Abstract: 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 optimised on the basis of a lateral variability parameter calculated for different values of the window parameter.

Abstract: A method and apparatus for processing or compressing an n-dimensional digital signal by constructing a sparse rep resentation 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 wraping 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.

Abstract: Methods and apparatus for processing n-dimensional digitized signals with a foveal processing which constructs a sparse representation by taking advantage of the geometrical regularity of the signal structures. This invention can compress, restore, match and classify signals. Foveal coefficients are computed with one-dimensional inner products along trajectories of an n-directional trajectory list. The invention includes a trajectory finder which computes an n-directional trajectory list from the input n-dimensional signal, in order to choose optimal locations to compute the foveal coefficients. From foveal coefficients, a foveal reconstruction processor recovers a signal approximation which has the same geometrical structures as the input signal along the trajectories and which is regular away from these trajectories. A foveal residue can be calculated as a difference with the input signal.

Abstract: Methods and apparatus for processing n-dimensional digitized signals with a foveal processing which constructs a sparse representation by taking advantage of the geometrical regularity of the signal structures. This invention can compress, restore, match and classify signals. Foveal coefficients are computed with one-dimensional inner products along trajectories of an n-directional trajectory list. The invention includes a trajectory finder which computes an n-directional trajectory list from the input n-dimensional signal, in order to choose optimal locations to compute the foveal coefficients. From foveal coefficients, a foveal reconstruction processor recovers a signal approximation which has the same geometrical structures as the input signal along the trajectories and which is regular away from these trajectories. A foveal residue can be calculated as a difference with the input signal.