Probabilistic Inverse Theory

Dębski, Wojciech

doi:10.1016/s0065-2687(10)52001-6

Cited by 32 publications

(25 citation statements)

References 205 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is entirely expected that within the framework laid out here and in the companion paper [1] displacement estimation performance will continue to improve. This improvement will come from increasingly sophisticated methods for computing prior information [20], [21]. …”

Section: Discussionmentioning

confidence: 99%

Bayesian speckle tracking. Part II: biased ultrasound displacement estimation

Byram

Trahey

Palmeri

2013

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

View full text Add to dashboard Cite

Ultrasonic displacement estimates have numerous clinical uses including blood-flow, elastography, therapeutic guidance and ARFI imaging. These clinical tasks could be improved with better ultrasonic displacement estimates. Traditional ultrasonic displacement estimates are limited by the Cramer-Rao lower bound (CRLB). The CRLB can be surpassed using biased estimates. In this paper a framework for biased estimation using Bayes’ theorem is described. The Bayesian displacement estimation method is tested against simulations of several common types of motion: bulk, step, compression, and acoustic radiation force induced motion. Bayesian estimation is also applied to in vivo acoustic radiation force imaging of cardiac ablation lesions. The Bayesian estimators are compared to the unbiased estimator, normalized cross-correlation. As an example, the peak displacement of the simulated acoustic radiation force response is reported since this position results in the noisiest estimates. Estimates were made with a 1.5 λ kernel and 20 dB SNR on 100 data realizations. Estimates using normalized cross-correlation and the Bayes’ estimator had mean-square errors of 17 and 7.6 μm2, respectively, and contextualized by the true displacement magnitude, 10.9 μm. Biases for normalized cross-correlation and the Bayes’ estimator are −.12 and −.28 μm, respectively. In vivo results show qualitative improvements. The results show that with small amounts of additional information significantly improved performance can be realized.

show abstract

Section: Discussionmentioning

confidence: 99%

Bayesian speckle tracking. Part II: biased ultrasound displacement estimation

Byram

Trahey

Palmeri

2013

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

View full text Add to dashboard Cite

show abstract

“…In addition, regularization with Cauchy norm (Amundsen 1991; Sacchi 1997; Wang and Sacchi 2007) is used in this paper. In the Bayesian framework (Aster, Borchers, and Thurber 2005; Debski 2010), the regularization corresponds to a negative logarithm of the a priori distribution of the model. The choice of Cauchy distribution is meant to capture the sparse nature of typical reflectivity models.…”

Section: Methodsmentioning

confidence: 99%

Multisource least‐squares migration of marine streamer and land data with frequency‐division encoding

Huang

Schuster

2012

Geophysical Prospecting

View full text Add to dashboard Cite

Multisource migration of phase‐encoded supergathers has shown great promise in reducing the computational cost of conventional migration. The accompanying crosstalk noise, in addition to the migration footprint, can be reduced by least‐squares inversion. But the application of this approach to marine streamer data is hampered by the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite‐difference modelling method. This leads to a strong mismatch in the misfit function and results in strong artefacts (crosstalk) in the multisource least‐squares migration image. To eliminate this noise, we present a frequency‐division multiplexing (FDM) strategy with iterative least‐squares migration (ILSM) of supergathers. The key idea is, at each ILSM iteration, to assign a unique frequency band to each shot gather. In this case there is no overlap in the crosstalk spectrum of each migrated shot gather m(x, ωi), so the spectral crosstalk product m(x, ωi)m(x, ωj) =δi, j is zero, unless i=j. Our results in applying this method to 2D marine data for a SEG/EAGE salt model show better resolved images than standard migration computed at about 1/10th of the cost. Similar results are achieved after applying this method to synthetic data for a 3D SEG/EAGE salt model, except the acquisition geometry is similar to that of a marine OBS survey. Here, the speedup of this method over conventional migration is more than 10. We conclude that multisource migration for a marine geometry can be successfully achieved by a frequency‐division encoding strategy, as long as crosstalk‐prone sources are segregated in their spectral content. This is both the strength and the potential limitation of this method.

show abstract

“…The price for choosing this robust measure I S is the necessity of performing the full probabilistic (Bayesian) inversion rather than the most popular optimization-based inversion (Debski 2010). Since the probabilistic inverse theory is still not commonly used, let us describe its very basic elements in the next section.…”

Section: Mathematics Of the Dd And Edd Location Algorithmsmentioning

confidence: 99%

“…Since the probabilistic inverse theory is still not commonly used, let us describe its very basic elements in the next section. Readers interested in the details of the probabilistic inverse theory are referred to the basic textbooks and review papers, for example, (Tarantola 1987(Tarantola , 2005Debski 2010;Mosegaard and Tarantola 2002;Mosegaard and Sambridge 2002;Lomax et al 2000;Matsu'ura 1984).…”

Section: Mathematics Of the Dd And Edd Location Algorithmsmentioning

confidence: 99%

See 1 more Smart Citation

Extending the double difference location technique—improving hypocenter depth determination

Rudziński

Dębski

2012

J Seismol

View full text Add to dashboard Cite

Locating the seismic event hypocenter is the very first issue undertaken when studying any seismological problem. Thus, the accuracy of the obtained solution can significantly influence consecutive stages of an analysis, so there is a continuous demand for new, more efficient, and accurate location algorithms. It is well recognized that there exists no single universal location algorithm which performs equally well in all situations. Seismic activity and its spatial variability over time, seismic network geometry, and the controlled area's geological complexity are factors influencing the performance of location algorithms. For example, in the case of mining applications, the planarity of the seismic network usually operated at the exploitation level becomes an important issue limiting the accuracy of location of the hypocenter depths. In this paper, we push forward the discussion on the performance of the newly proposed location algorithm called the extended double difference (EDD), concentrating on the reliability of source depth estimation for L. Rudziński (B) · W. Dȩbski Institute of Geophysics Polish Academy of Sciences, ul. Ks. Janusza 64, 01-452 Warsaw, Poland e-mail: rudzin@igf.edu.pl W. Dȩbski e-mail: debski@igf.edu.pl mining-induced seismic events. We demonstrate that the EDD algorithm very efficiently uses information originating from the nonplanarity of the seismic network, improving the hypocenter depth estimates with respect to the classical double difference technique. Methodological considerations are illustrated by real data analysis of selected events from the Rudna copper mine (Poland).

show abstract

Probabilistic Inverse Theory

Cited by 32 publications

References 205 publications

Bayesian speckle tracking. Part II: biased ultrasound displacement estimation

Bayesian speckle tracking. Part II: biased ultrasound displacement estimation

Multisource least‐squares migration of marine streamer and land data with frequency‐division encoding

Extending the double difference location technique—improving hypocenter depth determination

Contact Info

Product

Resources

About