Deterministic/Stochastic Wavelet Decomposition for Recovery of Signal From Noisy Data

Implementation of Adaptive-Bayesian DStoch technique for obtaining winds from MST radar covering higher altitudes

It is challenging to estimate winds accurately from higher altitudes using VHF-MST radar. The current study introduces the Adaptive-Bayesian Deterministic Stochastics Technique (ADStoch), which implements an Empirical Bayesian 1D prediction method using stochastics to analyze radar signals. A new and robust estimator for empirical wavelet shrinkage with Gaussian prior of the nonzero mean for wavelet coefficients is presented, which makes the current prior different from other priors. The mean parameters and the prior covariance hyperparameters follow a pseudo maximum likelihood method for computation. Details on the implemented algorithm developed from scratch using C# are also presented. This technique outperforms contemporary techniques discussed in this context that can recover signals buried in noise established based on the analysis of moment and quality. The estimated Wind is cross-validated for accuracy with the observed wind from the GPS radiosonde operated simultaneously. This technique can consistently extract 3D wind that can reach the range of 25.5 km-28.2 km, improving the conventional maximum altitude of 21.2 km in real time for the MST radar. It is concluded that the ADStoch analysis technique can effectively obtain VHF-MST radar signals at significantly higher altitudes, which is helpful in various scientific investigations.

Filtering of surface EMG using ensemble empirical mode decomposition

Surface electromyogram (EMG) is often corrupted by three types of noises, i.e. power line interference (PLI), white Gaussian noise (WGN), and baseline wandering (BW). A novel framework based primarily on empirical mode decomposition (EMD) was developed to reduce all the three noise contaminations from surface EMG. In addition to regular EMD, the ensemble EMD (EEMD) was also examined for surface EMG denoising. The advantages of the EMD based methods were demonstrated by comparing them with the traditional digital filters, using signals derived from our routine electrode array surface EMG recordings. The experimental results demonstrated that the EMD based methods achieved better performance than the conventional digital filters, especially when the signal to noise ratio of the processed signal was low. Among all the examined methods, the EEMD based approach achieved the best surface EMG denoising performance.

Deconvolution When Classifying Noisy Data Involving Transformations

In the present study, we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise. In this setting, we show that classifier performance can be improved if we carefully invert the data before the classifier is applied. However, the inverse transformation is not constructed so as to recover the original signal, and in fact, we show that taking the latter approach is generally inadvisable. We introduce a fully data-driven procedure based on cross-validation, and use several classifiers to illustrate numerical properties of our approach. Theoretical arguments are given in support of our claims. Our procedure is applied to data generated by light detection and ranging (Lidar) technology, where we improve on earlier approaches to classifying aerosols. This article has supplementary materials online.