Design &implementation of complex-valued FIR digital filters with application to migration of seismic data

One-dimensional (I-D) and two-dimensional (2-D) frequency-space seismic migration FIR digital filter coefficients are of complex values when such filters require special space domain as well as wavenumber domain characteristics. In this thesis, such FIR digital filters are designed using Vector Space Projection Methods (VSPMs), which can satisfy the desired predefined filters' properties, for 2-D and three-dimensional (3-D) seismic data sets, respectively. More precisely, the pure and the relaxed projection algorithms, which are part of the VSPM theory, are derived. Simulation results show that the relaxed version of the pure algorithm can introduce significant savings in terms of the number of iterations required. Also, due to some undesirable background artifacts on migrated sections, a modified version of the pure algorithm was used to eliminate such effects. This modification has also led to a significant reduction in the number of computations when compared to both the pure and relaxed algorithms. We further propose a generalization of the l-D (real/complex-valued) pure algorithm to multi-dimensional (m-D) complex-valued FIR digital filters, where the resulting frequency responses possess an approximate equiripple nature. Superior designs are obtained when compared with other previously reported methods. In addition, we also propose a new scheme for implementing the predesigned 2-D migration FIR filters. This realization is based on Singular Value Decomposition (SVD). Unlike the existing realization methods which are used for this geophysical application, this cheap realization via SVD, compared with the true 2-D convolution, results in satisfactory wavenumber responses. Finally, an application to seismic migration of 2-D and 3-D synthetic sections is shown to confirm our theoretical conclusions. The proposed resulting migration FIR filters are applied also to the challenging SEGIEAGE Salt model data. The migrated section (image) outperformed images obtained using other FIR filters and with other standard migration techniques where difficult structures contained in such a challenging model are imaged clearly

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

Numerical Issues When Using Wavelets

International audienceWavelets and related multiscale representations pervade all areas of signal processing. The recent inclusion of wavelet algorithms in JPEG 2000 – the new still-picture compression standard– testifies to this lasting and significant impact. The reason of the success of the wavelets is due to the fact that wavelet basis represents well a large class of signals, and therefore allows us to detect roughly isotropic elements occurring at all spatial scales and locations. As the noise in the physical sciences is often not Gaussian, the modeling, in the wavelet space, of many kind of noise (Poisson noise, combination of Gaussian and Poisson noise, long-memory 1/f noise, non-stationary noise, ...) has also been a key step for the use of wavelets in scientific, medical, or industrial applications [1]. Extensive wavelet packages exist now, commercial (see for example [2]) or non commercial (see for example [3, 4]), which allows any researcher, doctor, or engineer to analyze his data using wavelets

Adaptive interference suppression for DS-CDMA systems based on interpolated FIR filters with adaptive interpolators in multipath channels

In this work we propose an adaptive linear receiver structure based on interpolated finite impulse response (FIR) filters with adaptive interpolators for direct sequence code division multiple access (DS-CDMA) systems in multipath channels. The interpolated minimum mean-squared error (MMSE) and the interpolated constrained minimum variance (CMV) solutions are described for a novel scheme where the interpolator is rendered time-varying in order to mitigate multiple access interference (MAI) and multiple-path propagation effects. Based upon the interpolated MMSE and CMV solutions we present computationally efficient stochastic gradient (SG) and exponentially weighted recursive least squares type (RLS) algorithms for both receiver and interpolator filters in the supervised and blind modes of operation. A convergence analysis of the algorithms and a discussion of the convergence properties of the method are carried out for both modes of operation. Simulation experiments for a downlink scenario show that the proposed structures achieve a superior BER convergence and steady-state performance to previously reported reduced-rank receivers at lower complexity