Nonparametric Edge Detection in Speckled Imagery

We address the issue of edge detection in Synthetic Aperture Radar imagery. In particular, we propose nonparametric methods for edge detection, and numerically compare them to an alternative method that has been recently proposed in the literature. Our results show that some of the proposed methods display superior results and are computationally simpler than the existing method. An application to real (not simulated) data is presented and discussed.Comment: Accepted for publication in Mathematics and Computers in Simulatio

Distributed Detection of a Signal in Generalized Gaussian Noise

The problem of distributed detection of a signal in incompletely specified noise is considered. The noise assumed belongs to the generalized Gaussian family and the sensors in the distributed network employ the Wilcoxon test. The sensors pass the test statistics to a fusion center, where a hypothesis testing results in a decision regarding the presence or the absence of a signal. Three monotone and admissible fusion center tests are formulated. Restricted numerical evaluation over a certain parameter range of the noise distribution and the range of signal level indicates that these tests yield performances at comparable levels

Nonparametric sequential detection

This dissertation extends the theory of the Wilcoxon-Mann-Whitney U statistic so that this statistic can be used to perform sequential tests on hypotheses. This sequential test procedure makes use of a sequential ranking procedure similar to the one first introduced by Parent. The operating-characteristic function and average number of samples function for this new test are calculated as a function of the signal to noise ratio. The test is then shown to be efficient for several forms of alternatives with an efficiency of 95% against the Wald Sequential Probability Ratio Test for a constant signal in normal noise. Finally, the test procedure is modified so that it is capable of making measurements on the channel in order to adapt itself to changes in the channel characteristics. Simulation results are presented to show that this adaptive detector can operate with low probability of error --Abstract, page i

Distributed Nonparametric Sequential Spectrum Sensing under Electromagnetic Interference

A nonparametric distributed sequential algorithm for quick detection of spectral holes in a Cognitive Radio set up is proposed. Two or more local nodes make decisions and inform the fusion centre (FC) over a reporting Multiple Access Channel (MAC), which then makes the final decision. The local nodes use energy detection and the FC uses mean detection in the presence of fading, heavy-tailed electromagnetic interference (EMI) and outliers. The statistics of the primary signal, channel gain or the EMI is not known. Different nonparametric sequential algorithms are compared to choose appropriate algorithms to be used at the local nodes and the FC. Modification of a recently developed random walk test is selected for the local nodes for energy detection as well as at the fusion centre for mean detection. It is shown via simulations and analysis that the nonparametric distributed algorithm developed performs well in the presence of fading, EMI and is robust to outliers. The algorithm is iterative in nature making the computation and storage requirements minimal.Comment: 8 pages; 6 figures; Version 2 has the proofs for the theorems. Version 3 contains a new section on approximation analysi

Suppression of acoustic noise in speech using spectral subtraction

technical reportA stand alone noise suppression algorithm is presented for reducing the spectral effects of acoustically added noise in speech. Effective performance of digital speech processors operating in practical environments may require suppression of noise from the digital waveform. Spectral subtraction offers a computationally efficient, processor independent, approach to effective digital speech analysis. The method, requiring about the same computation as high-speed convolution, suppresses stationary noise for speech by subtracting the spectral noise bias calculated during non-speech activity. Secondary procedures and then applied to attenuate the residual noise left after subtraction. Since the algorithm resynthesizes a speech waveform, it can be used as a preprocessor to narrow band voice communications systems, speech recognition systems or speaker authentication systems

Permutation tests for nonparametric detection

In this paper, the authors provide a methodology to design nonparametric permutation tests and, in particular, nonparametric rank tests for applications in detection. In the first part of the paper, the authors develop the optimization theory of both permutation and rank tests in the Neyman?Pearson sense; in the second part of the paper, they carry out a comparative performance analysis of the permutation and rank tests (detectors) against the parametric ones in radar applications. First, a brief review of some contributions on nonparametric tests is realized. Then, the optimum permutation and rank tests are derived. Finally, a performance analysis is realized by Monte-Carlo simulations for the corresponding detectors, and the results are shown in curves of detection probability versus signal-to-noise rati

Testing the isotropy of high energy cosmic rays using spherical needlets

For many decades, ultrahigh energy charged particles of unknown origin that can be observed from the ground have been a puzzle for particle physicists and astrophysicists. As an attempt to discriminate among several possible production scenarios, astrophysicists try to test the statistical isotropy of the directions of arrival of these cosmic rays. At the highest energies, they are supposed to point toward their sources with good accuracy. However, the observations are so rare that testing the distribution of such samples of directional data on the sphere is nontrivial. In this paper, we choose a nonparametric framework that makes weak hypotheses on the alternative distributions and allows in turn to detect various and possibly unexpected forms of anisotropy. We explore two particular procedures. Both are derived from fitting the empirical distribution with wavelet expansions of densities. We use the wavelet frame introduced by [SIAM J. Math. Anal. 38 (2006b) 574-594 (electronic)], the so-called needlets. The expansions are truncated at scale indices no larger than some ${J^{\star}}$, and the $L^p$ distances between those estimates and the null density are computed. One family of tests (called Multiple) is based on the idea of testing the distance from the null for each choice of $J=1,\ldots,{J^{\star}}$, whereas the so-called PlugIn approach is based on the single full ${J^{\star}}$ expansion, but with thresholded wavelet coefficients. We describe the practical implementation of these two procedures and compare them to other methods in the literature. As alternatives to isotropy, we consider both very simple toy models and more realistic nonisotropic models based on Physics-inspired simulations. The Monte Carlo study shows good performance of the Multiple test, even at moderate sample size, for a wide sample of alternative hypotheses and for different choices of the parameter ${J^{\star}}$. On the 69 most energetic events published by the Pierre Auger Collaboration, the needlet-based procedures suggest statistical evidence for anisotropy. Using several values for the parameters of the methods, our procedures yield $p$-values below 1%, but with uncontrolled multiplicity issues. The flexibility of this method and the possibility to modify it to take into account a large variety of extensions of the problem make it an interesting option for future investigation of the origin of ultrahigh energy cosmic rays.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS619 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A comparative study of nonparametric methods for pattern recognition

The applied research discussed in this report determines and compares the correct classification percentage of the nonparametric sign test, Wilcoxon's signed rank test, and K-class classifier with the performance of the Bayes classifier. The performance is determined for data which have Gaussian, Laplacian and Rayleigh probability density functions. The correct classification percentage is shown graphically for differences in modes and/or means of the probability density functions for four, eight and sixteen samples. The K-class classifier performed very well with respect to the other classifiers used. Since the K-class classifier is a nonparametric technique, it usually performed better than the Bayes classifier which assumes the data to be Gaussian even though it may not be. The K-class classifier has the advantage over the Bayes in that it works well with non-Gaussian data without having to determine the probability density function of the data. It should be noted that the data in this experiment was always unimodal