A multiplicative regularization for force reconstruction

We consider an inverse scattering problem to identify the locations or shapes of unknown anomalies from scattering parameter data collected by a small number of dipole antennas. Most of researches does not considered the influence of dipole antennas but in the experimental simulation, they are significantly affect to the identification of anomalies. Moreover, opposite to the theoretical results, it is impossible to handle scattering parameter data when the locations of the transducer and receiver are the same in real-world application. Motivated by this, we design an imaging function with and without diagonal elements of the so-called scattering matrix. This concept is based on the Born approximation and the physical interpretation of the measurement data when the locations of the transducer and receiver are the same and different. We carefully explore the mathematical structures of traditional and proposed imaging functions by finding relationships with the infinite series of Bessel functions of integer order. The explored structures reveal certain properties of imaging functions and show why the proposed method is better than the traditional approach. We present the experimental results for small and extended anomalies using synthetic and real data at several angular frequencies to demonstrate the effectiveness of our technique.

“…Proof. First, we derive (14). Since |d n − r| 0.25/k and |d n − r | 0.25/k, applying the asymptotic form of the Hankel function…”

Section: Analysis Of Imaging Functionsmentioning

confidence: 99%

Real-time microwave imaging of unknown anomalies via scattering matrix

Park

2019

“…Incidentally, the optimal value of the regularization parameter λ (0) can not be directly estimated from the marginalized MAP [36], the L-curve principle [37] or the Generalized Cross Validation [16] before solving the minimization problem [see Ref. [35] for details]. To this end, the optimization problem is solved iteratively using an adapted Iteratively Reweighted (IR) algorithm, which allows determining in an iterative manner the regularized force vector as well as the optimal regularization parameter associated to the minimization problem.…”

Section: Initialization Of the Resolution Algorithmmentioning

confidence: 99%

An optimal Bayesian regularization for force reconstruction problems

Aucejo

Smet

2019

Self Cite

In a paper, recently published in Mechanical Systems and Signal Processing, we have proposed a full Bayesian inference for reconstructing mechanical sources acting on a linear and time invariant structure. The main interest of this approach is to propose an estimation of all the parameters of the model and quantify the posterior uncertainty associated to each parameter.Since all the necessary information about the problem is available, statistical measures, such as the mean, the median and the mode of the solution, can be easily estimated. In many practical situations, however, one only wants to determine the most probable parameters given the available data. Consequently, it is not relevant to implement a full Bayesian inference to only extract a point estimate. To overcome this potential issue, this paper introduces an optimal Bayesian regularization aiming at computing the Maximum a Posteriori estimate of the Bayesian formulation previously introduced by the authors. In doing so, the most probable parameters are obtained without heavy computations. The validity of the proposed method is assessed numerically and experimentally. In particular, obtained results highlight the ability of the proposed regularization strategy in computing solutions with a minimal amount of prior information on the sources to identify.

“…Incidentally, the optimal value of the regularization parameter λ (0) can not be directly estimated from the marginalized MAP [23], the L-curve principle [32] or the Generalized Cross Validation [33] before solving the minimization problem [see Ref. [34] for details]. To this end, the optimization problem is solved iteratively using an Iteratively Reweighted Least Squares (IRLS) algorithm [34,35], which allows determining in an iterative manner the regularized force vector as well as the optimal regularization parameter associated to the minimization problem.…”

mentioning

confidence: 99%

“…[34] for details]. To this end, the optimization problem is solved iteratively using an Iteratively Reweighted Least Squares (IRLS) algorithm [34,35], which allows determining in an iterative manner the regularized force vector as well as the optimal regularization parameter associated to the minimization problem.…”

mentioning

confidence: 99%

See 1 more Smart Citation

On a full Bayesian inference for force reconstruction problems

Aucejo

Smet

2018

Self Cite

To cite this version:M. Aucejo, Olivier de Smet. On a full Bayesian inference for force reconstruction problems. Mechanical Systems and Signal Processing, Elsevier, 2018, 104, pp. AbstractIn a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter's prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem.