BAYESIAN 3-D PATH SEARCH AND ITS APPLICATIONS TO FOCUSING SEISMIC DATA

The 3D-images studied here are essential to the analysis of cubes of seismic focalisation. In the detection of geological horizons, the improvement of migration techniques requires the construction of 3D “focal” paths. We start with blurred versions of (unknown) 3D-images consisting ideally of concentrated intensity spots which tend to lie on smooth isolated 3D-paths. The blur point-spread function is spatially dependent, roughly Gaussian in shape, and directly estimated on the blurred image. On the space of admissible paths, we describe the plausibility of a path by an energy function, using thus a 3D-Markov random field model. The adjustment of this Markov field model to the image data relies on an original interactive robust parameter localization approach.

[1]  M. Basseville.  Distance measures for signal processing and pattern recognition , 1989 .

[2]  John Sherwood,et al.  Depth migration before stack , 1980 .

[3]  Shin-Yee Lu,et al.  The Binary Consistency Checking Scheme and Its Applications to Seismic Horizon Detection , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Refining Prestack Depth-Migration Images Without Remigration , 1989 .

[5]  Bernard Chalmond,et al.  An iterative Gibbsian technique for reconstruction of m-ary images , 1989, Pattern Recognit..

[6]  Donald Geman,et al.  Boundary Detection by Constrained Optimization , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Benjamin B. Kimia,et al.  Deblurring Gaussian blur , 2015, Comput. Vis. Graph. Image Process..

[8]  Haluk Derin,et al.  Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Jon F. Claerbout,et al.  DOWNWARD CONTINUATION OF MOVEOUT‐CORRECTED SEISMOGRAMS , 1972 .

[11]  Jean-Pierre Faye,et al.  Prestack Migration Velocities From Focusing Depth Analysis , 1986 .

[12]  Patrick Bouthemy,et al.  Detection and Tracking of Moving Objects Based on a Statistical Regularization Method in Space and Time , 1990, European Conference on Computer Vision.

[13]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[14]  Jon F. Claerbout,et al.  Imaging the Earth's Interior , 1985 .

[15]  Tomaso Poggio,et al.  Probabilistic Solution of Ill-Posed Problems in Computational Vision , 1987 .

[16]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[17]  Oz Yilmaz,et al.  Migration velocity analysis by wave-field extrapolation , 1984 .

[18]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

[19]  J. W. Wiggins,et al.  Attenuation of complex water-bottom multiples by wave-equation-based prediction and subtraction , 1988 .

[20]  Eric Dubois,et al.  A Comparison Of Stochastic And Deterministic Solution Methods In Bayesian Estimation Of 2-D Motion , 1990, ECCV.

[21]  B. Chalmond.  Image restoration using an estimated Markov model , 1988 .

[22]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[23]  Bernard Chalmond,et al.  PSF estimation for image deblurring , 1991, CVGIP Graph. Model. Image Process..