Juan G. Gonzalez

Optimality of the myriad filter in practical impulsive-noise environments

Linear filtering theory has been largely motivated by the characteristics of Gaussian signals. In the same manner, the proposed myriad filtering methods are motivated by the need for a flexible filter class with high statistical efficiency in non-Gaussian impulsive environments that can appear in practice. We introduce several important properties of the myriad filter and prove its optimality in the family of /spl alpha/-stable distributions.

Zero-Order Statistics: A Mathematical Framework for the Processing and Characterization of Very Impulsive Signals

Impulsive or heavy-tailed processes with infinite variance appear naturally in a variety of practical problems that include wireless communications, teletraffic, hydrology, geology, and economics. Most signal processing and statistical methods available in the literature have been designed under the assumption that the processes possess finite variance, and they usually break down in the presence of infinite variance. Although methods based on fractional lower-order statistics (FLOS) have proven successful in dealing with infinite variance processes, they fail in general when the noise distribution has very heavy algebraic tails. In this paper, we introduce a new approach to statistical moment characterization which is well defined over all processes with algebraic or lighter tails. Unlike FLOS, these zero-order statistics (ZOS), as we will call them, provide a common ground for the analysis of basically any distribution of practical use known today. Three new parameters, namely the geometric power, the zero-order location and the zero-order dispersion, constitute the foundation of ZOS. They play roles similar to those played by the power, the expected value and the standard deviation, in the theory of second-order processes. We analyze the properties of the new parameters, and derive a ZOS framework for location estimation that gives rise to a novel mode-type estimator with important optimality properties under very impulsive noise. Several simulations are presented to illustrate the potential of ZOS methods

Optimal digital filtering for tremor suppression

Remote manually operated tasks such as those found in teleoperation, virtual reality, or joystick-based computer access, require the generation of an intermediate electrical signal which is transmitted to the controlled subsystem (robot arm, virtual environment, or a cursor in a computer screen). When human movements are distorted, for instance, by tremor, performance can be improved by digitally filtering the intermediate signal before it reaches the controlled device. This paper introduces a novel tremor filtering framework in which digital equalizers are optimally designed through pursuit tracking task experiments. Due to inherent properties of the man-machine system, the design of tremor suppression equalizers presents two serious problems: 1) performance criteria leading to optimizations that minimize mean-squared error are not efficient for tremor elimination and 2) movement signals show ill-conditioned autocorrelation matrices, which often result in useless or unstable solutions. To address these problems, a new performance indicator in the context of tremor is introduced, and the optimal equalizer according to this new criterion is developed, III-conditioning of the autocorrelation matrix is overcome using a novel method which we call pulled-optimization. Experiments performed with artificially induced vibrations and a subject with Parkinsons disease show significant improvement in performance. Additional results, along with MATLAB source code of the algorithms, and a customizable demo for PC joysticks, are available on the Internet at http://tremor-suppression.com.

Fast and Accurate Computation of the Myriad Filter via Branch-and-Bound Search

The myriad filter has demonstrated to be a robust countermeasure against the negative effect that impulsive noise has over electronic systems. However, its use is still limited in systems where processing speed is critical, as is the case of radar, sonar, and real-time audio and video processing. This limitation has its roots in the challenges imposed by the numerical approximation of the myriad filter. In particular, minimization operations at the interior of nonlinear operations are sensitive components that have a direct impact on the performance of the filtering algorithms. In the case of the myriad filter, the minimization of functions with multiple local minima is a common operation, and poorly chosen algorithms compromise the good behavior of the filter. In this correspondence, we present an alternative for the minimization of the objective function in the computation of the myriad filter. This solution exploits general concepts in global optimization and adapts them to the particular case of myriad filtering. This technique improves accuracy and speed in the computation of the myriad filter, making the method feasible in many problems.

Zero-order statistics: a signal processing framework for very impulsive processes

Techniques based on conventional higher-order statistics fail when the underlying processes become impulsive. Although methods based on fractional lower-order statistics (FLOS) have proven successful in dealing with heavy-tailed processes, they fail in general when the noise distribution has very heavy algebraic tails, i.e., when the algebraic tail constant is close to zero. In this paper we introduce a signal processing framework that we call zero-order statistics (ZOS). ZOS are well defined for any process with algebraic or lighter tails, including the full class of /spl alpha/-stable distributions. We introduce zero-order scale and location statistics and study several of their properties. The intimate link between ZOS and FLOS is presented. We also show that ZOS are the optimal framework when the underlying processes are very impulsive. All figures, simulations and source code utilized in this paper are reproducible and freely accessible in the Internet at http://www.ee.udel./edu//sup /spl sim//gonzalez/PUBS/HOS97a.

LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators

We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.

Robust time-frequency representations for signals in /spl alpha/-stable noise using fractional lower-order statistics

Characterizing signals jointly in the time and frequency domains through time-frequency representations (TFRs) such as the Wigner-Ville distribution (WVD) is a natural extension of Fourier analysis and gives a more complete representation of signal behavior particularly in the case of non-stationary signals. In the presence of additive impulsive noise, TFRs quickly break down and any information about the desired signal is lost. To combat these effects, we propose in this paper a family of memoryless nonlinearities which have been shown to produce a signal autocorrelation statistic which is well-behaved in the presence of stable noise. The result of this approach is a TFR which is both robust and simple to implement, and has many of the mathematical properties associated with the standard WVD. We illustrate the improvement in performance that can be obtained with several examples.

Weighted myriad filters for image processing

Median filters, developed in response to the need for nonlinear image filters, have been used extensively in image processing. However, median filters do not work well when the outlier concentration is small, and are constrained to be smoothers, among other limitations. In order to combat the problems of median filters, weighted myriad filters have been proposed. Although myriad filters are analogous to both mean and median filters, myriad filters prove more effective in image processing applications. Weighted myriad filters have a sound theoretical basis, work well in impulsive noise environments, and can act as both edge enhancers and smoothers. This paper discusses optimization of the filter weights, with the goal of providing better image filtering than that of either linear or median filters.

Customized optimal filter for eliminating operator's tremor

Remote manually operated tasks such as those found in teleoperation, virtual reality, or joystick-based computer access, require the generation of an intermediate signal which is transmitted to the controlled subsystem (robot arm, virtual environment or cursor). When man-machine movements are distorted by tremor, performance can be improved by digitally filtering the intermediate signal before it reaches the controlled device. This paper introduces a novel filtering framework in which digital equalizers are optimally designed after pursuit tracking task experiments. Due to inherent properties of the man-machine system, the design of tremor suppression equalizers presents two serious problems: (1) performance criteria leading to optimizations that minimize mean-squared error are not efficient for tremor elimination, and (2) movement signals show highly ill-conditioned autocorrelation matrices, which often result in useless or unstable solutions. A new performance indicator is introduced, namely the F-MSEd, and the optimal equalizer according to this new criterion is developed. Ill-condition of the autocorrelation matrix is overcome using a novel method which we call pulled-optimization. Experiments performed with both a person with tremor disability, and a vibration inducing device, show significant results.

The closest-to-mean filter: an edge preserving smoother for Gaussian environments

Median based filters have gained wide-spread use because of their ability to preserve edges and suppress impulses. In this paper, we introduce the closest-to-mean (CTM) filter, which outputs the input sample closest to the sample mean. The CTM filtering framework offers lower computational complexity and better performance in near Gaussian environments than median filters. The formulation of the CTM filter is derived from the theory of S-filters, which form a class of generalized selection-type filters with the features of edge preservation and impulse suppression. S-filters can play a significant role in image processing, where edge and detail preservation are of paramount importance. We compare the performance of CTM, median, and mean filters in the smoothing of edges and impulses immersed in Gaussian noise. A sufficient condition for a signal to be a root of the CTM filter is included.