Nonlocal Myriad Filters for Cauchy Noise Removal

The contribution of this paper is two-fold. First, we introduce a generalized myriad filter, which is a method to compute the joint maximum likelihood estimator of the location and the scale parameter of the Cauchy distribution. Estimating only the location parameter is known as myriad filter. We propose an efficient algorithm to compute the generalized myriad filter and prove its convergence. Special cases of this algorithm result in the classical myriad filtering, respective an algorithm for estimating only the scale parameter. Based on an asymptotic analysis, we develop a second, even faster generalized myriad filtering technique. Second, we use our new approaches within a nonlocal, fully unsupervised method to denoise images corrupted by Cauchy noise. Special attention is paid to the determination of similar patches in noisy images. Numerical examples demonstrate the excellent performance of our algorithms which have moreover the advantage to be robust with respect to the parameter choice

Faster Geometric Algorithms via Dynamic Determinant Computation

The computation of determinants or their signs is the core procedure in many important geometric algorithms, such as convex hull, volume and point location. As the dimension of the computation space grows, a higher percentage of the total computation time is consumed by these computations. In this paper we study the sequences of determinants that appear in geometric algorithms. The computation of a single determinant is accelerated by using the information from the previous computations in that sequence. We propose two dynamic determinant algorithms with quadratic arithmetic complexity when employed in convex hull and volume computations, and with linear arithmetic complexity when used in point location problems. We implement the proposed algorithms and perform an extensive experimental analysis. On one hand, our analysis serves as a performance study of state-of-the-art determinant algorithms and implementations. On the other hand, we demonstrate the supremacy of our methods over state-of-the-art implementations of determinant and geometric algorithms. Our experimental results include a 20 and 78 times speed-up in volume and point location computations in dimension 6 and 11 respectively.Comment: 29 pages, 8 figures, 3 table

Solutions for 10,000 Eclipsing Binaries in the Bulge Fields of OGLE II Using DEBiL

We have developed a fully-automated pipeline for systematically identifying and analyzing eclipsing binaries within large datasets of light curves. The pipeline is made up of multiple tiers which subject the light curves to increasing levels of scrutiny. After each tier, light curves that did not conform to a given criteria were filtered out of the pipeline, reducing the load on the following, more computationally intensive tiers. As a central component of the pipeline, we created the fully automated Detached Eclipsing Binary Light curve fitter (DEBiL), which rapidly fits large numbers of light curves to a simple model. Using the results of DEBiL, light curves of interest can be flagged for follow-up analysis. As a test case, we analyzed the 218699 light curves within the bulge fields of the OGLE II survey and produced 10862 model fits. We point out a small number of extreme examples as well as unexpected structure found in several of the population distributions. We expect this approach to become increasingly important as light curve datasets continue growing in both size and number.Comment: Accepted for publication in ApJ, 36 pages, 15 figures, 5 tables. See http://cfa-www.harvard.edu/~jdevor/DEBiL.html for high-resolution figures and further informatio

On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

Locally-adaptive Myriad Filtration of One-dimensional Complex Signal

Locally-adaptive algorithms of myriad filtering are proposed with adaptation of a sample myriad linearity parameter K, depending upon local estimates of a signal, and with “hard” switching of sliding window length settings and a coefficient which influences on the parameter K. Statistical estimates of the filters quality are obtained using a criterion of a minimum mean-square error for a model of one-dimensional complex signal that includes different elementary segments under conditions of additive Gaussian noise with zero mean and different variances and possible spikes presence. Improvement of integral and local performance indicators is shown in comparison to the highly effective non-linear locally-adaptive algorithms for the considered test signal. Having a complex signal of high efficiency, one of the proposed algorithms provides nearly optimal noise suppression at the segments of linear change of a signal; other algorithm provides higher quality of step edge preservation and the best noise suppression on a const signal. Better efficiency in cases of low and high noise levels is achieved by preliminary noise level estimation through comparison of locally-adaptive parameter and thresholds. It is shown that, in order to ensure better spikes removal, it is expedient to pre-process the signal by robust myriad filter with small window length. The considered adaptive nonlinear filters have possibility to be implemented in a real time mode