A wavelet based partial update fast LMS/Newton algorithm

This paper studies a wavelet based partial update fast LMS/Newton algorithm. Different from the conventional fast LMS/Newton algorithm, the proposed algorithm first uses a shorter-order, partial Haar transform-based NLMS adaptive filter to estimate the peak position of the long, sparse channel impulse response, and then employs the fast LMS/Newton algorithm integrated with partial update technique to fulfill the rest convergence task. The experimental results demonstrate the proposed algorithm outperforms its conventional counterpart in convergence performance and possesses a significantly lower computational complexity. © 2005 IEEE.published_or_final_versio

Discrete wavelet transform-based RI adaptive algorithm for system identification

In this paper, we propose a new adaptive filtering algorithm for system identification. The algorithm is based on the recursive inverse (RI) adaptive algorithm which suffers from low convergence rates in some applications; i.e., the eigenvalue spread of the autocorrelation matrix is relatively high. The proposed algorithm applies discrete-wavelet transform (DWT) to the input signal which, in turn, helps to overcome the low convergence rate of the RI algorithm with relatively small step-size(s). Different scenarios has been investigated in different noise environments in system identification setting. Experiments demonstrate the advantages of the proposed DWT recursive inverse (DWT-RI) filter in terms of convergence rate and mean-square-error (MSE) compared to the RI, discrete cosine transform LMS (DCTLMS), discrete-wavelet transform LMS (DWT-LMS) and recursive-least-squares (RLS) algorithms under same conditions

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

Hirschman optimal transform least mean square adaptive filters.

Abstract not available

Astronomical image manipulation in the transform domain

It is well known that images are usually stored and transmitted in the compressed form to save memory space and I/O bandwidth. Among many image compression schemes, transform coding is a widely used coding method. Traditionally, processing a compressed image requires decompression first. Following manipulations, the processed image is compressed again for storage. To reduce the computational complexity and processing time, manipulating images in the semi-compressed or transform domain is an efficient solution; Many astronomical images are compressed and stored by JPEG and HCOM-PRESS, which are based on the Discrete Cosine Transform (DCT) and the Discrete Wavelet Transform (DWT), respectively. In this thesis, a suite of image processing algorithms in the transform domain, DCT and DWT, is developed. In particular, new methods for edge enhancement and minimum (MIN)/maximum (MAX) gray scale intensity estimation in the DCT domain are proposed. Algebraic operations and image interpolation in the DWT domain are addressed. The superiority of new algorithms over the conventional ones is demonstrated by comparing the time complexities and qualities of the processed image in the transform domain to those in the spatial domain

Algoritmos adaptativos com sinal de entrada normalizado: modelagem estatística e aprimoramentos

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2010Este trabalho apresenta uma análise estatística de três importantes algoritmos adaptativos baseados no gradiente estocástico utilizando sinais de entrada normalizados. Os algoritmos com sinal de entrada normalizado são utilizados como uma alternativa ao algoritmo LMS (least-mean-square) convencional, visando melhorar a velocidade de convergência (especialmente para sinais de entrada correlacionados), tornando o desempenho do filtro adaptativo mais robusto frente a variações de potência do sinal de entrada. São apresentados modelos estatísticos mais precisos para os algoritmos considerados, a saber: LMS normalizado (NLMS), LMS no domínio transformado (LMS-DT) e gradiente estocástico com restrições (Constrained Stochastic Gradient - CSG). Em particular, o algoritmo CSG, aqui discutido, é utilizado em controle de arranjos de antenas para sistemas celulares. Através do modelo do algoritmo CSG, é verificado um comportamento anômalo e é proposta uma versão melhorada para esse algoritmo. Para os outros algoritmos adaptativos estudados, os modelos obtidos apresentam maior precisão quando comparados com outros modelos disponíveis na literatura, permitindo um melhor domínio desses algoritmos para diferentes condições de operação.This research work presents a statistical analysis for three important adaptive algorithms based on the stochastic gradient using normalized input signal. Algorithms with normalized input signal are used as an alternative to the standard least-mean-square (LMS) algorithm aiming to improve the convergence speed (especially for correlated input signal), increasing the adaptive filter robustness under input signal power variations. More accurate statistical models for the normalized LMS (NLMS), transform domain LMS (TDLMS), and constrained stochastic gradient (CSG) algorithms are presented. In particular, the CSG algorithm here considered is used for controlling antenna arrays in cellular systems. Through the CSG algorithm model, an anomalous behavior in its standard version is verified and an improved algorithm is also proposed. For the other algorithms, the obtained models are more accurate than the ones available in the literature, allowing a better and deeper understanding of theses algorithms under different operating conditions

Análise estatística do algoritmo £LMS no domínio transformado em ambientes estacionários e não-estacionários

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Elétrica.Este trabalho apresenta uma análise estatística do algoritmo LMS (least mean square) no domínio transformado (LMS DT) tanto para ambientes estacionários quanto não estacionários, resultando em um modelo mais preciso do que aqueles apresentados na literatura atual. A motivação para analisar tal algoritmo vem do fato de que este apresenta uma taxa de convergência mais alta para sinais correlacionados quando comparado com outros algoritmos adaptativos tendo complexidade computacional similar. Tal fato o torna bastante competitivo devido ao grande número de aplicações que consideram sinais de entrada coloridos. O algoritmo LMS DT apresenta uma etapa de transformação ortogonal, que promove uma separação do sinal de entrada em sinais ocupando bandas de freqüência distintas. As amostras intrabandas são correlacionadas, sendo esta correlação mais alta à medida que o número de bandas aumenta. Em nosso conhecimento, não existe um modelo estatístico que forneça uma solução geral e precisa levando em conta tal correlação. Assim, este trabalho propõe um modelo estatístico para o algoritmo LMS DT considerando as correlações existentes intrabandas. A partir deste modelo, são obtidos parâmetros de projeto, tais como passos de adaptação máximo e ótimo, como também o desajuste do algoritmo. Por meio de simulações numéricas, constata se uma boa concordância entre os resultados obtidos através do método de Monte Carlo e aqueles fornecidos pelo modelo estatístico proposto, tanto para sinais de entrada Gaussianos brancos quanto coloridos. This work presents a statistical analysis of the transform domain least mean square (TDLMS) algorithm for both stationary and nonstationary environment, resulting in a more accurate model than those discussed in the current open literature. The motivation to analyze such an algorithm comes from the fact that this presents, for correlated signals, a higher convergence speed as compared with other adaptive algorithms that possess a similar computational complexity. Such a fact makes it a highly competitive alternative to applications considering colored input signals. The TDLMS algorithm has an orthogonal transformation stage, providing a separation of the input signal into different frequency bands. The intra band samples are correlated, being the larger the number of bands, the higher is the correlation. Up to our knowledge, there is no other statistical model of this adaptive algorithm, providing a general and accurate solution, taking into account such correlations. In this way, this work proposes an accurate model allowing for these existing intra band correlations. Project parameters are obtained from the statistical model, such as upper bound for the step size, optimum step size value, and algorithm misadjustment. Through numerical simulations, a good agreement between the Monte Carlo method and the predictions from the proposed statistical model is verified for both white and colored Gaussian input signals

Contribuições à modelagem estocástica de algoritmos adaptativos normalizados

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2015.Este trabalho de pesquisa trata da modelagem estocástica de três algoritmos adaptativos bem conhecidos da literatura, a saber: o algoritmo NLMS (normalized least-mean-square), o algoritmo IAF PNLMS (individual-activation-factor proportionate NLMS) e o algoritmo TDLMS (transform-domain least-mean-square). Particularmente para o algoritmo NLMS, um modelo estocástico analítico é obtido levando em conta um ambiente não estacionário e sinais de entrada gaussianos complexos. Baseado nas expressões de modelo, o impacto dos parâmetros do algoritmo sobre o seu desempenho é discutido, evidenciando algumas das características de rastreamento do algoritmo NLMS frente ao ambiente não estacionário considerado. Para o algoritmo IAF-PNLMS, assumindo um ambiente estacionário, um modelo estocástico mais preciso do que os até então disponíveis na literatura é apresentado, considerando sinais de entrada gaussianos correlacionados tanto complexos quanto reais. Com respeito ao algoritmo TDLMS, um modelo estocástico melhorado é derivado focando em um ambiente não estacionário e sinais de entrada gaussianos correlacionados reais. A partir das expressões de modelo obtidas, o impacto dos parâmetros do algoritmo TDLMS sobre o seu desempenho é discutido. Resultados de simulação para diferentes cenários de operação são mostrados, confirmando a precisão dos modelos estocásticos propostos tanto na fase transitória quanto em regime permanente.Abstract : This research work focuses on the stochastic modeling of three well-known adaptive algorithms from the literature, namely: the normalized least-mean-square (NLMS) algorithm, the individual-activation-factor proportionate NLMS (IAF-PNLMS) algorithm, and the transform-domain least-mean-square (TDLMS) algorithm. Particularly for the NLMS algorithm, an analytical stochastic model is obtained taking into account a nonstationary environment and complex-valued Gaussian input data. Based on the obtained model expressions, the impact of the algorithm parameters on its performance is discussed, clarifying some of the tracking properties of the NLMS algorithm vis-à-vis the nonstationary environment considered. For the IAF-PNLMS algorithm, assuming a stationary environment, a more accurate stochastic model than those available so far in the literature is presented considering both complex- and real-valued Gaussian correlated input data. Regarding the TDLMS algorithm, an improved stochastic model is derived focusing on a nonstationary environment and real-valued Gaussian correlated input data. From the obtained model expressions, the impact of the TDLMS algorithm parameters on its performance is discussed. Simulation results for different operating scenarios are shown, confirming the accuracy of the proposed stochastic models for both transient and steady-state phases