WAVELET-THRESHOLD TUNING WITH A CONSTRAINT ON HAZARDOUS-EMISSION GAS DETECTION-PROBABILITY LOSS
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Soft wavelet-threshold tuning is studied for a sensor-node data-processing path under an explicit constraint on the loss of short hazardous-emission event detection probability. The threshold is defined as the product of the universal value and a dimensionless multiplier ranging from 0 to 1.05. A four-level Haar transform is used. Reconstruction of a 512-sample piecewise-smooth signal is evaluated over 3,000 realizations of additive Gaussian noise at an input signal-to-noise ratio of 0 dB. Event performance is assessed by Monte Carlo simulation for 128-sample blocks, three pulse morphologies, and a false-alarm probability of 0.01; 50,000 realizations are processed at each point. At a multiplier of 0.30, the output signal-to-noise ratio is 7.242 dB and the mean fraction of nonzero coefficients is 33.512%. For the most adverse case, a short pulse at -12 dB, the detection probability decreases from 0.6877 to 0.6109. With the admissible decrease set to 0.08, the multiplier of 0.30 is selected, whereas the next value of 0.45 violates the constraint. The setting supports joint design of denoising and detection and requires subsequent validation using field data from the specific gas-analysis channel.
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