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

Algorithms and structures for long adaptive echo cancellers

The main theme of this thesis is adaptive echo cancellation. Two novel independent approaches are proposed for the design of long echo cancellers with improved performance. In the first approach, we present a novel structure for bulk delay estimation in long echo cancellers which considerably reduces the amount of excess error. The miscalculation of the delay between the near-end and the far-end sections is one of the main causes of this excess error. Two analyses, based on the Least Mean Squares (LMS) algorithm, are presented where certain shapes for the transitions between the end of the near-end section and the beginning of the far-end one are considered. Transient and steady-state behaviours and convergence conditions for the proposed algorithm are studied. Comparisons between the algorithms developed for each transition are presented, and the simulation results agree well with the theoretical derivations. In the second approach, a generalised performance index is proposed for the design of the echo canceller. The proposed algorithm consists of simultaneously applying the LMS algorithm to the near-end section and the Least Mean Fourth (LMF) algorithm to the far-end section of the echo canceller. This combination results in a substantial improvement of the performance of the proposed scheme over both the LMS and other algorithms proposed for comparison. In this approach, the proposed algorithm will be henceforth called the Least Mean Mixed-Norm (LMMN) algorithm. The advantages of the LMMN algorithm over previously reported ones are two folds: it leads to a faster convergence and results in a smaller misadjustment error. Finally, the convergence properties of the LMMN algorithm are derived and the simulation results confirm the superior performance of this proposed algorithm over other well known algorithms

Adaptive filters for sparse system identification

Sparse system identification has attracted much attention in the field of adaptive algorithms, and the adaptive filters for sparse system identification are studied. Firstly, a new family of proportionate normalized least mean square (PNLMS) adaptive algorithms that improve the performance of identifying block-sparse systems is proposed. The main proposed algorithm, called block-sparse PNLMS (BS-PNLMS), is based on the optimization of a mixed ℓ2,1 norm of the adaptive filter\u27s coefficients. A block-sparse improved PNLMS (BS-IPNLMS) is also derived for both sparse and dispersive impulse responses. Meanwhile, the proposed block-sparse proportionate idea has been extended to both the proportionate affine projection algorithm (PAPA) and the proportionate affine projection sign algorithm (PAPSA). Secondly, a generalized scheme for a family of proportionate algorithms is also presented based on convex optimization. Then a novel low-complexity reweighted PAPA is derived from this generalized scheme which could achieve both better performance and lower complexity than previous ones. The sparseness of the channel is taken into account to improve the performance for dispersive system identification. Meanwhile, the memory of the filter\u27s coefficients is combined with row action projections (RAP) to significantly reduce the computational complexity. Finally, two variable step-size zero-point attracting projection (VSS-ZAP) algorithms for sparse system identification are proposed. The proposed VSS-ZAPs are based on the approximations of the difference between the sparseness measure of current filter coefficients and the real channel, which could gain lower steady-state misalignment and also track the change in the sparse system --Abstract, page iv

The Krylov-proportionate normalized least mean fourth approach: Formulation and performance analysis

Cataloged from PDF version of article.We propose novel adaptive filtering algorithms based on the mean-fourth error objective while providing further improvements on the convergence performance through proportionate update. We exploit the sparsity of the system in the mean-fourth error framework through the proportionate normalized least mean fourth (PNLMF) algorithm. In order to broaden the applicability of the PNLMF algorithm to dispersive (non-sparse) systems, we introduce the Krylov-proportionate normalized least mean fourth (KPNLMF) algorithm using the Krylov subspace projection technique. We propose the Krylov-proportionate normalized least mean mixed norm (KPNLMMN) algorithm combining the mean-square and mean-fourth error objectives in order to enhance the performance of the constituent filters. Additionally, we propose the stable-PNLMF and stable-KPNLMF algorithms overcoming the stability issues induced due to the usage of the mean fourth error framework. Finally, we provide a complete performance analysis, i.e., the transient and the steady-state analyses, for the proportionate update based algorithms, e.g., the PNLMF, the KPNLMF algorithms and their variants; and analyze their tracking performance in a non-stationary environment. Through the numerical examples, we demonstrate the match of the theoretical and ensemble averaged results and show the superior performance of the introduced algorithms in different scenarios. (C) 2014 Elsevier B.V. All rights reserved

SPARSE ECHO CANCELLATION USING VARIANTS OF LEAST MEAN FOURTH AND LEAST MEAN SQUARE ALGORITHMS

Echo cancellation is the most essential and indispensable component of telephone networks. The impulse responses of most of the networks are sparse in nature; that is, the impulse response has a small percentage of its components with a significant magnitude (large energy), while the rest are zero or small. In these sparse environments, conventional adaptive algorithms like least mean square (LMS) and normalized LMS (NLMS) show substandard and inferior performances. In this paper, the performances of the normalized least mean square (NLMS) algorithm, the normalized least mean fourth (NLMF) and the proportionate normalized least mean fourth (PNLMF) are compared for sparse echo cancellation. The sparseness of both the echo response and the input signal is exploited in this algorithm to achieve improved results at a low computational cost. The PNLMF algorithm showed better results and faster convergence in sparse and non sparse systems, but its results in sparse environments are more impressive. The NLMF algorithm shows good results in sparse environments but not in non-sparse environments. The PNLMS algorithm can be considered superior to the NLMF and NLMS algorithms with respect to the error profile. A modified algorithm, the sparse controlled modified proportionate normalized LMF (SCMPNLMF) algorithm, is proposed, and its performances are compared with the other algorithms

Echo Cancellation - A Likelihood Ratio Test for Double-talk Versus Channel Change

Echo cancellers are in wide use in both electrical (four wire to two wire mismatch) and acoustic (speaker-microphone coupling) applications. One of the main design problems is the control logic for adaptation. Basically, the algorithm weights should be frozen in the presence of double-talk and adapt quickly in the absence of double-talk. The control logic can be quite complicated since it is often not easy to discriminate between the echo signal and the near-end speaker. This paper derives a log likelihood ratio test (LRT) for deciding between double-talk (freeze weights) and a channel change (adapt quickly) using a stationary Gaussian stochastic input signal model. The probability density function of a sufficient statistic under each hypothesis is obtained and the performance of the test is evaluated as a function of the system parameters. The receiver operating characteristics (ROCs) indicate that it is difficult to correctly decide between double-talk and a channel change based upon a single look. However, post-detection integration of approximately one hundred sufficient statistic samples yields a detection probability close to unity (0.99) with a small false alarm probability (0.01)