Vitor H. Nascimento

Improving the Tracking Capability of Adaptive Filters via Convex Combination

As is well known, Hessian-based adaptive filters (such as the recursive-least squares algorithm (RLS) for supervised adaptive filtering, or the Shalvi-Weinstein algorithm (SWA) for blind equalization) converge much faster than gradient-based algorithms [such as the least-mean-squares algorithm (LMS) or the constant-modulus algorithm (CMA)]. However, when the problem is tracking a time-variant filter, the issue is not so clear-cut: there are environments for which each family presents better performance. Given this, we propose the use of a convex combination of algorithms of different families to obtain an algorithm with superior tracking capability. We show the potential of this combination and provide a unified theoretical model for the steady-state excess mean-square error for convex combinations of gradient- and Hessian-based algorithms, assuming a random-walk model for the parameter variations. The proposed model is valid for algorithms of the same or different families, and for supervised (LMS and RLS) or blind (CMA and SWA) algorithms.

A Regularized Robust Design Criterion for Uncertain Data

This paper formulates and solves a robust criterion for least-squares designs in the presence of uncertain data. Compared with earlier studies, the proposed criterion incorporates simultaneously both regularization and weighting and applies to a large class of uncertainties. The solution method is based on reducing a vector optimization problem to an equivalent scalar minimization problem of a provably unimodal cost function, thus achieving considerable reduction in computational complexity.

Convex Combination of Adaptive Filters with Different Tracking Capabilities

Recently, an adaptive convex combination of two LMS (least mean-square) filters was proposed and its tracking performance analyzed. Motivated by the performance of such scheme and by the differences between the tracking capabilities of the RLS (recursive least-squares) and LMS algorithms, we propose a convex combination of one LMS and one RLS filter. The resulting combination should profit of the best tracking behavior of each component filter. A steady-state analysis via energy conservation relation is also presented for stationary and non-stationary environments.

Crowdsourcing subjective image quality evaluation

Subjective tests are generally regarded as the most reliable and definitive methods for assessing image quality. Nevertheless, laboratory studies are time consuming and expensive. Thus, researchers often choose to run informal studies or use objective quality measures, producing results which may not correlate well with human perception. In this paper we propose a cost-effective and convenient subjective quality measure called crowdMOS, obtained by having internet workers participate in MOS (mean opinion score) subjective quality studies. Since these workers cannot be supervised, we propose methods for detecting and discarding inaccurate or malicious scores. To facilitate this process, we offer an open source set of tools for Amazon Mechanical Turk, which is an internet marketplace for crowdsourcing. These tools completely automate the test design, score retrieval and statistical analysis, abstracting away the technical details of Mechanical Turk and ensuring a user-friendly, affordable and consistent test methodology. We demonstrate crowdMOS using data from the LIVE subjective quality image dataset, showing that it delivers accurate and repeatable results.

Estimation and control with bounded data uncertainties

The paper describes estimation and control strategies for models with bounded data uncertainties. We shall refer to them as BDU estimation and BDU control methods, for brevity. They are based on constrained game-type formulations that allow the designer to explicitly incorporate into the problem statement a priori information about bounds on the sizes of the uncertainties. In this way, the effect of uncertainties is not unnecessarily over-emphasized beyond what is implied by the a priori bounds; consequently, overly conservative designs, as well as overly sensitive designs, are avoided. A feature of these new formulations is that geometric insights and recursive techniques, which are widely known and appreciated for classical quadratic-cost designs, can also be pursued in this new framework. Also, algorithms for computing the optimal solutions with the same computational effort as standard least-squares solutions exist, thus making the new formulations attractive for practical use. Moreover, the framework is broad enough to encompass applications across several disciplines, not just estimation and control. Examples will be given of a quadratic control design, an H∞ control design, a total-least-square design, image restoration, image separation, and co-channel interference cancellation. A major theme in this paper is the emphasis on geometric and linear algebraic arguments, which lead to useful insights about the nature of the new formulations. Despite the interesting results that will be discussed, several issues remain open and indicate potential future developments; these will be briefly discussed.

Transient and Steady-State Analysis of the Affine Combination of Two Adaptive Filters

In this paper, we propose an approach to the transient and steady-state analysis of the affine combination of one fast and one slow adaptive filters. The theoretical models are based on expressions for the excess mean-square error (EMSE) and cross-EMSE of the component filters, which allows their application to different combinations of algorithms, such as least mean-squares (LMS), normalized LMS (NLMS), and constant modulus algorithm (CMA), considering white or colored inputs and stationary or nonstationary environments. Since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant, its adaptation is also taken into account in the transient analysis. Furthermore, we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance. Good agreement between analysis and simulation results is always observed.

On the learning mechanism of adaptive filters

This paper highlights, both analytically and by simulations, some interesting phenomena regarding the behavior of ensemble-average learning curves of adaptive filters that may have gone unnoticed. Among other results, the paper shows that even ensemble-average learning curves of single-tap LMS filters actually exhibit two distinct rates of convergence: one for the initial time instants and another, faster one, for later time instants. In addition, such curves tend to converge faster than predicted by mean-square theory and can converge even when a mean-square stability analysis predicts divergence. These effects tend to be magnified by increasing the step size. Two of the conclusions that follow from this work are (1) the mean-square stability alone may not be the most appropriate performance measure, especially for larger step sizes. A combination of mean-square stability and almost sure (a.s.) stability seems to be more appropriate. (2) Care is needed while interpreting ensemble-average curves for larger step sizes. The curves can lead to erroneous conclusions unless a large number of experiments are averaged (at times of the order of tens of thousands or higher).

Unbiased and stable leakage-based adaptive filters

The paper develops a leakage-based adaptive algorithm, referred to as circular-leaky, which in addition to solving the drift problem of the classical least mean squares (LMS) adaptive algorithm, it also avoids the bias problem that is created by the standard leaky LMS solution. These two desirable properties of unbiased and bounded estimates are guaranteed by circular-leaky at essentially the same computational cost as LMS. The derivation in the paper relies on results from averaging theory and from Lyapunov stability theory, and the analysis shows that the above properties hold not only in infinite-precision but also in finite-precision arithmetic. The paper further extends the results to a so-called switching-/spl sigma/ algorithm, which is a leakage-based solution used in adaptive control.

Improving the initial convergence of adaptive filters: variable-length LMS algorithms

Despite its qualities of robustness, low cost, and good tracking performance, in many situations the LMS algorithm suffers from slow initial convergence. We propose a method to speed up this convergence rate by varying the length of the adaptive filter, taking advantage of the larger step-sizes allowed for short filters. The results presented here show that variable-length adaptive filters have the potential to achieve quite fast convergence rates, with a modest increase in the computational complexity.

Combinations of Adaptive Filters: Performance and convergence properties

Adaptive filters are at the core of many signal processing applications, ranging from acoustic noise supression to echo cancelation [1], array beamforming [2], channel equalization [3], to more recent sensor network applications in surveillance, target localization, and tracking. A trending approach in this direction is to recur to in-network distributed processing in which individual nodes implement adaptation rules and diffuse their estimation to the network [4], [5].