Work

Adaptive Weighted Total Variation Boosted by Learning Techniques in Few-View Tomographic Imaging

Year: 2026

Type: article

Abstract: This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method relies on the rapid computation of an accurate approximation of the true image (or its gradient magnitude) through a neural network. Our approach operates without requiring prior knowledge of the noise intensity in the data and avoids the iterative recomputation of weights. Additionally, the paper includes a theoretical analysis of the proposed method, establishing its validity as a regularization approach. This framework integrates advanced neural network capabilities within a regularization context, thereby making the results of the networks interpretable. The results are promising as they enable high-quality reconstructions from limited-view tomographic measurements.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-026-03199-7

Authors: Elena Morotti, Davide Evangelista, Andrea Sebastiani, Elena Loli Piccolomini

Institutions: University of Bologna, University of Modena and Reggio Emilia

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: European Commission, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni