2026-06-17T21:16:23Zhttps://riubu.ubu.es/oai/request

oai:riubu.ubu.es:10259/83712024-06-06T22:42:07Zcom_10259_6229com_10259_4534com_10259.4_106com_10259_2604col_10259_6230

Carpio, Ana Cebrián de Barrio, Elena Gutiérrez, Andrea 2024-01-17T11:55:52Z 2024-01-17T11:55:52Z 2023 0266-5611 http://hdl.handle.net/10259/8371 10.1088/1361-6420/acd5f8 1361-6420 We develop a computational framework to quantify uncertainty in shear elastography imaging of anomalies in tissues. We adopt a Bayesian inference formulation. Given the observed data, a forward model and their uncertainties, we find the posterior probability of parameter fields representing the geometry of the anomalies and their shear moduli. To construct a prior probability, we exploit the topological energies of associated objective functions. We demonstrate the approach on synthetic two dimensional tests with smooth and irregular shapes. Sampling the posterior distribution by Markov Chain Monte Carlo (MCMC) techniques we obtain statistical information on the shear moduli and the geometrical properties of the anomalies. General affine-invariant ensemble MCMC samplers are adequate for shapes characterized by parameter sets of low to moderate dimension. However, MCMC methods are computationally expensive. For simple shapes, we devise a fast optimization scheme to calculate the maximum a posteriori (MAP) estimate representing the most likely parameter values. Then, we approximate the posterior distribution by a Gaussian distribution found by linearization about the MAP point to capture the main mode at a low computational cost. This research has been partially supported by the FEDER /Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación grants No. MTM2017-84446-C2-1-R and PID2020- 112796RB-C21. application/pdf eng IOP Publishing Inverse Problems. 2023, V. 39, n. 7, 075007 https://doi.org/10.1088/1361-6420/acd5f8 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Inverse scattering Full waveform inversion Topological energy Bayesian inference Markov Chain Monte Carlo PDE constrained optimization Laplace approximation Matemáticas Ciencias biomédicas Mathematics Medical sciences Object based Bayesian full-waveform inversion for shear elastography info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Inverse Problems 39 7 075007