and establishing solid mathematical foundations for emerging techniques.

IPMI at RICAM offers a collaborative environment for research at the interface of theory
and applications. Through national and international projects, close interaction with partner
institutions, and the mentoring of young researchers, the group contributes to the advance-
ment of inverse problems and mathematical imaging as a vibrant and evolving area of applied
mathematics