Andres Camacho

Semi-blind source extraction of atrial activity by combining statistical and spectral features

Atrial fibrillation is the most common human arrhythmia. During atrial fibrillation episodes, the surface electrocardiogram contains the linear superposition of the atrial and ventricular rhythms in addition to other non-cardiac artifacts. Since these signals can be considered statistically independent, a Blind Source Separation (BSS) approach fits the problem properly. The signal that contains useful clinical information is the atrial one. We present a solution that focuses on the extraction of the atrial activity, enforcing simultaneously the statistical and temporal properties of the atrial signal. In addition, we propose the use of kurtosis as a parameter to measure the quality of the extraction. The algorithm is applied successfully to synthetic and real data. It improves the extraction of the atrial signal in comparison to other BSS methods, recovers only the interesting atrial rhythm using the information contained in all the leads and reduces the computational cost. The results obtained are shown to be highly satisfactory, with an average of 53.9% of spectral concentration, -0.04 of kurtosis value, 2.98 of ventricular residua and 4.77% of significant QRS residua over a database of thirty patients.

Independent component analysis with prior information about the mixing matrix

Abstract In the Independent Component Analysis (ICA) problem, a linear transformation of the original statistically independent sources is observed. ICA algorithms usually do not include any prior information about the mixing matrix that models the linear transformation. We investigate in this paper in a general framework how the criterion functions can be modified if a prior information about the entries of the mixing matrix is available. We find that the prior can be nicely introduced in the ICA formulation, so a direct modification of traditional algorithms can be carried out. Including prior information in the learning rule does not only improve convergence properties but also extends the application of ICA techniques to data that do not satisfy exactly ICA assumptions.

A Blind Source Separation Technique for Extracting Sinusoidal Interferences in Ultrasonic Non-Destructive Testing

Sinusoidal interferences are found in ultrasonic signals when we try to characterize a material, as for example interferences coming from PC cards. We are interested in obtaining a robust method that cancels these interferences preserving the waveform of the signal. A Blind Source Separation method to extract these sinusoids is presented in this paper. We will get so many linear mixtures of the backscattering echo of the material and the sinusoids as we need from different pulse responses of the material.

Atrial activity estimation using periodic component analysis

The interest in the study and analysis of Atrial Fibrillation (AF) has increased significantly in the last decades. A correct estimation of the atrial activity is a crucial previous step for AF analysis. Different methods based on Blind Source Separation of 12-lead electrocardiogram (ECG) have been proposed. However, these techniques are based only on the statistical independence of the sources, and usually require a postprocessing step to identify the signal of interest. We present a method that also uses a multilead approach in order to use all the information available in the leads, but it focuses on the discriminative properties of the spectrum of the atrial signal with respect to the non-atrial components. The atrial rhythm can be considered as a pseudo-periodic signal with a main atrial frequency in the range 3–10 Hz. The bandwidth and shape of the spectrum is related to the patient and the kind of tachyrhythmia. Another advantage is that the way the atrial component is extracted is based on algebraic methods, avoiding the adjustment of learning rates and other parameters. The method is applied successfully to real data.

A maximum a posteriori estimate for the source separation problem with statistical knowledge about the mixing matrix

In the blind source separation (BSS) problem, nothing is supposed about the mixing matrix entries. When a prior knowledge about their values is available, the BSS algorithms can be optimized considering this information. We obtain the maximum a posteriori estimate of the source separation problem for prewhitened observed signals and prior statistical knowledge about the mixing matrix for the real, linear, instantaneous case. As new information is included in the formulation of the problem, the variance of classical BSS algorithms can be reduced.

Analysis of astrophysical ice analogs using regularized alternating least squares

The determination of the compounds that are present in molecular clouds is carried out from the study of the infrared spectrum of astrophysical ices. This analysis plays a fundamental role in the prediction of the future evolution of the cloud under study. The process is simulated in the laboratory under similar conditions of thermal and energetic processing, recording the infrared absorption spectrum of the resultant ice. The spectrum of each ice can be modeled as the linear instantaneous superposition of the spectrum of the different compounds, so a Source Separation approach is proper. We propose the use of Alternating Least Squares (ALS) and a Regularized version (RALS) to identify the molecules that are present in the ice mixtures. Since the spectra and abundances are non-negative, a non-negativity constraint can be applied to obtain solutions with physical meaning. We perform several simulations of synthetic mixtures of ices in order to compare both solutions and to show the usefulness of the approach.

Application of regularized Alternating Least Squares to an astrophysical problem

Abstract Determination of the compounds that are present in molecular clouds is carried out from the study of the infrared spectrum of astrophysical ices. This analysis plays a fundamental role in the prediction of the future evolution of the cloud under study. The process is simulated in the laboratory under similar conditions of thermal and energetic processing, recording the infrared absorption spectrum of the resultant ice. The spectrum of each ice can be modeled as the linear instantaneous superposition of the spectrum of the different compounds, so a Source Separation approach is appropriate. We propose the use of Alternating Least Squares and a Regularized version to identify the molecules that are present in the ice mixtures. Since the spectra and abundances are non-negative, a non-negativity constraint can be applied to obtain solutions with physical meaning. We perform several simulations of synthetic and real mixtures of ices in order to compare both solutions and to show how the proposed approach provides an efficient way to recover underlying spectral patterns that are physically meaningful.