Aprendizaje anticausal en problemas inversos y su aplicación a tomografía optoacústica

Matías Vera, Martín Germán González, Leonardo Rey Vega

Resumen


Los algoritmos de inteligencia artificial habitualmente fallan cuando la distribución de los datos se desvía de la utilizada durante el entrenamiento. Esta vulnerabilidad puede ser corregida post-entrenamiento, pero la misma puede requerir una etapa de ajuste computacionalmente pesada y/o una gran necesidad de nuevos datos. En este contexto, la teoría de causalidad suele ser un excelente paradigma para diferenciar los mecanismos propensos a variaciones de los invariantes. Esto permitiría hacer un ajuste solamente sobre el modelo variable, reduciendo la complejidad del problema. Sin embargo, este paradigma está muy poco estudiado en lo referido a problemas inversos, principalmente porque estos problemas son por definición anticausales. En este trabajo se analiza el desempeño y limitaciones de algoritmos básicos en problemas inversos que cumplan el requisito de aprender de forma anticausal. En particular, se estudian estos algoritmos en el contexto de reconstrucción de imágenes en tomografía optoacústica.

Palabras clave


problemas inversos; modelos guiados por la física; teoría de causalidad; tomografía optoacústica

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Referencias


G. Daras, H. Chung, C.-H. Lai, Y. Mitsufuji, J. C. Ye, P. Milanfar,A. Dimakis, and M. Delbracio, “A survey on diffusion models for inverse problems,” CoRR, 2024, arXiv e-prints: 2410.00083.

Y. Song, L. Shen, L. Xing, and S. Ermon, “Solving inverse problems in medical imaging with score-based generative models,” in International Conference on Learning Representations (ICLR), 2022.

P. Lailly, “The seismic inverse problem as a sequence of before stack migrations,” in Conference on Inverse Scattering, Theory and application, 1983, pp. 206–220.

M. Xu and L. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum., vol. 77, p. 041101, 2006.

M. Vera, M. G. González, and L. R. Vega, “Invariant representations in deep learning for optoacoustic imaging,” Review of Scientific Instruments, vol. 94, no. 5, p. 054904, 05 2023. [Online]. Available: https://doi.org/10.1063/5.0139286

B. Schölkopf, D. Janzing, J. Peters, E. Sgouritsa, K. Zhang, and J. Mooij, “On causal and anticausal learning,” in International Conference on Machine Learning (ICML), ser. ICML’12. Madison, WI, USA:Omnipress, 2012, p. 459–466.

H. Daumé III, “Frustratingly easy domain adaptation,” in Annual Meeting of the Association of Computational Linguistics (ACL). Prague, Czech Republic: Association for Computational Linguistics, 2007, pp. 256–263.

M. Rojas-Carulla, B. Schölkopf, R. Turner, and J. Peters, “Invariant models for causal transfer learning,” Journal of Machine Learning Research (JMLR), vol. 19, no. 36, pp. 1–34, 2018.

M. Arjovsky, L. Bottou, I. Gulrajani, and D. Lopez-Paz, “Invariant risk minimization,” CoRR, Jul. 2019, arXiv e-prints: 1907.02893.

B. Aubin, A. Slowik, M. Arjovsky, L. Bottou, and D. Lopez-Paz, “Linear unit-tests for invariance discovery,” CoRR, Feb. 2021, arXiv e-prints: 2102.10867.

L. Wang and H. Wu, Biomedical Optics: Principles and Imaging, 1st ed. Hoboken, N.J: Wiley-Interscience, May 2007.

R. Kruger, P. Liu, Y. Fang, and R. Appledorn, “Photoacoustic ultrasound (paus)—reconstruction tomography,” Medical Physics, vol. 22, no. 10, p. 1605–1609, 1995.

C. Lutzweiler and D. Razansky, “Optoacoustic imaging and tomography: reconstruction approaches and outstanding challenges in image performance and quantification,” Sensors, vol. 13, pp. 7345–7384, 2013.

M. Xu and L. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E, vol. 71, p. 016706,2005.

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Problems, vol.23, no. 6, p. S65–S80, Nov 2007.

A. Rosenthal, V. Ntziachristos, and D. Razansky, “Acoustic inversion in optoacoustic tomography: A review,” Current Medical Imaging Reviews, vol. 9, pp. 318–336, 2013.

C. Tian, M. Pei, K. Shen, S. Liu, Z. Hu, and T. Feng, “Impact of system factors on the performance of photoacoustic tomography scanners,” Phys. Rev. Applied, vol. 13, p. 014001, 2020.

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Transactions on Medical Imaging, vol. 29, no. 6, p. 1275–1285, Jun 2010.

L. Hirsch, M. G. González, and L. Rey Vega, “On the robustness of model-based algorithms for photoacoustic tomography: Comparison between time and frequency domains,” Review of Scientific Instruments, vol. 92, no. 11, p. 114901, Nov 2021.

G. Paltauf, P. R. Torke, and R. Nuster, “Modeling photoacoustic imaging with a scanning focused detector using monte carlo simulation of energy deposition,” Journal of biomedical optics, vol. 23, no. 12, 2018.

A. Rosenthal, V. Ntziachristos, and D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Medical Physics, vol. 38, no. 7, pp. 4285–4295, 2011.

A. D. Cezaro and F. T. D. Cezaro, “Regularization approaches for quantitative photoacoustic tomography using the radiative transfer equation,” Journal of Computational and Applied Mathematics, vol. 292, pp. 1–14, 2015.

S. R. Arridge, M. M. Betcke, B. T. Cox, F. Lucka, and B. E. Treeby, “On the adjoint operator in photoacoustic tomography,” Inverse Problems, vol. 32, no. 11, p. 115012, Oct 2016.

M. G. González, M. Vera, and L. J. R. Vega, “Combining band-frequency separation and deep neural networks for optoacoustic imaging,” Optics and Lasers in Engineering, vol. 163, p. 107471, 2023.

A. Hyvärinen, “Estimation of non-normalized statistical models by score matching,” Journal of Machine Learning Research, vol. 6, no. 24, pp. 695–709, 2005.

DRIVE, “DRIVE: Digital retinal images for vessel extraction,” 2020. [Online]. Available: https://drive.grand-challenge.org/

ARIA, “Automated retinal image analysis,” 2006. [Online]. Available: http://www.damianjjfarnell.com/

RITE, “Retinal images vessel tree extraction,” 2013. [Online]. Available: https://medicine.uiowa.edu/eye/rite-dataset

STARE, “Structured analysis of the retina,” 2000. [Online]. Available: https://cecas.clemson.edu/ ∼ ahoover/stare/

A. Hatamizadeh, H. Hosseini, N. Patel, J. Choi, C. Pole, C. Hoeferlin, S. Schwartz, and D. Terzopoulos, “RAVIR: A dataset and methodology for the semantic segmentation and quantitative analysis of retinal arteries and veins in infrared reflectance imaging,” IEEE Journal of Biomedical and Health Informatics, 2022.

M. González, M. Vera, A. Dreszman, and L. Rey Vega, “Diffusion assisted image reconstruction in optoacoustic tomography,” Optics and Lasers in Engineering, vol. 178, p. 108242, 2024.

K. B. Petersen and M. S. Pedersen, “The matrix cookbook,” 2008.




DOI: https://doi.org/10.37537/rev.elektron.9.2.222.2025

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