Gaussian Detection Research Articles

Semi‐empirical procedures for correcting detector size effect on clinical MV x‐ray beam profilesa)

The measured radiation beam profiles need to be corrected for the detector size effect to derive the real profiles. This paper describes two new semi-empirical procedures to determine the real profiles of high-energy x-ray beams by removing the detector size effect from the measured profiles. Measured profiles are corrected by shifting the position of each measurement point by a specific amount determined from available theoretical and experimental knowledge in the literature. The authors developed two procedures to determine the amount of shift. In the first procedure, which employs the published analytical deconvolution procedure of other investigators, the shift is determined from the comparison of the analytical fit of the measured profile and the corresponding analytical real profile derived from the deconvolution of the fitted measured profile and the Gaussian detector response function. In the second procedure, the amount of shift at any measurement point is considered to be proportional to the value of an analytical function related to the second derivative of the real profile at that point. The constant of proportionality and a parameter in the function are obtained from the values of the shifts at the 90%, 80%, 20%, and 10% dose levels, which are experimentally known from the published results of other investigators to be approximately equal to half of the radius of the detector. These procedures were tested by correcting the profiles of 6 and 18 MV x-ray beams measured by three different ionization chambers and a stereotactic field diode detector with 2.75, 2, 1, and 0.3 mm radii of their respective active cylindrical volumes. The corrected profiles measured by different detectors are found to be in close agreement. The detector size corrected penumbra widths also agree with the expected values based on the results of an earlier investigation. Thus, the authors concluded that the proposed procedures are accurate and can be used to derive the real profiles of clinical high-energy x-ray beams.

Evidence for Poisson processes in change detection

Comparisons between two stimuli (e.g., "which stimulus was louder?") and change detection ("same or different?") are often assumed to operate on the same decision basis. In the Gaussian signal detection theory, each of the two stimuli to be compared is transformed into a number, and the comparison is then made between these two numbers. If both stimuli are well above absolute threshold, the numbers to be compared have to be large, which motivates the use of normal distributions. The present study tests this assumption by measuring same-different ROC curves for the detection of small changes in the intensity of sinusoids. In contrast to previous studies, change detection was measured not only when the possible direction of change was a priori unknown, but also in two conditions where changes had a fixed direction. The obtained ROCs are asymmetric. This points to Poisson processes with low means. Moreover, the sensitivity to increments was significantly higher than the sensitivity to decrements. The results put into question the Gaussian theory of sensory comparisons and change detection.

BayesSDT: Software for Bayesian inference with signal detection theory

This article describes and demonstrates the BayesSDT MATLAB-based software package for performing Bayesian analysis with equal-variance Gaussian signal detection theory (SDT). The software uses WinBUGS to draw samples from the posterior distribution of six SDT parameters: discriminability, hit rate, false alarm rate, criterion, and two alternative measures of bias. The software either provides a simple MATLAB graphical user interface or allows a more general MATLAB function call to produce graphs of the posterior distribution for each parameter of interest for each data set, as well as to return the full set of posteriorsamples.

Degree of polarization estimation in the presence of nonuniform illumination and additive Gaussian noise

Within the general framework of active imaging we address the degree of polarization (DOP) estimation in the presence of additive Gaussian detector noise. We first study the performance of standard DOP estimators and propose a method to increase estimation precision using physically relevant a priori information. We then consider the realistic case of nonuniform illumination distribution. We derive the Cramer-Rao lower bound and determine a profile likelihood-based estimator. We demonstrate the efficiency of this new estimator and compare its performance with other standard estimators as a function of the degree of nonuniformity of the illumination.

Edge Detection in Gray Level Images based on the Shannon Entropy

Most of the classical mathematical methods for edge detection based on the derivative of the pixels of the original image are Gradient operators, Laplacian and Laplacian of Gaussian operators. Gradient based edge detection methods, such as Roberts, Sobel and Prewitts, have used two 2-D linear filters to process vertical edges and horizontal edges separately to approximate first-order derivative of pixel values of the image. The Laplacian edge detection method has used a 2-D linear filter to approximate second-order derivative of pixel values of the image. Major drawback of second-order derivative approach is that the response at and around the isolated pixel is much stronger. In this research study, a novel approach utilizing Shannon entropy other than the evaluation of derivates of the image in detecting edges in gray level images has been proposed. The proposed approach solves this problem at some extent. In the proposed method, we have used a suitable threshold value to segment the image and achieve the binary image. After this the proposed edge detector is introduced to detect and locate the edges in the image. A standard test image is used to compare the results of the proposed edge detector with the Laplacian of Gaussian edge detector operator. In order to validate the results, seven different kinds of test images are considered to examine the versatility of the proposed edge detector. It has been observed that the proposed edge detector works effectively for different gray scale digital images. The results of this study were quite promising.

Testing a neurocomputational model of recollection, familiarity, and source recognition.

The authors assess whether the complementary learning systems model of the medial temporal lobes (Norman & O'Reilly, 2003) is able to account for source recognition receiver operating characteristics (ROCs). The model assumes that recognition reflects the contribution of a hippocampally mediated recollection process and a cortically mediated familiarity process. The hippocampal process is found to produce threshold output functions that lead to U-shaped zROCs, whereas the cortical process produces Gaussian signal detection functions and linear zROCs. The model is consistent with several dual process theories of recognition and is capable of producing the types of zROCs observed in studies of item and source recognition. In addition, the model makes the novel prediction that as the level of feature similarity across items increases, the ability of the hippocampus to encode distinct representations for each stimulus will diminish, and the threshold nature of recollection will break down, leading source zROCs to become more linear. The authors conducted 3 new behavioral source experiments that confirmed the model's prediction. The results demonstrate that the model provides a viable account of item and source recognition performance.

Precision of degree of polarization estimation in the presence of additive Gaussian detector noise

We address the problem of degree of polarization (DOP) estimation in images limited by additive Gaussian detector noise. We derive and analyze the probability density function (PDF) of the pixelwise DOP estimate, which is shown to have significantly different statistical properties than when noise is Gamma distributed (speckle). We then determine the Cramer–Rao Lower Bound and the maximum likelihood estimator of the DOP. We deduce from this study practical solutions for characterizing and reducing the noise in these images.

Gaussian Approximation Based Mixture Reduction for Joint Channel Estimation and Detection in MIMO Systems

A novel Gaussian approximation based mixture reduction algorithm is proposed for semi-blind joint channel tracking and symbol detection for spatial multiplexing multiple-input multiple-output (MIMO) systems with frequency-flat time-selective channels. The proposed algorithm is based on a modified sequential Gaussian approximation detector (SGA) which takes into account channel uncertainty, and the first order generalized pseudo-Bayesian (GPB1) channel estimator. Simulation results show that the proposed algorithm performs better than the conventional and computationally expensive decision-directed method with Kalman filter based channel estimation and a posteriori probability (APP) symbol detection.

Bayesian Fusion Performance and System Optimization for Distributed Stochastic Gaussian Signal Detection Under Communication Constraints

The problem of decentralized detection and fusion of a Gaussian signal is considered under the assumption of analog relay-amplifier local processing. It is shown that under an average global (system) power constraint, there always exists an optimal number of nodes that achieves the best possible performance under both orthogonal and nonorthogonal sensor-to-fusion center communication. Any increase in the number of nodes beyond the optimal value leads to degraded performance. This implies that each node needs to maintain a certain minimum received power level at the fusion center in order to make a useful contribution to the final decision. This is contrasted with the monotonic performance improvement observed under individual node power constraints as well as in the case of deterministic signal detection under a global power constraint. Three communication scenarios are studied in detail: 1) orthogonal; 2) equicorrelated; and 3) random signaling waveforms. In each case, error exponents and resulting bounds for Bayesian fusion performance are derived. A sensor system optimization method based on Bhattacharya error exponent, that leads to simple rules for determining the optimal number of nodes under a global average power constraint is also proposed

Feature-specific structured imaging

We present a feature-specific imaging system based on the use of structured light. Feature measurements are obtained by projecting spatially structured illumination onto an object and collecting all the reflected light onto a single photodetector. Principal component features are used to define the illumination patterns. The optimal linear minimum mean-square error (LMMSE) operator is used to generate object estimates from the measured features. We study the optimal allocation of illumination energy into each feature measurement in the presence of additive white Gaussian detector noise and optical blur. We demonstrate that this new imaging approach reduces imager complexity and provides improved image quality in high noise environments. Compared to the optimal LMMSE postprocessing of a conventional image, feature-specific structured imaging provides a 38% rms error reduction and requires 400 times fewer measurements for a noise standard deviation of sigma = 2 x 10(-3). Experimental results validate these theoretical predictions.

A Parametric Approach to Suboptimal Signal Detection in $\alpha$-Stable Noise

This paper deals with the detection of a known deterministic signal embedded in alpha-stable noise. The implementation of the optimal receiver requires the explicit expression of the probability density function (pdf) of the noise. Unfortunately, since there exists no closed-form for the pdf of alpha-stable distributed random variables, numerical integrations are required. To avoid such numerical approximations, we suggest a low-complexity parametric suboptimal detector well matched to essential properties of alpha-stable noises. This receiver does not require the explicit expression of the noise pdf. In addition, parameter optimization is fast for several optimization criteria and the selected receiver allows retrieval of the optimal Gaussian detector (matched filter) as well as the locally optimal detector in the Cauchy context. The performance of the detector is studied and a comparison with the optimal solution along with a variety of classical detectors is given. The robustness of the detector against the signal amplitude and the stability index alpha of the noise is discussed

Multitaper scan-free spectrum estimation using a rotational shear interferometer

Multitaper methods for a scan-free spectrum estimation that uses a rotational shear interferometer are investigated. Before source spectra can be estimated the sources must be detected. A source detection algorithm based upon the multitaper F-test is proposed. The algorithm is simulated, with additive, white Gaussian detector noise. A source with a signal-to-noise ratio (SNR) of 0.71 is detected 2.9 degrees from a source with a SNR of 70.1, with a significance level of 10(-4), approximately 4 orders of magnitude more significant than the source detection obtained with a standard detection algorithm. Interpolation and the use of prewhitening filters are investigated in the context of rotational shear interferometer (RSI) source spectra estimation. Finally, a multitaper spectrum estimator is proposed, simulated, and compared with untapered estimates. The multitaper estimate is found via simulation to distinguish a spectral feature with a SNR of 1.6 near a large spectral feature. The SNR of 1.6 spectral feature is not distinguished by the untapered spectrum estimate. The findings are consistent with the strong capability of the multitaper estimate to reduce out-of-band spectral leakage.

The gravitational wave 'probability event horizon' for double neutron star mergers

Gravitational waves generated by the final merger of double neutron star (DNS) binary systems are a key target for the gravitational wave (GW) interferometric detectors, such as LIGO (Laser Interferometer Gravitational-wave Observatory), and the next generation detectors, Advanced LIGO. The cumulative GW signal from DNS mergers in interferometric data will manifest as ‘geometrical noise’: a non-continuous stochastic background with a unique statistical signature dominated by the spatial and temporal distribution of the sources. Because geometrical noise is highly non-Gaussian, it could potentially be used to identify the presence of a stochastic GW background from DNS mergers. We demonstrate this by fitting to a simulated distribution of transients using a model for the DNS merger rate and idealized Gaussian detector noise. Using the cosmological ‘probability event horizon’ concept and recent bounds for the Galactic DNS merger rate, we calculate the evolution of the detectability of DNS mergers with observation time. For Advanced LIGO sensitivities and a detection threshold assuming optimal filtering, there is a 95 per cent probability that a minimum of one DNS merger signal will be detectable from the ensemble of events comprising the stochastic background during 12–211 d of observation. For initial LIGO sensitivities, we identify an interesting regime where there is a 95 per cent probability that at least one DNS merger with signal-to-noise ratio greater than unity will occur during 4–68 d of observation. We propose that there exists an intermediate detection regime with pre-filtered signal-to-noise ratio less than unity, where the DNS merger rate is high enough that the geometrical signature could be identified in interferometer data.

GeneralizedF-statistic: Multiple detectors and multiple gravitational wave pulsars

The F-statistic, derived by Jaranowski, Krolak & Schutz (1998), is the optimal (frequentist) statistic for the detection of nearly periodic gravitational waves from known neutron stars, in the presence of stationary, Gaussian detector noise. The F-statistic was originally derived for the case of a single detector, whose noise spectral density was assumed constant in time, and for a single known neutron star. Here we show how the F-statistic can be straightforwardly generalized to the cases of 1) a network of detectors with time-varying noise curves, and 2) a population of known sources. Fortunately, all the important ingredients that go into our generalized F-statistics are already calculated in the single-source/single-detector searches that are currently implemented, e.g., in the LIGO Software Library, so implementation of optimal multi-detector, multi-source searches should require negligible additional cost in computational power or software development.

Hidden messages in heavy-tails: DCT-domain watermark detection using alpha-stable models

This paper addresses issues that arise in copyright protection systems of digital images, which employ blind watermark verification structures in the discrete cosine transform (DCT) domain. First, we observe that statistical distributions with heavy algebraic tails, such as the alpha-stable family, are in many cases more accurate modeling tools for the DCT coefficients of JPEG-analyzed images than families with exponential tails such as the generalized Gaussian. Motivated by our modeling results, we then design a new processor for blind watermark detection using the Cauchy member of the alpha-stable family. The Cauchy distribution is chosen because it is the only non-Gaussian symmetric alpha-stable distribution that exists in closed form and also because it leads to the design of a nearly optimum detector with robust detection performance. We analyze the performance of the new detector in terms of the associated probabilities of detection and false alarm and we compare it to the performance of the generalized Gaussian detector by performing experiments with various test images.

A Blind Additive Watermarking Algorithm Under Intense Interference Background

Traditional blind additive SS (spread spectrum) watermarking systems have such features: high robustness, low detection value and small capacity. The main reason leading to low detection value is the host signal’s interference. Based on the Gaussian signal detection principle under Gaussian noise, the correlation detection is analyzed in theory. In addition, the using condition of correlation detector and the relationship between the normalized correlation detector and SNR (signal noise ratio) are discussed in this paper. Based on these analyses, an improved blind additive watermarking algorithm is designed. Experimental results show that the algorithm effectively holds back the interference of host signal and the performance of detection has been greatly improved. Furthermore, it has greater robustness and imperceptibility.

Locally Optimum Nonlinearities for DCT Watermark Detection

The issue of copyright protection of digital multimedia data has attracted a lot of attention during the last decade. An efficient copyright protection method that has been gaining popularity is watermarking, i.e., the embedding of a signature in a digital document that can be detected only by its rightful owner. Watermarks are usually blindly detected using correlating structures, which would be optimal in the case of Gaussian data. However, in the case of DCT-domain image watermarking, the data is more heavy-tailed and the correlator is clearly suboptimal. Nonlinear receivers have been shown to be particularly well suited for the detection of weak signals in heavy-tailed noise, as they are locally optimal. This motivates the use of the Gaussian-tailed zero-memory nonlinearity, as well as the locally optimal Cauchy nonlinearity for the detection of watermarks in DCT transformed images. We analyze the performance of these schemes theoretically and compare it to that of the traditionally used Gaussian correlator, but also to the recently proposed generalized Gaussian detector, which outperforms the correlator. The theoretical analysis and the actual performance of these systems is assessed through experiments, which verify the theoretical analysis and also justify the use of nonlinear structures for watermark detection. The performance of the correlator and the nonlinear detectors in the presence of quantization is also analyzed, using results from dither theory, and also verified experimentally.

The Performance of the GLRT for the Spatial Signals Detection With a Small Number of Observations

In this letter, the generalized likelihood ratio test (GLRT) is used for the detection of multidimensional Gaussian complex signals with unknown spatial covariance matrix on a background of additive Gaussian complex noise of a unknown power is solved. The exact analytical expressions for test-statistical moments were found for any numbers of observations. The expansion in a series of probability density functions of a resolving statistic for orthogonal Jacobi polynomials were obtained by method of moments. The accuracy of the GLRT-statistic cumulative distribution function approximation and the accuracy of threshold calculations for the given false alarm probability for various numbers of approximating series terms were checked by simulation. The results are correct for any number of samples.

A model subspace method for matched field source localization in a shallow-water acoustic waveguide

Model subspace methods for parameter estimation can yield promising results when temporal or spatial variability dominate the model inputs. Application of Gaussian signal detection theory, summarized by Van Trees, is applied to the localization problem. Model inputs, such as the sound velocity profile in water, bottom properties, and array position, rather than being deterministic, are characterized using a Gaussian random vector. This, in turn, yields a random signal model which is represented as a vector space. Detection and localization via a maximum-likelihood estimator becomes a question of whether the received signal fits the subspace defined by the random signal model.

Design and optimization of on-chip capillary electrophoresis.

We present a systematic, experimentally validated method of designing electrokinetic injections for on-chip capillary electrophoresis applications. This method can be used to predict point-wise and charge-coupled device (CCD)-imaged electropherograms using estimates of species mobilities, diffusivities and initial sample plug parameters. A simple Taylor dispersion model is used to characterize electrophoretic separations in terms of resolution and signal-to-noise ratio (SNR). Detection convolutions using Gaussian and Boxcar detector response functions are used to relate optimal conditions for resolution and signal as a function of relevant system parameters including electroosmotic mobility, sample injection length, detector length scale, and the length-to-detector. Analytical solutions show a tradeoff between signal-to-noise ratio and resolution with respect to dimensionless injection width and length to the detector. In contrast, there is no tradeoff with respect to the Peclet number as increases in Peclet number favor both SNR and separation solution (R). We validate our model with quantitative epifluorescence visualizations of electrophoretic separation experiments in a simple cross channel microchip. For the pure advection regime of dispersion, we use numerical simulations of the transient convective diffusion processes associated with electrokinetics together with an optimization algorithm to design a voltage control scheme which produces an injection plug that has minimal advective dispersion. We also validate this optimal injection scheme using fluorescence visualizations. These validations show that optimized voltage scheme produces injections with a standard deviation less than one-fifth of the width of the microchannel.