Columbia University

Bhp Billiton Innovation Pty Ltd

Zoran (france)

Jerome Kalifa

Stephane Mallat

Christophe Bernard

Michael Edwin Glinsky

Erwan Le Pennec

Andrew F Laine

Peter Esser

A method and apparatus for processing or compressing an n-dimensional digital signal by constructing a sparse representation which takes advantage of the signal geometrical regularity. The invention comprises a warped wavelet packet transform which performs a cascade of warped subband filtering along warping grids of sampling points adapted to the signal geometry. It also comprises a bandeletisation which decorrelates the warped wavelet packet coefficients to produce a sparse representation. An inverse warped wavelet packet transform and an inverse bandeletisation reconstruct a signal from its bandelet representation. The invention comprises a compression system which quantizes and codes the bandelet representation, a decompression system, a restoration system which enhances a signal by filtering its bandelet representation, and a feature vector extraction system for pattern recognition applications of a bandelet representation.

Processing or compressing n-dimensional signals with warped wavelet packets and bandelets

A method for determining impedance coefficients of a seismic trace comprises determining reflection coefficients of the seismic trace, for example using a sparse spike inversion, integrating the reflection coefficients with respect to time to obtain impedance coefficients, and filtering the impedance coefficients by applying a low-cut window filter. The window size and/or shape may be defined by a variable parameter which may be either specified by a user or optimized on the basis of a lateral variability parameter calculated for different values of the window parameter.

Method for determining impedance coefficients of a seismic trace

Techniques for tomographic reconstruction using non-linear diagonal estimators are disclosed. In a preferred embodiment, tomographic data from a tomographic device is decomposed in a wavelet vector family. Regularization of the tomographic data is accomplished by performing a thresholding operation on coefficients of the decomposed data. The regularized data is reconstructed into image data that may he displayed. In another preferred embodiment, a wavelet packet vector family is used to decompose the tomographic data. The wavelet packet is selected from a dictionary of wavelet packets using the best basis algorithm.

Method for tomographic reconstruction with non-linear diagonal estimators

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Paris, France

Jerome Kalifa