Noise contaminated transmittance

The authors compare the efficiency of a classifier based on probabilistic neural networks and the general least squares method. Both methods must accommodate noise due to uncertainty in the measured spectrum at each wavelength. The evaluation of both methods is based on a simulated transmittance spectrum, in which the received signal is supplemented by an additive admixture of noise. To obtain a realistic description of the noise model, they generate several hundred laser pulses for each wavelength under consideration. These pulses have a predetermined correlation matrix for different wavelengths; furthermore, they are composed of three components accounting for the randomness of the observed spectrum. The first component is the correlated 1/f noise; the second component is due to uncorrelated 1/f noise; the third one is the uncorrelated white noise. The probabilistic neural network fails to retrieve the species concentration correctly for large noise levels; on the other hand, its predictions being confined to a fixed number of concentration bins, the network produces relatively small variances. To a large extent, the general least square method avoids the false alarms. It reproduces the average concentrations correctly; however, the concentration variances can be large