Optimización del modelo de regresión espacio-temporal multivariado basado en Fourier para la predicción de la presencia de la clorofila-a alrededor de las Islas Galápagos

Chlorophyll-a (Chl-a) is an indicator of phytoplankton biomass, which can be used to predict the presence of fish in the ocean. By predicting the Chl-a with sufficient time, this data can be used to better plan naval operations that combat illegal, unreported and unregulated fishing by increasing surveillance of the identified areas where the greatest fishing activity would take place. In this work, a new technique is proposed, based on the application of the discrete Fourier transform theory to develop multivariate spatial-temporal regression model, which considers physical and biogeochemical ocean variables to predict the presence of  Chlorophyll-a around Galápagos Islands. This work considers open access data taken from the Copernicus space program, used in the European Union.La Clorofila-a es un indicador de la biomasa del fitoplancton, que puede ser utilizado para predecir la presencia de peces en el océano. Al predecir la Chl-a con suficiente tiempo, se puede utilizar en la planificación de las operaciones navales que combaten la pesca ilegal, no regulada y no reglamentada, por cuanto se identifica el lugar donde existirá mayor actividad pesquera, para incrementar su vigilancia. En este trabajo, proponemos una novel técnica basada en la aplicación de la teoría de la transformada discreta de Fourier, al modelo de regresión multivariable espacio-temporal desarrollado, que considera las variables físicas y biogeoquímicas del océano para la predicción de la clorofila-a, alrededor de las Islas Galápagos. Este trabajo considera datos de acceso libre del programa espacial Copérnico de la Unión Europea

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error