A Kalman filtering framework for virtual sensor-enhanced photoacoustic imaging

Photoacoustic imaging (PAI) combines the high contrast of optical absorption with the spatial resolution of ultrasound detection; however, its performance is often constrained by incomplete angular sampling and measurement noise. In this work, we introduce a model-based Kalman filtering framework for estimating virtual sensor measurements at intermediate angular positions of a circular detection array.Instead of adding new detector elements, the method generates statistically consistent virtual measurements from the existing array, effectively enriching the angular information available to the reconstruction algorithm without altering the physical hardware. The Kalman formulation exploits the directional propagation of acoustic waves and the temporal coherence of photoacoustic signals to produce noise-aware, minimum-variance estimates of the pressure field. Using extensive k-Wave simulations that incorporate finite-aperture detectors, acoustic attenuation, and heterogeneous media,we demonstrate that the proposed virtual sensing strategy substantially improves structural preservation and yields higher quantitative image quality compared with interpolation-based methods. These results establish Kalman-domain virtual sensing as a practical and physically grounded approach for augmenting PAI acquisition systems and enhancing reconstruction quality without modifying the detector hardware.

We gratefully acknowledge Kamran Avanki for his valuable and insightful discussions. M.R.R.T. would like to express his appreciation to the German Science Foundation (DFG) for supporting this work through the Mercator Guest Professorship award.

Department of Physics, Sharif University of Technology, Tehran, Iran

Bahareh Khishkhah, Rasoul Sadighi-Bonabi & M. Reza Rahimi Tabar

Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129, Oldenburg, Germany

The authors declare no competing interests.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Khishkhah, B., Sadighi-Bonabi, R. & Tabar, M.R.R. A Kalman filtering framework for virtual sensor–enhanced photoacoustic imaging. Sci Rep (2026). https://doi.org/10.1038/s41598-026-53324-7

DOI: https://doi.org/10.1038/s41598-026-53324-7

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative