Detection Matched filter

At this stage, the problem is to maximise SNIR at the instant of detection to over the input signal s(t) of finite energy and duration. Grouping the expressions for both whitening filter and matched filter ... 

The single matched filter can be used only when the target s position and velocity are known. To detect a target at an unknown position, it is necessary to utilize a bank of filters matched to all possible target ranges and velocities. This approach leads directly to the range-Doppler correlation function, described by the formula... 

To detect the reflected signal in the presence of thermal white noise, the correlation process (matched filtering) is used according to the fundamentals given above. The received signal will be detected when its power is higher than the thermal noise power P/v multiplied by detectability factor D, e.g. 

Figure 4.2 AR-based detection, P=50. (a) Prediction error filter (b) Matched filter.

Dyer, S.A. and Hardin, D.S., Enhancement of Raman spectra obtained at low signal-to-noise ratios matched filtering and adaptive peak detection, Appl. Spectrosc., 39, 655, 1985. 

Figure 2 Zoom of the region showing tiie etiiane detection, (a) Physics-based signatures detection, (b) Clutter matched filter detection, (c) CIR image of region of detection for context. The detection images are perfectly registered (they are based on die same input LWIR image) but the CIR image is not and has a different spatial resolution. The detections are approximately in die center of the CIR image.

Here, the detection using the physics-based signatures algorithm produces a small, compact, plume-shaped object with a conical shape indicative of a source and diffusion downwind. The detection strength across the plume in the physics-based signature result is relatively uniform and continuous. This is in contrast to the clutter matched filter results which, while showing strong detections, are discontinuous and do not exhibit the same spatial characteristics. 

Figure 4 shows results for the second methane plume detection with the physics-based signatures detection algorithm. Again, the clutter-matched filter fails to detect any methane at this level while the physics-based signatures algorithm detects a spatially compact, well-defined source. 

While the physics-based approach provides detections where the clutter matched filter does not, it is also important to note the nature of the false alarms generated by each method. The clutter-matched filter is essentially a projection operator and is susceptible to false alarms on pixels with large spectral magnitude i.e., bright pixels). The physics-based approach tends to false alarm on background materials not well characterized and on sensor artifacts. The latter is because the detection is in the native radiance space of the image and in the presence of miscalibration or artifacts, the predicted signatures will not match well with the measurement. 

Funk, C.C., Theiler, J., Roberts, D.A, and Borel, C.C., Clustering to improve matched filter detection of weak gas plumes in hyperspectral thermal imagery, IEEE Transactions on Geoscience and Remote Sensing, 39(7), 410-1420 (2001)... 

The matched filter theorem states that if we want to detect matches between / and g by cross-correlating a filter h with /, and the criterion for detection is the ratio of signal power to expected noise power, then the best filter to use is the template g itself Depending on the nature of / and the detection criterion, however, other filters may be better for example, if / is relatively smooth, better results are obtained by correlating the derivative of / with the derivative of g, or / with the second derivative of g. 

The simple cross-correlation estimator is used extensively in the form of a matched filter implementation to detect a finite number of known signals (in other words, simultaneous acquisition of multiple chaimels of known signals). When these deterministic signals are embedded in white Gaussian noise, the matched filter (obtained from cross-correlation estimate at zero lag, k = 0, between the known signal sequence and the observed noisy signal sequence) gives the optimum detection performance (in the Bayes sense ). 

APPLICATION Matched filters can be used to detect and sort action potentials in noise. The multiunit data in Fig. 18.8b were collected from the ventral posteriolateral thalamic nuclei using a... 

In contrast to the principal component (PCA)-based approach for detection and discrimination, the cross-correlation or matched-filter approach is based on a priori knowledge of the shape of the deterministic signal to be detected. However, the PCA-based method also requires some initial data (although the data could be noisy, and the detector does not need to know a priori the label or the class of the diHerent signals) to evaluate the sample covariance matrix K and its eigenvectors. In this sense, the PCA-based detector operates in an unsupervised mode. Further, the matched-filter approach is optimal only when the interfering noise is white Gaussian. When the noise is colored, the PCA-based approach will he preferred. 

The FT of the reference is done off line on a computer and is defined as the matched filter R(u,v) for that particular reference r(x,y). In fact, the generation of the filter may be more complicated (to include invariances), and it is advantageous to use only the phase information of the reference FT rather than the full complex amplitude and phase as it gives a more detectable narrow peak [21]. The product of the input FT and the filter then undergoes a further FT to give the correlation in plane 4. The object in the reference r x,y) is centered in the process of generating the filter R(u,v), so that if a correlation peak occurs, its position is directly proportional to the object in the input... 

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