“UTILIZING” SIGNAL DETECTION THEORY
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Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns called stimulus in living organisms, signal in machines and random patterns that distract from the information called noiseconsisting of background stimuli and random activity of the detection machine and of the nervous system of the operator.
Binary signal detection theory nedirectory the field of electronicsthe separation of such patterns from a disguising background is referred to as signal recovery. According to the theory, there are a number of determiners of how a detecting system will detect a signal, and where its threshold binary signal detection theory nedirectory will be.
The theory can explain how changing the threshold will affect the ability to discern, often exposing how adapted the system is to the task, purpose or goal at which it is aimed. Another binary signal detection theory nedirectory which is closely related to signal detection theory is called compressed sensing or compressive sensing.
The objective of compressed sensing is to recover high dimensional but with low complexity entities from only a few measurements. Thus, one of binary signal detection theory nedirectory most important applications of compressed sensing is in the recovery of high dimensional signals which are known to be sparse or nearly sparse with only a few linear measurements.
The number of measurements needed in the recovery of signals is by far smaller than what Nyquist sampling theorem requires provided that the signal is sparse, meaning that it only contains a few non-zero elements. There are different methods of signal recovery in compressed sensing including basis pursuitexpander recovery algorithm CoSaMP  and also fast non-iterative algorithm .
In all of binary signal detection theory nedirectory recovery methods mentioned above, choosing an appropriate measurement matrix using probabilistic constructions or deterministic constructions, is of great importance. In other words, measurement matrices must satisfy certain specific conditions such as RIP Restricted Isometry Property binary signal detection theory nedirectory Null-Space property in order to achieve robust sparse recovery.
Back to the detecting theory, when the detecting system is a human being, characteristics such as experience, expectations, physiological state e. For instance, a sentry in wartime might be likely to detect fainter stimuli than the same sentry in peacetime due to a lower criterion, however they might also be more binary signal detection theory nedirectory to treat innocuous stimuli as a threat.
Much of the early work in detection theory was done by radar researchers. Green, and John A. Swetsalso in Swets and David M. Detection theory has applications in many fields such as diagnostics of any kind, quality controltelecommunicationsand psychology. The concept binary signal detection theory nedirectory similar to the signal to noise ratio used in the sciences and confusion matrices used in artificial intelligence.
It is also usable in alarm managementwhere it is important binary signal detection theory nedirectory separate important events from background noise. Signal detection theory SDT is used when psychologists want to measure the way we make decisions under conditions of uncertainty, such as how we would perceive distances in foggy conditions.
SDT assumes that the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgments under conditions of uncertainty.
In foggy circumstances, we are forced to decide how far away from us an object is, based solely upon visual stimulus which is impaired by the fog. Since the brightness of the object, such as a traffic light, is used by the brain to discriminate the distance of an object, and the fog reduces the brightness of objects, we perceive the object to be much farther away than it actually is see binary signal detection theory nedirectory decision theory.
To apply signal detection theory to a data set where stimuli were either present or absent, and the observer categorized each trial as having the stimulus present or absent, the trials are sorted into one of four categories:. Signal detection theory can also be applied to memory experiments, where items are presented on a study list for later testing. A test list is created by combining these 'old' items with novel, 'new' items that did not appear on the study list.
On each test trial the subject will respond 'yes, this was on the study list' or 'no, this was not on the study list'. Items presented on the study list are called Targets, and new items are called Distractors.
Saying 'Yes' to a target constitutes a Hit, while saying 'Yes' to a distractor constitutes a False Alarm. Signal Detection Theory has wide application, both in humans and animals.
Topics include memorystimulus characterists of schedules of reinforcement, etc. Conceptually, sensitivity refers to how hard or easy it is to detect that a target stimulus is present from background events.
For example, in a recognition memory paradigm, having longer to study to-be-remembered words makes it easier to recognize previously seen or heard words. In contrast, having to remember 30 words rather than 5 makes the discrimination harder. One of the most commonly used statistics for computing sensitivity is the so-called sensitivity index or d'. There are also non-parametric measures, such as the area under the ROC-curve.
Bias is the extent to which one response is more probable than another. That is, a receiver may be more likely to binary signal detection theory nedirectory that a stimulus is present or more likely to respond that a stimulus is not present. Bias is independent of sensitivity. For example, if there is a penalty for either false alarms or misses, this may influence bias. If the stimulus is a bomber, then a miss failing to detect the plane may increase deaths, so a liberal bias is likely.
In contrast, crying wolf a false alarm too often may make people less likely to respond, grounds for a conservative bias. The a priori probabilities of H1 and H2 can guide this choice, e. In some cases, it is far more important to respond appropriately to H1 than it is to respond appropriately to H2. The Bayes criterion is an approach suitable for such cases. Here a utility is associated with each of four situations:. From Wikipedia, the free encyclopedia. Binary classification Constant false alarm rate Decision theory Demodulation Detector radio Estimation theory Just-noticeable difference Likelihood-ratio test Modulation Neyman—Pearson lemma Psychometric function Receiver operating characteristic Statistical hypothesis testing Statistical signal processing Two-alternative forced choice Type I and type II errors.
Signal Recovery from Noise in Electronic Instrumentation 2nd ed. Iterative binary signal detection theory nedirectory recovery from incomplete and inaccurate samples". Applied and Computational Harmonic Analysis. Behavior Research Methods, Instruments, and Computers. This article includes a list of referencesbut its sources remain unclear because it has insufficient inline citations.
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