Merging Multi-Level Decompositions and Feature Extraction to Optimize Biological Data Analysis, Proc Portuguese Physics for Health Summer School - PPHSS, Covilhã, Portugal, Vol. I, pp. 13 - 13, July, 2010.
Biological signals are relentlessly superimposed with artifacts, external interferences, and noise. The nonlinear and non-stationary processes involved in the generation of both signals and disturbances, often limit the ability of classical techniques, and even wavelet transforms, to isolate the part of interest. In order to improve biological images and signals, feature extraction techniques are of great interest.
Signal processing techniques to filter biological signals, or to do data compression, are likely to use wavelet transforms. One alternative to wavelets is Empirical Mode Decomposition (EMD), a nonlinear, adaptive, and fully data-driven technique which obtains the oscillatory modes present in the data, thus producing a variable number of components. However, the problem of minimizing the data set while maximizing the information provided has a different answer varying with the subject, measurement conditions, and noise. This happens in discrete wavelet transform (DWT), and even in EMD, because each component generated will not keep the same physiological relations.
An optimal solution would be obtained by gathering the intrinsic elements of the signal of interest, by some feature transformation, applied to the output of the decomposition (DWT, EMD, or other). Therefore, to complement the results of the transformations, two computationally reasonable approaches, based on multivariate analysis, with some degree of optimality, may be suggested. Principal Component Analysis (PCA) is optimal in the least squares sense, and removes the correlations from the different modes, thus generating orthogonal components. A second approach is Independent Component Analysis (ICA), which ensures statistical independence of the components by minimization of mutual information among the components identified, considering additive Gaussian noise is involved.
Bringing the optimal selective power of PCA/ICA to the multi-resolution mode discrimination of DWT/EMD allows a better understanding of the data, either 1D signal, image or video. Consequently it is of great interest to explore such approach.