Correlation Detection Research Articles

DCT-domain Watermark Detection Using Gaussian Mixture Model

An audio watermark detector is developed based on the statistical characteristics of audio in DCT domain. Watermarks are embedded in DCT domain on a spread spectrum basis. A Gaussian mixture model (GMM) is introduced to model both the watermarked and unwatermarked audio signals in DCT domain. At the receiver a maximum likelihood detector is employed. Simulation results indicate that the proposed method allows for common signal processing and provides a better detecting accuracy compared with the linear correlation detector.

Correlation detection of bat echolocation calls

In an experiment comparing detection of echolocation calls between humans and automated methods, an optimal linear detector (matched filter) out-performed humans by 5 dB and model-based automated methods by 9 dB [Skowronski and Fenton, J. Acoust. Soc. Am. 125, 513–521 (2009)]. While optimal linear performance cannot be achieved in practice, near-optimal performance may be reached if the detection filter nearly matches the target calls. Bat calls from a species are fairly stereotypic, so designing a test call (or bank of test calls) for a correlation detector is feasible. Model-based detectors collect information over short analysis windows and piece that information together to form a detection decision, a bottom-up strategy that is good at collecting local information but poor at arranging local information to form a global detection decision. By contrast, a correlation detector operates at one time scale, the global call duration, and may be considered a top-down strategy of detection. The strengths and...

Estimation of arrival-times in intense seismic sequences using a Master-Events methodology based on waveform similarity

SUMMARY Intense seismic sequences involve a large number of earthquakes densely clustered in space and time. Their detailed analysis is important for the geometry of the activated faults, which contributes to studies of the seismotectonic characteristics of an area. The sheer number of small events as well as their low energy content renders their processing problematic. In this work, we have developed and applied a methodology to automatically pick the arrival-times of P- and S-waves using a correlation detector. Event detection is performed using the waveform recordings of a reference station located close to the epicentral area of an intense seismic sequence such as aftershocks or swarms. Cross-correlation matrices are constructed, followed by nearest-neighbour clustering and the formation of multiplets. A Master-Event is chosen from each cluster and its arrival-times are picked manually. The automatic algorithm uses the P -o rS-wave of each Master-Event as a correlation detector, searches the waveforms of the other events of the same multiplet and imposes the corresponding arrival-time when the bestfit is achieved. The picks are characterized by observation weights, which derive from the quality of thefit, the type of the available waveform components and the consistency between multiple measurements. The proposed methodology was applied to an important seismic sequence that occurred between 2010 January 18 and 26 near the city of Efpalio, Greece. This procedure has the potential to increase 10-fold the amount of information and provide sufficient detail for a subsequent analysis of the spatiotemporal distribution of a seismic series.

One Magnitude Unit Reduction in Detection Threshold by Cross Correlation Applied to Parkfield (California) and China Seismicity

Abstract From a local high-resolution base catalog at Parkfield, California, 5076 earthquakes ( M 0.2 to 6) are used to study the comparative performance of a correlation detector and standard energy detector on the sparse regional network of continuously operating stations. Eighty-six percent of the events detected by a standard energy detector can also be detected by cross correlation. Correlation detection is able to find additional events by lowering the detection threshold by about 1 unit beyond what standard processing detects for Parkfield, a factor of 10 increase in number of events such as those predicted by Gutenberg–Richter. Most event separation distances for events that correlate at Parkfield are less than 1 km. The distribution of magnitude differences for events that correlate at Parkfield is not distinguishable from the input magnitude distribution. More robust measures to quantify reduction in detection threshold are introduced. Detection magnitude threshold reduction of about 1 unit holds for large-scale application to the 18,886 events in China and 5,076 events in Parkfield with false-alarm rates of a few percent. Large and small events are seen to correlate well enough for detection. Two examples are shown with magnitude differences as large as 2.3 and 3.3 units. The correlation detector also finds two cases of buried aftershocks in the coda of mainshocks that were previously unreported in the Annual Bulletin of Chinese Earthquakes (ABCE).

Multiple carrier ultra-wideband systems using an optical pulse modulation scheme

This study proposes a new optical pulse modulation scheme for multiple carrier ultra-wideband (MC-UWB) wireless systems to achieve a reliable high-bit-rate transmission. The scheme can decrease the system complexity and lowering cost. Moreover, the UWB receiver is adapted with a modified single-user correlation detector to recover original data signal by a narrow carrier spacing. Finally, we set up a practical experimental system to prove our proposed scheme. Experiment results demonstrate that the scheme can provide high spectral efficiency and reduce interference noise for MC-UWB wireless communications. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52:2735–2738, 2010; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25584

Why correlation, energy and gradient motion models are not equivalent

Claims that some instantiations of generic low-level motion models are mathematically equivalent have led to a widely held view that differences between models are minor and of little significance. The question of equivalence is addressed at a number of levels. We first identify the computational principle by which motion is extracted in each case. Each model is defined by the computational theory implemented. Questions about equivalence relate to the algorithmic and implementation levels. The units of measurement of the models cannot be equated; this alone guarantees that they are not mathematically equivalent. The output of a gradient motion model encodes speed directly (e.g. in pixels per frame), whereas a correlation or energy model encodes the degree of match between the stimulus and the tuned detector. Speed is not computed. Arguments for the equivalence of correlation and energy detectors [1] ignore contrast normalisation whereas contrast normalisation is essential to the argument for an equivalence between gradient and energy models [2,3]. In the latter case the inner product in the gradient model is expanded (4a.b=|a+b|2-|a-b|2) to generate terms, e.g.|a+b|, that might be synthesised from linear space-time oriented filters. However in an energy model space-time oriented filters in quadrature phase are combined to deliver phase invariance. In the expanded gradient model these filters are not in quadrature phase and are not phase invariant. Phase invariance specifically from the combination of space-time filters in spatiotemporal quadrature is considered the defining property of an energy model and this is not shared with any implementation of the gradient model.

Frequency-Domain Correlation: An Asymptotically Optimum Approximation of Quadratic Likelihood Ratio Detectors

An approximate implementation is formulated and analyzed for the detection of wide-sense stationary Gaussian stochastic signals in white Gaussian noise. For scalar processes, the approximate detector can be realized as the correlation between the periodogram of the observations and an appropriately selected spectral mask, and thus is termed the frequency-domain correlation detector. Through the asymptotic properties of Toeplitz matrices, it is shown that, as the length of the observation interval grows without bound, the frequency-domain correlation detector and the optimum quadratic detector achieve identical asymptotic performance, characterized by the decay rate of the miss probability under the Neyman-Pearson criterion. The frequency-domain correlation detector is further extended to the detection of vector-valued wide-sense stationary Gaussian stochastic signals, and the asymptotic optimality of its performance is established through the asymptotic properties of block Hermitian Toeplitz matrices.

Selective correlation detector for additive spread spectrum watermarking in transform domain

As an improvement on additive spread spectrum (ASS) watermarking, this paper proposes the selective correlation detector (SCD), which performs correlation detection on a portion rather than the whole block of the signal. The portion is determined based on the watermark-to-cover signal power ratio (WCR) and the estimated variance of the correlation. A similar improvement has been obtained by improved spread spectrum (ISS) watermarking [6] (Malvar and Florencio, 2003), but we show that a better performance can be achieved by combining both algorithms. Experiments with or without a psychoacoustic model are conducted on several audio signals, and confirm the improvements by the SCD and by the combined ISS and SCD.

Detection and Analysis of Near-Surface Explosions on the Kola Peninsula

Seismic and infrasonic observations of signals from a sequence of near-surface explosions at a site on the Kola Peninsula have been analyzed. NORSAR’s automatic network processing of these events shows a significant scatter in the location estimates and, to improve the automatic classification of the events, we have performed full waveform cross-correlation on the data set. Although the signals from the different events share many characteristics, the waveforms do not exhibit a ripple-for-ripple correspondence and cross-correlation does not result in the classic delta-function indicative of repeating signals. Using recordings from the ARCES seismic array (250 km W of the events), we find that a correlation detector on a single channel or three-component station would not be able to detect subsequent events from this source without an unacceptable false alarm rate. However, performing the correlation on each channel of the full ARCES array, and stacking the resulting traces, generates a correlation detection statistic with a suppressed background level which is exceeded by many times its standard deviation on only very few occasions. Performing f-k analysis on the individual correlation coefficient traces, and rejecting detections indicating a non-zero slowness vector, results in a detection list with essentially no false alarms. Applying the algorithm to 8 years of continuous ARCES data identified over 350 events which we confidently assign to this sequence. The large event population provides additional confidence in relative travel-time estimates and this, together with the occurrence of many events between 2002 and 2004 when a temporary network was deployed in the region, reduces the variability in location estimates. The best seismic location estimate, incorporating phase information for many hundreds of events, is consistent with backazimuth measurements for infrasound arrivals at several stations at regional distances. At Lycksele, 800 km SW of the events, as well as at ARCES, infrasound is detected for most of the events in the summer and for few in the winter. At Apatity, some 230 km S of the estimated source location, infrasound is detected for most events. As a first step to providing a Ground Truth database for this useful source of infrasound, we provide the times of explosions for over 50 events spanning 1 year.

Improvements to detection capability by cross-correlating for similar events: a case study of the 1999 Xiuyan, China, sequence and synthetic sensitivity tests

Comparisons are made of the performance of a correlation detector compared to a standard short-term average window/long-term average window (STA/LTA) detector for 90 events in the 1999 Xiuyan, China, earthquake sequence. Triggers on three component data verify independent detections to the nearest sample. Unrelated signals that trigger above a threshold do not align on the three components and do not constructively interfere when the cross-correlation traces are stacked or averaged. Semi-similar events due to less than perfect matches arising from substantial mechanism differences can provide useful detections. Synthetic tests on 78 028 focal mechanisms indicate that statistically significant detections are still triggered for strike, dip and rake variations as large as 55°. The correlation detector finds 90 out of 90 or 100 per cent of the events whereas a STA/LTA detector finds 10 out of 90 or 11 per cent. This represents a 1.3 magnitude unit reduction in detection threshold for these events or nearly a factor of 20 improvement.

On the integrated cross-noise term in correlation detectors

An integrated cross-noise component frequently arises in communications and in signal processing. One typical example is the autocorrelation receiver. Integrated cross-noise generally appears when a noisy signal is recovered (detected) using correlation techniques with a noisy signal as the reference. The statistics of the integrated cross-noise component are analyzed in general for both the cases of uncorrelated and correlated noise terms in the integrand. The exact 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order statistics of the integrated cross-noise are derived, and new improved expressions are derived for an approximate probability density function. Accurate computer simulations are performed to evaluate the actual probability density function of the integrated cross-noise component and these results are compared with the approximations. The convergence of the approximation to a Gaussian distribution is also discussed.

Performance of Orthogonal Fingerprinting Codes Under Worst-Case Noise

We study the effect of the noise distribution on the error probability of the detection test when a class of randomly rotated spherical fingerprints is used. The detection test is performed by a focused correlation detector, and the spherical codes studied here form a randomized orthogonal constellation. The colluders create a noise-free forgery by uniform averaging of their individual copies, and then add a noise sequence to form the actual forgery. We derive the noise distribution that maximizes the error probability of the detector under average and almost-sure distortion constraints. Moreover, we characterize the noise distribution that minimizes the decoder's error exponent under a large-deviations distortion constraint.

Regular Simplex Fingerprints and Their Optimality Properties

This paper addresses the design of additive fingerprints that are maximally resilient against linear collusion attacks on a focused correlation detector, as defined below. Let <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> be the length of the host vector and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> les <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> + 1 the number of users. The focused detector performs a correlation test in order to decide whether a user of interest is among the colluders. Both the fingerprint embedder and the colluders are subject to squared-error distortion constraints. We show that simplex fingerprints maximize a geometric figure of merit for this detector. In that sense they outperform orthogonal fingerprints but the advantage vanishes as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> rarr infin. They are also optimal in terms of minimizing the probability of error of the focused detector when the attack is a uniform averaging of the marked copies followed by the addition of white Gaussian noise. Reliable detection is guaranteed provided that the number of colluders <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> Lt radic( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ). Moreover, we study the probability of error performance of simplex fingerprints for the focused correlation detector when the colluders use nonuniform averaging plus white Gaussian noise attacks.

Evaluation of bistable systems for binary signal detection in symmetric non-Gaussian noise

For detecting binary signals in symmetric noise with unknown probability density functions (PDF), a nonlinear receiver is proposed based on the bistable systems with autoregressive models of order 1 [AR(1)]. The bistable systems are utilized to pre-process the noisy observations ahead of the linear correlation (LC) detector. The permutations of the observations are utilized to bypass the design of the optimal LC vector which depends on the noise PDF. The detection performances, in the form of probabilities of error, in some non-Gaussian noise are evaluated versus the matched filter (MF) and Volterra filter (VF) through numerical simulations. The results show that the bistable receiver performs better than MF receiver when the noise deviates from Gaussian distribution, and seems more robust compared to the VF receiver.

Performance of Distributed-Antenna DS-CDMA Systems Over Composite Lognormal Shadowing and Nakagami-&lt;formula formulatype="inline"&gt;&lt;tex Notation="TeX"&gt;$m$&lt;/tex&gt;&lt;/formula&gt;-Fading Channels

This paper investigates the uplink performance of a high-capacity direct-sequence code-division multiple-access (DS-CDMA) wireless communication system, where numerous antennas are distributed in the area covered by the system. Following the description of the system, typical characteristics of the distributed-antenna DS-CDMA (DA/DS-CDMA) system are summarized, in comparison with conventional DS-CDMA systems that employ centralized base station (BS) antennas. Then, the bit error rate (BER) performance of the DA/DS-CDMA system without using power control is investigated when the low-complexity correlation and minimum mean square error (MMSE) detectors are employed and when composite transmission pass loss, lognormal shadowing slow fading, and Nakagami- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fast fading are considered. Our analytical and numerical results suggest that the DA/DS-CDMA system constitutes a high-power-efficiency wireless system. For the same set of system parameters, the DA/DS-CDMA system is capable of providing a much higher capacity than the conventional DS-CDMA system. The DA/DS-CDMA system can be free from power control. Furthermore, the hand-over in the DA/DS-CDMA system is also very simple.

Generalized Embedding of Multiplicative Watermarks

This paper constructs a class of generalized embeddings of multiplicative watermarks. Ordinary multiplicative and additive methods are included as special cases. The new watermarks automatically adapt to the local contents of host signals, benefiting the perceptual quality. The decoding makes use of the optimal generalized correlation detector. The host interference is precanceled at the embedder side and very high gains are obtained in terms of decoding capability. We develop performance analysis for this new class of embeddings. It turns out that the plain multiplicative watermark is far outperformed by the new embedding. Further, the multiplicative watermark with host interference rejection is still suboptimal. The best embeddings and configurations are specified for typical scenarios. Our construction and performance analyses of the generalized embedding offer a class of new methods. The construction and analyses are confirmed by empirical experiments.

Semi Fragile Watermark With Self Authentication And Self Recovery

Robust watermarks are suitable for copyright protection in a DRM scenario. On the other hand, fragile watermarks are good for tamper detection applications. Semi fragile watermarks possess some properties of both robust and fragile watermarks at a moderate level. The need for semi fragile watermarks arises from the requirements of content authentication where the watermark must highlight malicious attacks while tolerating legitimate changes that do not alter the content severely. Very few watermarking scheme has both self authentication and self recovery features. We developed and evaluated a semi fragile watermarking scheme that offers these features. The scheme embeds a downscaled version of an image into the image’s discrete wavelet transform subbands. Our scheme provides content authentication by allowing high quality JPEG compression, minor local distortion, and minimal noise insertion. Other changes such as histogram equalisation, cropping, rotation, and mean filtering are classified as malicious attacks because it affects the visual quality of the image. The scheme is practical because it does not require a reference image during content authentication. Tampered regions can be located correctly, and its original content can be recovered. The watermark information is secured by a secret key that randomises the watermark pixel positions. The single transform, correlator detector, and down-scaled processing spaces of the scheme offer low computational cost.

Broad‐scale applicability of correlation detectors to China seismicity

It is demonstrated that cross‐correlation methods can successfully be applied on a large scale to the detection of seismic events arising in a variety of tectonic settings. The locations of about thousand earthquakes a year occurring in and near China are reported using phase picks from a large national network. We performed more than 100 million cross correlations on the waveforms of more than 18,800 events over 20 years, as recorded by a relatively sparse network; and detected about two thirds of the nationally reported events. Additional events (70% increase), beyond what standard processing detects for China on the sparse network, were also found. A corresponding reduction in detection threshold approaches 0.9 magnitude units for increasing station distance. As networks densify and archives grow, cross‐correlation is likely to become more and more useful for purposes of maximizing the number of detected events and hence to improve knowledge of seismicity.

Speed encoding in correlation motion detectors as a consequence of spatial structure

For animals to carry out a wide range of detection, recognition and navigation tasks, visual motion signals are crucial. The encoding of motion information has therefore, attracted much attention in the experimental and computational study of brain function. Two main alternative mechanisms have been proposed on the basis of behavioural and physiological experiments. On one hand, correlation-type and motion energy detectors are simple and efficient in the design of their basic mechanism but are tuned to temporal frequency rather than to speed. On other hand, gradient-type motion detectors directly represent an estimate of speed, but may require more demanding processing mechanisms. We demonstrate here how the temporal frequency dependence observed for sine-wave gratings can disappear for less constrained stimuli, to be replaced by responses reflecting speed for stimuli like square waves when a phase-sensitive detection mechanism is employed. We conclude from these observations that temporal frequency tuning is not necessarily a limitation for motion vision based on correlation detectors, and more generally demonstrate in view of the typical Fourier composition of natural scenes, that correlation detectors operating in such environments can encode image speed. In the context of our results, we discuss the implications of the loss of phase sensitivity inherent in using a linear system approach to describe neural processing.

A maximum a-posteriori identification criterion for wavelet domain watermarking

A detector based on Maximum A-posteriori Probability (MAP) criterion has been introduced for identifying image watermark in the Discrete Cosine Transform (DCT) domain. This type of detector has been shown to be optimum and robust to common image processing operations. In this paper, an MAP detector in the Discrete Wavelet Transform (DWT) domain is proposed. It is based on modelling the wavelet coefficients by a generalised Gaussian distribution. Simulations are used to compare the proposed detector with the conventional correlation detector in terms of detection effectiveness.