Effective Parameter Dimension via Bayesian Model Selection in the Inverse Acoustic Scattering Problem

González, Abel Palafox; Capistrán, Marcos A.; Christen, J. Andrés

doi:10.1155/2014/427203

Cited by 7 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, EOE˛ D 0.25 and varOE˛ D 0.625. See in Algorithm 1 our MCMC method with the affine invariant moves defined by (18), (19), and (20).…”

Section: Markov Chain Monte Carlo Designmentioning

confidence: 99%

“…Point move (18) Translate (19) Alpha move (20) 4: Compute the energy ". tC1 /, where tC1 is obtained from point cloud tC1 P,˛w ith alpha shape algorithm.…”

Section: Algorithm 1 Point Cloud Affine Invariant Random Walk Metropomentioning

confidence: 99%

“…In the Bayesian setting, finite dimensional approximations to the infinite dimensional Bayesian posterior measure use a Karhunen-Loève representation of the scatterer to analyze the contribution of errors coming from the likelihood [18] and prior to provide convergence estimates. However, numerical implementation of such method is not available yet as the prior measure is formulated on the infinite dimensional space of scatterers, and moreover, global representations for the scatterer, as finite Karhunen-Loève, may be numerically unstable, as evidenced in [19]. Moreover, although it is possible to compute the Laplace approximation in the inverse scattering problem by computing the derivative of the posterior distribution with respect to the obstacle boundary in order to build the Hessian of the posterior distribution, as carried out in [20], obtaining a stable method to represent the obstacle boundary in order to compute the maximum a posterior (MAP) is a nontrivial problem as studied in [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Point cloud‐based scatterer approximation and affine invariant sampling in the inverse scattering problem

González

Capistrán

Christen

2016

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

We study the problem of recovering a scatterer object boundary by measuring the acoustic far field using Bayesian inference. This is the inverse acoustic scattering problem, and Bayesian inference is used to quantify the uncertainty on the unknowns (e.g., boundary shape and position). Aiming at sampling efficiently from the arising posterior probability distribution, we introduce a probability transition kernel (sampler) that is invariant under affine transformations of space. The sampling is carried out over a cloud of control points used to interpolate candidate boundary solutions. We demonstrate the performance of our method through a classical problem.

show abstract

“…Furthermore, EOE˛ D 0.25 and varOE˛ D 0.625. See in Algorithm 1 our MCMC method with the affine invariant moves defined by (18), (19), and (20).…”

Section: Markov Chain Monte Carlo Designmentioning

confidence: 99%

“…Point move (18) Translate (19) Alpha move (20) 4: Compute the energy ". tC1 /, where tC1 is obtained from point cloud tC1 P,˛w ith alpha shape algorithm.…”

Section: Algorithm 1 Point Cloud Affine Invariant Random Walk Metropomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Point cloud‐based scatterer approximation and affine invariant sampling in the inverse scattering problem

González

Capistrán

Christen

2016

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Previous work in 3D light holographic settings also applied MCMC sampling to infer the location, size and refractive index of single spherical particles [19]. In [50][51][52], scattering from single 2D sound-soft objects is considered. Here, the objects are placed at known locations and inference is based on far-field, small-noise, complex data.…”

Section: Introductionmentioning

confidence: 99%

Bayesian approach to inverse scattering with topological priors

Carpio¹,

Iakunin²,

Stadler³

2020

Inverse Problems

View full text Add to dashboard Cite

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field representing the objects. To construct the prior distribution we use a topological sensitivity analysis. We demonstrate the approach on the Bayesian solution of 2D inverse problems in light and acoustic holography with synthetic data. Statistical information on objects such as their center location, diameter size, orientation, as well as material properties, are extracted by sampling the posterior distribution. Assuming the number of objects known, comparison of the results obtained by Markov Chain Monte Carlo sampling and by sampling a Gaussian distribution found by linearization about the maximum a posteriori estimate show reasonable agreement. The latter procedure has low computational cost, which makes it an interesting tool for uncertainty studies in 3D. However, MCMC sampling provides a more complete picture of the posterior distribution and yields multi-modal posterior distributions for problems with larger measurement noise. When the number of objects is unknown, we devise a stochastic model selection framework.

show abstract

“…(a), (b). Palafox et al[16] introduced this procedure to estimate the boundary of a smooth sound obstacle from far field data. A detailed description of the algorithm is as follows: Spline interpolation of the non-convex hull of a point cloud in 2D Data: Let us Q = {p i } m t=1 a set of m points within the domain of the problem, Q ⊂ G ⊂ R 2 , and α a positive real number.…”

mentioning

confidence: 99%

A computational geometry method for the inverse scattering problem

Daza-Torres,

del Río,

Capistrán

et al. 2018

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the support of a scatterer by a point cloud. Secondly, we use the Bayesian paradigm to model the joint conditional probability distribution of the non-convex hull of the point cloud and the constant refractive index of the scatterer given near field data. Of note, we use the non-convex hull of the point cloud as spline control points to evaluate, on a finer mesh, the volume potential arising in the integral equation formulation of the direct problem. Finally, in order to sample the arising posterior distribution, we propose a probability transition kernel that commutes with affine transformations of space. Our findings indicate that our method is reliable to retrieve the support and constant refractive index of the scatterer simultaneously. Indeed, our sampling method is robust to estimate a quantity of interest such as the area of the scatterer. We conclude pointing out a series of generalizations of our method.

show abstract

Effective Parameter Dimension via Bayesian Model Selection in the Inverse Acoustic Scattering Problem

Cited by 7 publications

References 15 publications

Point cloud‐based scatterer approximation and affine invariant sampling in the inverse scattering problem

Point cloud‐based scatterer approximation and affine invariant sampling in the inverse scattering problem

Bayesian approach to inverse scattering with topological priors

A computational geometry method for the inverse scattering problem

Contact Info

Product

Resources

About