An Accurate and Efficient Zero-Crossing Line Classifier for Multiscale Parameter Estimation of Gaussian Signals Subject to Noise

The multiscale parameter estimation framework is a method for estimating the true parameters of signals subject to noise. The method is based on detecting lines of zero-crossings within the Continuous Wavelet Transform and substituting their locations in time into analytical equations directly expressing the unknown signal parameters. Evidently, this approach depends on selecting the correct lines, corresponding to the signal of interest and not to other phenomena related to noise. This task can be posed as the binary classification problem of determining for each zero-crossing line found whether or not it should be used for parameter estimation. It has been shown that even for very high noise levels, a correct classification leads to very accurate estimates, while a wrong classification results in highly inaccurate estimates. Therefore, with this particular approach the classification of zero-crossing lines poses the limiting factor to the accuracy of the estimated parameters. In this work, we propose a novel, efficient and more robust classifier called “stencil operator” which accurately detects the best combination of zero-crossing lines of Gaussian input signals. We evaluate the performance of this new classifier using synthetic Gaussian signals subject to white (Gaussian) noise with signal-to-noise ratios ranging from 50 dB to - 20 dB. By studying the error between estimated and ground truth parameters, we show that the new classifier outperforms the current method for all noise levels considered and for a noise level of e.g. -12 dB improves the median error from 132% to 28%. The proposed classifier pushes the boundary for analyzing heavily disturbed signals using multiscale parameter estimation to a new level.