Bayesian off-line detection of multiple change-points corrupted by multiplicative noise : application to SAR image edge detection

This paper addresses the problem of Bayesian off-line change-point detection in synthetic aperture radar images. The minimum mean square error and maximum a posteriori estimators of the changepoint positions are studied. Both estimators cannot be implemented because of optimization or integration problems. A practical implementation using Markov chain Monte Carlo methods is proposed. This implementation requires a priori knowledge of the so-called hyperparameters. A hyperparameter estimation procedure is proposed that alleviates the requirement of knowing the values of the hyperparameters. Simulation results on synthetic signals and synthetic aperture radar images are presented

Classifying LISA gravitational wave burst signals using Bayesian evidence

We consider the problem of characterisation of burst sources detected with the Laser Interferometer Space Antenna (LISA) using the multi-modal nested sampling algorithm, MultiNest. We use MultiNest as a tool to search for modelled bursts from cosmic string cusps, and compute the Bayesian evidence associated with the cosmic string model. As an alternative burst model, we consider sine-Gaussian burst signals, and show how the evidence ratio can be used to choose between these two alternatives. We present results from an application of MultiNest to the last round of the Mock LISA Data Challenge, in which we were able to successfully detect and characterise all three of the cosmic string burst sources present in the release data set. We also present results of independent trials and show that MultiNest can detect cosmic string signals with signal-to-noise ratio (SNR) as low as ~7 and sine-Gaussian signals with SNR as low as ~8. In both cases, we show that the threshold at which the sources become detectable coincides with the SNR at which the evidence ratio begins to favour the correct model over the alternative.Comment: 21 pages, 11 figures, accepted by CQG; v2 has minor changes for consistency with accepted versio

Bayesian joint analysis of cluster weak lensing and Sunyaev-Zel'dovich effect data

As the quality of the available galaxy cluster data improves, the models fitted to these data might be expected to become increasingly complex. Here we present the Bayesian approach to the problem of cluster data modelling: starting from simple, physically motivated parameterised functions to describe the cluster's gas density, gravitational potential and temperature, we explore the high-dimensional parameter spaces with a Markov-Chain Monte-Carlo sampler, and compute the Bayesian evidence in order to make probabilistic statements about the models tested. In this way sufficiently good data will enable the models to be distinguished, enhancing our astrophysical understanding; in any case the models may be marginalised over in the correct way when estimating global, perhaps cosmological, parameters. In this work we apply this methodology to two sets of simulated interferometric Sunyaev-Zel'dovich effect and gravitational weak lensing data, corresponding to current and next-generation telescopes. We calculate the expected precision on the measurement of the cluster gas fraction from such experiments, and investigate the effect of the primordial CMB fluctuations on their accuracy. We find that data from instruments such as AMI, when combined with wide-field ground-based weak lensing data, should allow both cluster model selection and estimation of gas fractions to a precision of better than 30 percent for a given cluster.Comment: 13 pages, 7 figures, submitted to MNRAS; accepted 14/8/03 after minor revisio

Measuring the primordial power spectrum: Principal component analysis of the cosmic microwave background

We implement and investigate a method for measuring departures from scale-invariance, both scale-dependent as well as scale-free, in the primordial power spectrum of density perturbations using cosmic microwave background (CMB) C_l data and a principal component analysis technique. The primordial power spectrum is decomposed into a dominant scale-invariant Gaussian adiabatic component plus a series of orthonormal modes whose detailed form only depends the noise model for a particular CMB experiment. However, in general these modes are localised across wavenumbers with 0.01 < k < 0.2 Mpc^-1, displaying rapid oscillations on scales corresponding the acoustic peaks where the sensitivity to primordial power spectrum is greatest. The performance of this method is assessed using simulated data for the Planck satellite, and the full cosmological plus power spectrum parameter space is integrated out using Markov Chain Monte Carlo. As a proof of concept we apply this data compression technique to the current CMB data from WMAP, ACBAR, CBI and VSA. We find no evidence for the breaking of scale-invariance from measurements of four PCA mode amplitudes, which is translated to a constraint on the scalar spectral index n_S(k_0=0.04 Mpc^-1)=0.94+-0.04 in accordance with WMAP studies.Comment: 9 pages with 13 figures. MNRAS accepted versio

Broadband Direction-Of-Arrival Estimation Based On Second Order Statistics

N wideband sources recorded using N closely spaced receivers can feasibly be separated based only on second order statistics when using a physical model of the mixing process. In this case we show that the parameter estimation problem can be essentially reduced to considering directions of arrival and attenuations of each signal. The paper presents two demixing methods operating in the time and frequency domain and experimentally shows that it is always possible to demix signals arriving at different angles. Moreover, one can use spatial cues to solve the channel selection problem and a post-processing Wiener filter to ameliorate the artifacts caused by demixing. 1 Introduction Blind source separation (BSS) is capable of dramatic results when used to separate mixtures of independent signals. The method relies on simultaneous recordings of signals from two or more input sensors and separates the original sources purely on the basis of statistical independence between them. Unfortunatel..

A Bayesian Approach To Spread Spectrum Watermark Detection and Secure Copyright Protection for Digital Image Libraries

Digital watermarks have been proposed as a method for discouraging illicit copying and distribution of copyrighted material, and to create secure digital image libraries by adding to images copyright and userright information. Using a robust digital watermark to detect and trace copyright violations has therefore lot of interest. This paper describes an approach to embedding a digital watermark using the Fourier transform. The paper also addresses the difficult problem of oblivious watermark detection. It is shown that, for the CDMA spread spectrum signal described in the paper, it is still possible to positively detect the presence of a watermark without being able to decode it (and even infer the number of bits contained in the watermark) given only the key used to generate it. Finally, through experimental results the usefulness of such measure is shown