An efficient hierarchical Bayesian method for the Kuopio tomography challenge 2023 (2405.03343v1)
Abstract: The aim of Electrical Impedance Tomography (EIT) is to determine the electrical conductivity distribution inside a domain by applying currents and measuring voltages on its boundary. Mathematically, the EIT reconstruction task can be formulated as a non-linear inverse problem. The Bayesian inverse problems framework has been applied expensively to solutions of the EIT inverse problem, in particular in the cases when the unknown conductivity is believed to be blocky. Recently, the Sparsity Promoting Iterative Alternating Sequential (PS-IAS) algorithm, originally proposed for the solution of linear inverse problems, has been adapted for the non linear case of EIT reconstruction in a computationally efficient manner. Here we introduce a hybrid version of the SP-IAS algorithms for the nonlinear EIT inverse problem, providing a detailed description of the implementation details, with a specific focus on parameters selection. The method is applied to the 2023 Kuopio Tomography Challenge dataset, with a comprehensive report of the running times for the different cases and parameter selections.
- Multichannel impedance pneumography for apnea monitoring. In [1990] Proceedings of the Twelfth Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pages 1048–1049, 1990.
- Eit in a layered anisotropic medium, 2018.
- Tushar Kanti Bera. Applications of electrical impedance tomography (eit): A short review. IOP Conference Series: Materials Science and Engineering, 331(1):012004, mar 2018.
- Adaptive anisotropic bayesian meshing for inverse problems. Inverse Problems, 2024.
- A primal–dual interior-point framework for using the l1 or l2 norm on the data and regularization terms of inverse problems. Inverse Problems, 28(9):095011, 2012.
- A hierarchical Krylov–Bayes iterative inverse solver for MEG with physiological preconditioning. Inverse Problems, 31(12):125005, 2015.
- Brain activity mapping from MEG data via a hierarchical Bayesian algorithm with automatic depth weighting. Brain topography, 32:363–393, 2019.
- Bayes meets Krylov: Statistically inspired preconditioners for CGLS. SIAM Review, 60(2):429–461, 2018.
- Sparsity promoting hybrid solvers for hierarchical Bayesian inverse problems. SIAM Journal on Scientific Computing, 42(6):A3761–A3784, 2020.
- A computationally efficient EIT algorithm for imaging of blocky targets. arXiv preprint arXiv submit/5567110., 2024.
- Sparse reconstructions from few noisy data: analysis of hierarchical Bayesian models with generalized gamma hyperpriors. Inverse Problems, 36(2):025010, 2020.
- D. Calvetti and E. Somersalo. Bayesian Scientific Computing, volume 215. Springer Nature, 2023.
- D. Calvetti and E. Somersalo. Computationally efficient sampling methods for sparsity promoting hierarchical Bayesian models. arXiv preprint arXiv:2303.16988, 2023.
- Hierachical Bayesian models and sparsity: ℓ2superscriptℓ2\ell^{2}roman_ℓ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-magic. Inverse Problems, 35(3):035003, 2019.
- Experimental evaluation of 3d electrical impedance tomography with total variation prior. Inverse Problems in Science and Engineering, 24(8):1411–1431, 2016.
- Edge-enhancing reconstruction algorithm for three-dimensional electrical impedance tomography. SIAM Journal on Scientific Computing, 37(1):B60–B78, 2015.
- Statistical inversion and monte carlo sampling methods in electrical impedance tomography. Inverse problems, 16(5):1487, 2000.
- Existence and uniqueness for electrode models for electric current computed tomography. SIAM Journal on Applied Mathematics, 52(4):1023–1040, 1992.
- Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 4:600–612, 2004.
- C. Wu and M. Soleimani. Frequency difference eit with localization: A potential medical imaging tool during cancer treatment. IEEE Access, 7:21870–21878, 2019.
- Eit measurement system with high phase accuracy for the imaging of spectral induced polarization properties of soils and sediments. Measurement Science and Technology, 19(9):094010, jul 2008.