A multichannel sampling method for 2-D finite-rate-of-innovation signals

We address the problem of sampling and reconstruction of two-dimensional (2-D) finite-rate-of-innovation (FRI) signals. We propose a three-channel sampling method for efficiently solving the problem. We consider the sampling of a stream of 2-D Dirac impulses and a sum of 2-D unit-step functions. We propose a 2-D causal exponential function as the sampling kernel. By causality in 2-D, we mean that the function has its support restricted to the first quadrant. The advantage of using a multichannel sampling method with causal exponential sampling kernel is that standard annihilating filter or root-finding algorithms are not required. Further, the proposed method has inexpensive hardware implementation and is numerically stable as the number of Dirac impulses increases.

How general is a female mating preference for clustered males in lekking species? a meta-analysis

A principal hypothesis for the evolution of leks (rare and intensely competitive territorial aggregations) is that leks result from females preferring to mate with clustered males. This hypothesis predicts more female visits and higher mating success per male on larger leks. Evidence for and against this hypothesis has been presented by different studies, primarily of individual populations, but its generality has not yet been formally investigated. We took a meta-analytical approach towards formally examining the generality of such a female bias in lekking species. Using available published data and using female visits as an index of female mating bias, we estimated the shape of the relationship between lek size and total female visits to a lek, female visits per lekking male and, where available, per capita male mating success. Individual analyses showed that female visits generally increased with lek size across the majority of taxa surveyed; the meta-analysis indicated that this relationship with lek size was disproportionately positive. The findings from analysing per capita female visits were mixed, with an increase with lek size detected in half of the species, which were, however, widely distributed taxonomically. Taken together, these findings suggest that a female bias for clustered males may be a general process across lekking species. Nevertheless, the substantial variation seen in these relationships implies that other processes are also important. Analyses of per capita copulation success suggested that, more generally, increased per capita mating benefits may be an important selective factor in lek maintenance.

Antelope mating strategies facilitate invasion of grasslands by a woody weed

Intra and interspecific variation in frugivore behaviour can have important consequences for seed dispersal outcomes. However, most information comes from among-species comparisons, and within-species variation is relatively poorly understood. We examined how large intraspecific differences in the behaviour of a native disperser, blackbuck antelope Antilope cervicapra, influence dispersal of a woody invasive, Prosopis juliflora, in a grassland ecosystem. Blackbuck disperse P. juliflora seeds through their dung. In lekking blackbuck populations, males defend clustered or dispersed mating territories. Territorial male movement is restricted, and within their territories males defecate on dung-piles. In contrast, mixed-sex herds range over large areas and do not create dung-piles. We expected territorial males to shape seed dispersal patterns, and seed deposition and seedling recruitment to be spatially localized. Territorial males had a disproportionately large influence on seed dispersal. Adult males removed twice as much fruit as females, and seed arrival was disproportionately high on territories. Also, because lek-territories are clustered, seed arrival was spatially highly concentrated. Seedling recruitment was also substantially higher on territories compared with random sites, indicating that the local concentration of seeds created by territorial males continued into high local recruitment of seedlings. Territorial male behaviour may, thus, result in a distinct spatial pattern of invasion of grasslands by the woody P. juliflora. An ex situ experiment showed no beneficial effect of dung and a negative effect of light on seed germination. We conclude that large intraspecific behavioural differences within frugivore populations can result in significant variation in their effectiveness as seed dispersers. Mating strategies in a disperser could shape seed dispersal, seedling recruitment and potentially plant distribution patterns. These mating strategies may aid in the spread of invasives, such as P. juliflora, which could, in turn, negatively influence the behaviour and ecology of native dispersers.

Environments of extended radio sources in the Australia Telescope Low-Brightness Survey

We present a study of the environments of extended radio sources in the Australia Telescope Low-Brightness Survey (ATLBS). The radio sources were selected from the ATLBS Extended Source Sample, which is a well defined sample containing the most extended of radio sources in the ATLBS sky survey regions. The environments were analysed using 4-m Cerro-Tololo Inter-American Observatory Blanco telescope observations carried out for ATLBS fields in the Sloan Digital Sky Survey r(') band. We have estimated the properties of the environments using smoothed density maps derived from galaxy catalogues constructed using these optical imaging data. The angular distribution of galaxy density relative to the axes of the radio sources has been quantified by defining anisotropy parameters that are estimated using a new method presented here. Examining the anisotropy parameters for a subsample of extended double radio sources that includes all sources with pronounced asymmetry in lobe extents, we find good evidence for environmental anisotropy being the dominant cause for lobe asymmetry in that higher galaxy density occurs almost always on the side of the shorter lobe, and this validates the usefulness of the method proposed and adopted here. The environmental anisotropy parameters have been used to examine and compare the environments of Fanaroff-Riley Class I (FRI) and Fanaroff-Riley Class II (FRII) radio sources in two redshift regimes (z < 0.5 and z > 0.5). Wide-angle tail sources and head-tail sources lie in the most overdense environments. The head-tail source environments (for the HT sources in our sample) display dipolar anisotropy in that higher galaxy density appears to lie in the direction of the tails. Excluding the head-tail and wide-angle tail sources, subsamples of FRI and FRII sources from the ATLBS appear to lie in similar moderately overdense environments, with no evidence for redshift evolution in the regimes studied herein.

Super-Resolution Reconstruction in Frequency-Domain Optical-Coherence Tomography Using the Finite-Rate-of-Innovation Principle

The standard approach to signal reconstruction in frequency-domain optical-coherence tomography (FDOCT) is to apply the inverse Fourier transform to the measurements. This technique offers limited resolution (due to Heisenberg's uncertainty principle). We propose a new super-resolution reconstruction method based on a parametric representation. We consider multilayer specimens, wherein each layer has a constant refractive index and show that the backscattered signal from such a specimen fits accurately in to the framework of finite-rate-of-innovation (FRI) signal model and is represented by a finite number of free parameters. We deploy the high-resolution Prony method and show that high-quality, super-resolved reconstruction is possible with fewer measurements (about one-fourth of the number required for the standard Fourier technique). To further improve robustness to noise in practical scenarios, we take advantage of an iterated singular-value decomposition algorithm (Cadzow denoiser). We present results of Monte Carlo analyses, and assess statistical efficiency of the reconstruction techniques by comparing their performance against the Cramer-Rao bound. Reconstruction results on experimental data obtained from technical as well as biological specimens show a distinct improvement in resolution and signal-to-reconstruction noise offered by the proposed method in comparison with the standard approach.

ELLIPSE FITTING USING FINITE RATE OF INNOVATION PRINCIPLES

We address the problem of parameter estimation of an ellipse from a limited number of samples. We develop a new approach for solving the ellipse fitting problem by showing that the x and y coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals. Uniform samples of x and y coordinate functions of the ellipse are modeled as a sum of weighted complex exponentials, for which we propose an efficient annihilating filter technique to estimate the ellipse parameters from the samples. The FRI framework allows for estimating the ellipse parameters reliably from partial or incomplete measurements even in the presence of noise. The efficiency and robustness of the proposed method is compared with state-of-art direct method. The experimental results show that the estimated parameters have lesser bias compared with the direct method and the estimation error is reduced by 5-10 dB relative to the direct method.

Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x- and y-coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.