Markus V. S. Lima

Bio: Markus V. S. Lima is an academic researcher from Federal University of Rio de Janeiro. The author has contributed to research in topics: Adaptive filter & Mean squared error. The author has an hindex of 12, co-authored 40 publications receiving 479 citations.

Sparsity-Aware Data-Selective Adaptive Filters

Abstract: We propose two adaptive filtering algorithms that combine sparsity-promoting schemes with data-selection mechanisms. Sparsity is promoted via some well-known nonconvex approximations to the l 0 norm in order to increase convergence speed of the algorithms when dealing with sparse/compressible signals. These approximations circumvent some difficulties of working with the l 0 norm, thus allowing the development of online data-selective algorithms. Data selection is implemented based on set-membership filtering, which yields robustness against noise and reduced computational burden. The proposed algorithms are analyzed in order to set properly their parameters to guarantee stability. In addition, we characterize their updating processes from a geometrical viewpoint. Simulation results show that the proposed algorithms outperform the state-of-the-art algorithms designed to exploit sparsity.

A Steered-Response Power Algorithm Employing Hierarchical Search for Acoustic Source Localization Using Microphone Arrays

Abstract: The localization of a speaker inside a closed environment is often approached by real-time processing of multiple audio signals captured by a set of microphones. One of the leading related methods for sound source localization, the steered-response power (SRP), searches for the point of maximum power over a spatial grid. High-accuracy localization calls for a dense grid and/or many microphones, which tends to impractically increase computational requirements. This paper proposes a new method for sound source localization (called H-SRP), which applies the SRP approach to space regions instead of grid points. This arrangement makes room for the use of a hierarchical search inspired by the branch-and-bound paradigm, which is guaranteed to find the global maximum in anechoic environments and shown experimentally to also work under reverberant conditions. Besides benefiting from the improved robustness of volume-wise search over point-wise search as to reverberation effects, the H-SRP attains high performance with manageable complexity. In particular, an experiment using a 16-microphone array in a typical presentation room yielded localization errors of the order of 7 cm, and for a given fixed complexity, competing methods' errors are two to three times larger.

Affine projection algorithms for sparse system identification

Abstract: We propose two versions of affine projection (AP) algorithms tailored for sparse system identification (SSI). Contrary to most adaptive filtering algorithms devised for SSI, which are based on the l1 norm, the proposed algorithms rely on homotopic l0 norm minimization, which has proven to yield better results in some practical contexts. The first proposal is obtained by direct minimization of the AP cost function with a penalty function based on the l0 norm of the coefficient vector, whereas the second algorithm is a simplified version of the first proposal. Simulation results are presented in order to evaluate the performance of the proposed algorithms considering three different homotopies to the l0 norm as well as competing algorithms.

Steady-State MSE Performance of the Set-Membership Affine Projection Algorithm

Abstract: The set-membership affine projection (SM-AP) algorithm has many desirable characteristics such as fast convergence speed, low power consumption due to data-selective updates, and low misadjustment. The main reason hindering the widespread use of the SM-AP algorithm is the lack of analytical results related to its steady-state performance. In order to bridge this gap, this paper presents an analysis of the steady-state mean square error (MSE) of a general form of the SM-AP algorithm. The proposed analysis results in closed-form expressions for the excess MSE and misadjustment of the SM-AP algorithm, which are also applicable to many other algorithms. This work also provides guidelines for the analysis of the whole family of SM-AP algorithms. The analysis relies on the energy conservation method and has the attractive feature of not assuming a specific model for the input signal. In addition, the choice of the upper bound for the error of the SM-AP algorithm is addressed for the first time. Simulation results corroborate the accuracy of the proposed analysis.

On the robustness of set-membership adaptive filtering algorithms

Abstract: In this paper, we address the robustness, in the sense of l 2-stability, of the set-membership normalized least-mean-square (SM-NLMS) and the set-membership affine projection (SM-AP) algorithms. For the SM-NLMS algorithm, we demonstrate that it is robust regardless of the choice of its parameters and that the SM-NLMS enhances the parameter estimation in most of the iterations in which an update occurs, two advantages over the classical NLMS algorithm. Moreover, we also prove that if the noise bound is known, then we can set the SM-NLMS so that it never degrades the estimate. As for the SM-AP algorithm, we demonstrate that its robustness depends on a judicious choice of one of its parameters: the constraint vector (CV). We prove the existence of CVs satisfying the robustness condition, but practical choices remain unknown. We also demonstrate that both the SM-AP and SM-NLMS algorithms do not diverge, even when their parameters are selected naively, provided the additional noise is bounded. Numerical results that corroborate our analyses are presented.

A Survey of Stochastic Simulation and Optimization Methods in Signal Processing

Abstract: Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inference in models that are analytically intractable and beyond the scope of deterministic inference methods. They have been recently successfully applied to many difficult problems involving complex statistical models and sophisticated (often Bayesian) statistical inference techniques. This survey paper offers an introduction to stochastic simulation and optimization methods in signal and image processing. The paper addresses a variety of high-dimensional Markov chain Monte Carlo (MCMC) methods as well as deterministic surrogate methods, such as variational Bayes, the Bethe approach, belief and expectation propagation and approximate message passing algorithms. It also discusses a range of optimization methods that have been adopted to solve stochastic problems, as well as stochastic methods for deterministic optimization. Subsequently, areas of overlap between simulation and optimization, in particular optimization-within-MCMC and MCMC-driven optimization are discussed.

Advances In Network And Acoustic Echo Cancellation

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A survey of sound source localization methods in wireless acoustic sensor networks

Abstract: Wireless acoustic sensor networks (WASNs) are formed by a distributed group of acoustic-sensing devices featuring audio playing and recording capabilities. Current mobile computing platforms offer great possibilities for the design of audio-related applications involving acoustic-sensing nodes. In this context, acoustic source localization is one of the application domains that have attracted the most attention of the research community along the last decades. In general terms, the localization of acoustic sources can be achieved by studying energy and temporal and/or directional features from the incoming sound at different microphones and using a suitable model that relates those features with the spatial location of the source (or sources) of interest. This paper reviews common approaches for source localization in WASNs that are focused on different types of acoustic features, namely, the energy of the incoming signals, their time of arrival (TOA) or time difference of arrival (TDOA), the direction of arrival (DOA), and the steered response power (SRP) resulting from combining multiple microphone signals. Additionally, we discuss methods not only aimed at localizing acoustic sources but also designed to locate the nodes themselves in the network. Finally, we discuss current challenges and frontiers in this field.