Probability Of Correct Detection Research Articles

Receiver operating characteristic analysis for the selection of threshold values for detection of capping in powder compression

The acoustic emission (AE) energy obtained from compressing lactose powder to form pharmaceutical tablets was chosen for condition monitoring of the tablets. The method used was based on the setting of an AE energy decision threshold such that problems of tablet capping and lamination were successfully identified. Capping and lamination are the most common types of problem that can occur in tablets manufacturing using a powder compression process. To assess the performance of a classifier, use was made of a receiver operating characteristic curve (ROC) obtained by plotting the correct detection probability against the false alarm probability based on AE energy distributions for capped and non-capped tablets. The area under the ROC curve, referred to as the AUC, determines the level of competency of the classifier. A value of 0.5 suggests a mere hazarding of guesses whilst a value of 1 indicates correct classification every time. The AE energy approach for tablet capping monitoring gives an AUC value of 0.96, thereby suggesting the possibility of a highly accurate classifier. With the assumption that penalties for false alarm and missed detection are equally severe, using the graphical method of expected penalty cost (EPC), the optimal AE energy decision threshold was established to be 1.2 × 10 8 units, at which the maximum correct capping detection rate of 95% was achieved. The paper also explains how a decision threshold can be obtained when the two penalties are not equal.

Algorithm for Detecting a Sequence of Pulsed Signals with Random Appearance Times

Using the methods of optimal nonlinear Markov filtering, we obtain an algorithm for optimal detection of a sequence of pulsed signals with random times of appearance against the background of white Gaussian noise in discrete time. Statistical characteristics of the synthesized algorithm are studied by computer simulation. The dependences of correct-detection probability on the signal-to-noise ratio and the intervals between pulses are obtained. It is shown that using the optimal nonlinear filtering methods we can improve the quality of detection of a sequence of pulsed signals compared with the methods based on the matched filtering of individual pulses in a packet.

Orthogonal and projected orthogonal matched filter detection

This paper considers the generic problem of detecting in the presence of additive noise, which one from a set of known signals has been received. In place of the classical matched filter (MF) receiver we propose a modified receiver. When the transmitted signals are linearly independent this receiver is referred to as an orthogonal matched filter (OMF) receiver, and when the transmitted signals are linearly dependent it is referred to as a projected orthogonal matched filter (POMF) receiver. Two equivalent representations of the receiver are developed with different implications in terms of implementation. In the first, the demodulator consists of a MF demodulator followed by an optimal whitening transformation on a space formed by the transmitted signals, that optimally decorrelates the MF outputs prior to detection. In the second, the demodulator consists of a bank of correlators with correlating signals that are projections of a set of orthogonal signals, and are closest in a least-squares sense to the transmitted signals. We provide simulation results that suggest that in certain cases the OMF and POMF receivers can significantly increase the probability of correct detection over the MF receiver in non-Gaussian noise with only a minor impact on performance in Gaussian noise.

Influence of Statistical Properties of Multidimensional Signals on the Probability of Their Optimum Detection

The approximate analytical dependences of the probability of correct detection of multidimensional radar signals (images) with independent readings on the statistical properties (probability density function) of the readings, described by the moments of frequency distribution, have been established.

Mixed-quantum-state detection with inconclusive results

We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a sufficient condition for the scaled inverse measurement to maximize the probability of correct detection for the case in which the rate of inconclusive results exceeds a certain threshold. Using this condition we derive the optimal measurement for linearly independent pure-state sets, and for mixed-state sets with a broad class of symmetries. Specifically, we consider geometrically uniform (GU) state sets and compound geometrically uniform (CGU) state sets with generators that satisfy a certain constraint. We then show that the optimal measurements corresponding to GU and CGU state sets with arbitrary generators are also GU and CGU respectively, with generators that can be computed very efficiently in polynomial time within any desired accuracy by solving a semidefinite programming problem.

Detection of small objects on a textured image

This paper presents experimental results on the detection by an observer of small objects of known shape on textured images. A method is proposed for describing the texture as a sum of random Gaussian fields of various intensities and spatial scales. The effect of the spatial scale of the texture elements and their intensity on the detectivity of the observer is investigated. Based on the resulting experimental data, expressions are proposed for estimating the correctdetection and false-alarm probabilities.

Synthesis of filters for multichannel Doppler processing of signals

The paper is devoted to synthesis of a multichannel filter based on such a criterion as maximum probability of proper detection of the signal, when the probability is averaged over Doppler channels. The gain in probability of correct detection with the use of the known and synthesized time windows makes up 15%. The comparative analysis of frequency properties of the synthesized and classical weighting windows is performed.

Detectability of the negative event: effect on the acceptance of pre- or post-event risk-defusing actions

In risky decision situations, many decision makers search for risk-defusing operators (RDOs). An RDO is an action intended by the decision maker to be performed additionally to a specific alternative and is expected to decrease the risk. Pre-event RDOs (e.g., vaccination) have to be applied before a negative event (e.g., infection) occurs. Post-event RDOs do not need to be initiated before and unless the event happens (e.g., medical treatment). For the successful application of Post-event RDOs, the negative event must be detected in time. Two experiments investigated the effect of uncertainty in the detection of the negative event. In Experiment 1, only a small minority of subjects noted this uncertainty without a cue, and even with cue, only a minority actively searched for probability information. In Experiment 2, the probability for correctly detecting the negative event was varied. When detection was certain, most subjects chose the alternative with a Post-event RDO, whereas this percentage decreased significantly with decreasing probability of correct detection. Also, in the conditions with a more extreme negative outcome, less decision makers chose the alternative with the Post-event RDO.

Techniques for minimizing error propagation in decision feedback detectors for recording channels

Decision feedback equalization (DFE) is a low-cost approach for signal detection in magnetic recording channels. However it suffers from the phenomenon of error propagation (EP). In this paper two approaches are proposed for minimizing EP in DFE. The first approach imposes appropriate constraints on the feedback equalizer. The second approach uses simple threshold techniques to detect the presence of decision errors and to either correct these errors or minimize the possibility of further errors. Computer simulations show that the proposed techniques reduce EP very significantly. Theoretical analyses of the threshold techniques are presented to quantify the associated false and correct detection probabilities. By combining the analysis with an existing EP simulation method, a fast simulation procedure is derived for estimating EP and bit error rate (BER).

Detection of hail by means of polarimetric radar data and hailpads: results from four storms

AbstractHailfall is one of the most dangerous and damaging phenomena associated with severe thunderstorms. Its remote identification is still under investigation, especially by means of polarimetric radar data. The need to use polarimetric measurements is a limit to operational implementation of the techniques developed up till now. The routine sampling of radar allows the computation of the differential hail signal HDR (Aydin et al., 1986) every 15 minutes. The assessment of the HDR is performed by comparison with the ground truth from a hailpad network. The spatial resolution of this network is quite coarse (one pad per 16 km2) for the collection of all the hail shafts, as they generally have a small horizontal extent and are short lived. Such bounds have been considered in the analysis of four large hailfalls recorded in 1997. This study reveals also the limitation on radar hail detection arising from the frequent occurrence of strong differential attenuation. Nevertheless, to identify regions where a sharp rain–hail transition occurs, polarimetric measurements work much better than algorithms based only on horizontal reflectivity. Results show that use of HDR gives a high probability of correct hail detection as well as an acceptable number of false alarms. Copyright © 2000 Royal Meteorological Society

Optimization of NQR Pulse Parameters using Feedback Control

A new method for increasing the probability of detecting nuclear resonance signals is demon-strated experimentally. It is well known that the detection of signals with a low signal to noise ratio (SNR) results in missed detections of false alarms. In situations where the noise is correlated or where limited data is averaging, it may not be possible to achieve a desired SNR through averaging alone. We present an alternative approach in which a feedback algorithm automatically adjusts pulse parameters so that the SNR and probability of correct detection are increased. Experimental results are presented for the detection of 14N NQR signals.

Optimality of the maximum average correlation height filter for detection of targets in noise

A statistical analysis is provided for the properties of the re- cently developed maximum average correlation height (MACH) filter (Mahalanobis et al. 1994). It is shown that the MACH filter can be inter- preted as an optimum filter for the detection of targets in additive noise. A rationale is given for using a popular peak-to-sidelobe ratio metric to characterize the output of the MACH filter. Finally, the performance of the MACH filter is compared to that of the matched spatial filter (MSF) in terms of the relation between the probabilities of correct detection and false alarm, which is represented as a receiver operating characteristic (ROC) curve. © 1997 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(97)00910-0)

Random perturbation models for boundary extraction sequence

Computer vision algorithms are composed of different sub-algorithms often applied in sequence. Determination of the performance of a total computer vision algorithm is possible if the performance of each of the sub-algorithm constituents is given. The performance characterization of an algorithm has to do with establishing the correspondence between the random variations and imperfections in the output data and the random variations and imperfections in the input data. In this paper we illustrate how random perturbation models can be set up for a vision algorithm sequence involving edge finding, edge linking, and gap filling. By starting with an appropriate noise model for the input data we derive random perturbation models for the output data at each stage of our example sequence. By utilizing the perturbation model for edge detector output derived, we illustrate how pixel noise can be successively propagated to derive an error model for the boundary extraction output. It is shown that the fragmentation of an ideal boundary can be described by an alternating renewal process and that the parameters of the renewal process are related to the probability of correct detection and grouping at the edge linking step. It is also shown that the characteristics of random segments generated due to gray-level noise are functions of the probability of false alarm of the edge detector. Theoretical results are validated through systematic experiments.

The strong simplex conjecture is false

The design of M average-energy-constrained signals in additive white Gaussian noise is addressed. The long-standing strong simplex conjecture, which postulates that the regular simplex signal set maximizes the probability of correct detection under an average-energy constraint, is disproven. A signal set is presented that performs better than the regular simplex signal set at low signal-to-noise ratios for all M/spl ges/7. This leads to the result that, for all M/spl ges/7, there is no signal set of M signals which is optimal at all signal-to-noise ratios. Furthermore, the optimal signal set at low signal-to-noise ratios is not an equal energy set for any M/spl ges/7. The regular simplex is shown to be the unique signal set which maximizes the minimum distance between signals. It follows that a signal set which maximizes the minimum distance is not necessarily optimum. However, the regular simplex is shown to be globally optimum in the sense of uniquely maximizing the union bound on error probability at all signal-to-noise ratios. >

Analysis of compressive receivers for the optimal interception of frequency-hopped waveforms

Establishes that the compressive receiver is a practical interceptor of high performance. Given a signal of a particular duration, a compressive receiver can estimate simultaneously all frequency components within a set wide band. This processing is similar to a parallel bank of narrowband filters, which is the optimal detector of frequency-hopped signals. Furthermore, hop frequency is estimated to yield performance equal to the parallel filter configuration. The authors assume interference to be stationary, colored Gaussian noise, and present a model of the compressive receiver that contains all its salient features. Low energy coherence detection is achieved by taking the compressive receiver output as an observation and applying likelihood ratio theory at small signal-to-noise ratios. For small signals, this approach guarantees the largest probability of correct detection for a given probability of false alarm, and thus provides a reference, to which simplified or ad hoc schemes can be compared. Since the low energy coherence detector has an unwieldy structure, a simplified suboptimal detector structure is developed that consists of a simple filter, followed by a sampler and a square-envelope detector. Several candidates for the filter's response are presented. The performance of the low energy coherence detector based on compressive receiver observations is compared to the optimal filter-bank detector based on direct observations, thus showing the exact loss incurred when a compressive receiver is used. The performance of various simplified schemes, based on compressive receiver observations, is analyzed. >

Range/velocity limitations for time-domain blood velocity estimation

The traditional range/velocity limitation for blood velocity estimation systems using ultrasound is elucidated. It is stated that the equation is a property of the estimator used, not the actual physical measurement situation, as higher velocities can be estimated by the time domain cross-correlation approach. It is demonstrated that the time domain technique under certain measurement conditions will yield unsatisfactory results, when trying to estimate high velocities. Various methods to avoid these artifacts using temporal and spatial clustering techniques are suggested. The improvement in probability of correct detection is derived, and several examples of simulations are shown.

Stationary echo canceling in velocity estimation by time-domain cross-correlation

The application of stationary echo canceling to ultrasonic estimation of blood velocities using time-domain cross-correlation is investigated. Expressions are derived that show the influence from the echo canceler on the signals that enter the cross-correlation estimator. It is demonstrated that the filtration results in a velocity-dependent degradation of the signal-to-noise ratio. An analytic expression is given for the degradation for a realistic pulse. The probability of correct detection at low signal-to-noise ratios is influenced by signal-to-noise ratio, transducer bandwidth, center frequency, number of samples in the range gate, and number of A-lines employed in the estimation. Quantitative results calculated by a simple simulation program are given for the variation in probability from these parameters. An index reflecting the reliability of the estimate at hand can be calculated from the actual cross-correlation estimate by a simple formula and used in rejecting poor estimates or in displaying the reliability of the velocity estimated.

Header detection in a centralised packet radio system with common DS/BPSK spread-spectrum modulation

The author addresses a multiple header detection issue for the centralised spread-spectrum packet radio system with common directsequence/ binary phase-shift-keying (DS/BPSK) modulation. Chernoff bounds on the false alarm and missed detection probabilities of the header are derived and computed for a specific class of spreading codes and header sequences. Using these performance bounds, the author compares the header sequences and finds a good one which can be received with small probability of false alarm and high probability of correct detection. He also determines a proper randomisation time to minimise the two bounds for given system parameters, and then calculates the allowable number of transmitting radios subject to a constraint on the bounds for this randomisation time.

Automatic decision threshold level control (ADTLC) in direct-sequence spread-spectrum systems based on matched filtering

An automatic decision threshold level control (ADTLC) algorithm for direct-sequence spread-spectrum systems is described and analyzed. Two parameters of interest, probability of false alarm P/sub a/ and probability of correct signal detection P/sub d/, are controlled simultaneously. As an example, the implementation of the algorithm in several practical direct-sequence spread-spectrum receivers is discussed. A considerable advantage of this algorithm compared to the classical approach (constant false alarm probability control) to the problem is demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Rapid Acquisition for Direct Sequence Spread-Spectrum Communications Using Parallel SAW Convolvers

In this paper, a technique is described which uses multiple surface acoustic wave (SAW) devices in parallel to reduce the acquisition time of a direct sequence spread-spectrum communication system. Analysis of system performance in both the search and lock modes is presented, and key quantities such as probability of false alarm, probability of correct detection, mean dwell time, and mean time to lose lock are derived.