Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise I: Frequentist analyses

Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as a stationary Gaussian process. However most experiments exhibit a non-Gaussian ``tail'' in the probability distribution. This ``excess'' of large signals can be a troublesome source of false alarms. This article derives an optimal (in the Neyman-Pearson sense, for weak signals) signal processing strategy when the detector noise is non-Gaussian and exhibits tail terms. This strategy is robust, meaning that it is close to optimal for Gaussian noise but far less sensitive than conventional methods to the excess large events that form the tail of the distribution. The method is analyzed for two different signal analysis problems: (i) a known waveform (e.g., a binary inspiral chirp) and (ii) a stochastic background, which requires a multi-detector signal processing algorithm. The methods should be easy to implement: they amount to truncation or clipping of sample values which lie in the outlier part of the probability distribution.Comment: RevTeX 4, 17 pages, 8 figures, typos corrected from first version

A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by: i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior; and iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of `hundreds' as compared to existing Bayesian source extraction methods that use MCMC to explore the parameter space, such as that presented by Hobson & McLachlan. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (Version-I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted for publication in MNRA

Using baseline-dependent window functions for data compression and field-of-interest shaping in radio interferometry

In radio interferometry, observed visibilities are intrinsically sampled at some interval in time and frequency. Modern interferometers are capable of producing data at very high time and frequency resolution; practical limits on storage and computation costs require that some form of data compression be imposed. The traditional form of compression is a simple averaging of the visibilities over coarser time and frequency bins. This has an undesired side effect: the resulting averaged visibilities "decorrelate", and do so differently depending on the baseline length and averaging interval. This translates into a non-trivial signature in the image domain known as "smearing", which manifests itself as an attenuation in amplitude towards off-centre sources. With the increasing fields of view and/or longer baselines employed in modern and future instruments, the trade-off between data rate and smearing becomes increasingly unfavourable. In this work we investigate alternative approaches to low-loss data compression. We show that averaging of the visibility data can be treated as a form of convolution by a boxcar-like window function, and that by employing alternative baseline-dependent window functions a more optimal interferometer smearing response may be induced. In particular, we show improved amplitude response over a chosen field of interest, and better attenuation of sources outside the field of interest. The main cost of this technique is a reduction in nominal sensitivity; we investigate the smearing vs. sensitivity trade-off, and show that in certain regimes a favourable compromise can be achieved. We show the application of this technique to simulated data from the Karl G. Jansky Very Large Array (VLA) and the European Very-long-baseline interferometry Network (EVN)

SGD Frequency-Domain Space-Frequency Semiblind Multiuser Receiver with an Adaptive Optimal Mixing Parameter

A novel stochastic gradient descent frequency-domain (FD) space-frequency (SF) semiblind multiuser receiver with an adaptive optimal mixing parameter is proposed to improve performance of FD semiblind multiuser receivers with a fixed mixing parameters and reduces computational complexity of suboptimal FD semiblind multiuser receivers in SFBC downlink MIMO MC-CDMA systems where various numbers of users exist. The receiver exploits an adaptive mixing parameter to mix information ratio between the training-based mode and the blind-based mode. Analytical results prove that the optimal mixing parameter value relies on power and number of active loaded users existing in the system. Computer simulation results show that when the mixing parameter is adapted closely to the optimal mixing parameter value, the performance of the receiver outperforms existing FD SF adaptive step-size (AS) LMS semiblind based with a fixed mixing parameter and conventional FD SF AS-LMS training-based multiuser receivers in the MSE, SER and signal to interference plus noise ratio in both static and dynamic environments

Fourier based high-resolution near-field sound imaging

Noise pollution is a generally acknowledged problem in modern day society. The current tendencies towards lightweight and cheaper product design are primarily responsible for increasing nuisance, annoyance and environmental problems caused by acoustic noise. There are several reasons for research towards technologies that facilitate acoustic noise reduction. Nowadays, low noise design of consumer electronics, high-tech systems and automotive are restricted to increasingly stringent regulations and quality aspects. Effective countermeasures in order to reduce sound radiation are only taken when the source of sound is known. "Inverse Acoustics" is a very effective method to visualize and quantize the sound sources, which reconstructs source information based on measurements away from the source, yet in the near-field. In fact, the system is able to reconstruct the entire acoustic message that a source radiates in the direction of interest. The current methods for source reconstruction produce sound images with very little detail, they often require cumbersome numerical calculations and models, and they are often highly impractical for industrial applications. This research focuses on fast and accurate measurement and signal processing methods for inverse acoustics that are applicable in practical situations which require high resolutions under hazardous acoustic conditions. The inverse process is based upon spatial and wavenumber domain Fourier techniques, also referred to as Near-field Acoustic Holography. More in detail, spatial properties with respect to aliasing, leakage, signal-to-noise ratio and sensor set-ups are investigated and explicit methods and rules are developed to assist in proper determination of the acoustic holograms. In order to correctly transform the spatial hologram data into the wavenumber domain or k-space, a method called border-padding is developed. This method, which is an alternative to spatial windowing, is highly accurate without slowing down the processing time considerably. Another important factor is regularization, which is required since the inverse process is highly ill-posed. Without proper filtering action taken, noise blows up as the hologram-source distance or the wavenumber grows. In this research project a method is developed to automatically determine the proper filter function and filter parameters, which is a near-optimal trade-off between noise blow-up and deterioration of useful source information. These important properties are combined in a fully automated near-field sound imaging system design. At the Technical University of Eindhoven two versions of this system were developed and built; a large version that is based in the semi-anechoic room of the laboratory and a portable system that is suitable for small electronic devices and high-tech systems. A number of practical cases are used to qualitatively as well as quantitatively validate the improvements with respect to existing methods and illustrate the possibilities for industrial application

Coil combination using linear deconvolution in k-space for phase imaging

Background: The combination of multi-channel data is a critical step for the imaging of phase and susceptibility contrast in magnetic resonance imaging (MRI). Magnitude-weighted phase combination methods often produce noise and aliasing artifacts in the magnitude images at accelerated imaging sceneries. To address this issue, an optimal coil combination method through deconvolution in k-space is proposed in this paper. Methods: The proposed method firstly employs the sum-of-squares and phase aligning method to yield a complex reference coil image which is then used to calculate the coil sensitivity and its Fourier transform. Then, the coil k-space combining weights is computed, taking into account the truncated frequency data of coil sensitivity and the acquired k-space data. Finally, combining the coil k-space data with the acquired weights generates the k-space data of proton distribution, with which both phase and magnitude information can be obtained straightforwardly. Both phantom and in vivo imaging experiments were conducted to evaluate the performance of the proposed method. Results: Compared with magnitude-weighted method and MCPC-C, the proposed method can alleviate the phase cancellation in coil combination, resulting in a less wrapped phase. Conclusions: The proposed method provides an effective and efficient approach to combine multiple coil image in parallel MRI reconstruction, and has potential to benefit routine clinical practice in the future

Low-rank filter and detector for multidimensional data based on an alternative unfolding HOSVD: application to polarimetric STAP

International audienceThis paper proposes an extension of the classical Higher Order Singular Value Decomposition (HOSVD), namely the Alternative Unfolding HOSVD (AU-HOSVD), in order to exploit the correlated information in multidimensional data. We show that the properties of the AU-HOSVD are proven to be the same as those for HOSVD: the orthogonality and the low-rank (LR) decomposition. We next derive LR-filters and LR-detectors based on AU-HOSVD for multidimensional data composed of one LR structure contribution. Finally, we apply our new LR-filters and LR-detectors in Polarimetric Space Time Adaptive Processing (STAP). In STAP, it is well known that the response of the background is correlated in time and space and has a LR structure in space-time. Therefore, our approach based on AU-HOSVD seems to be appropriate when a dimension (like polarimetry in this paper) is added. Simulations based on Signal to Interference plus Noise Ratio (SINR) losses, Probability of Detection (Pd) and Probability of False Alarm (Pfa) show the interest of our approach: LR-filters and LR-detectors which can be obtained only from AU-HOSVD outperform the vectorial approach and those obtained from a single HOSVD