Experience: The IFCA is an active part of several scientific projects at the forefront of modern astronomy that, due to their complexity and the enormous volume of data they generate, require special attention to the statistical analysis of signals. Thus the group has extensive experience in fuzzy component separation, signal detection and statistical analysis of distributions with a wide range of applications in other sectors apart from astronomy, such as medicine, security, etc.
Among the various analysis techniques used, the following stand out:
Separation of fuzzy components: Development of component separation algorithms based on Maximum Entropy techniques. Other methods include the Independent Component Method (ICA) and Internal Linear Combination and Template Fitting.
Wavelets: Multi-resolution analysis, data compression and denoising.
Detection and estimation of compact signals: These include adapted filters, wavelets, Neyman-Pearson filters based on maximums statistics, linear and non-linear fusion techniques, sparse approximations and Bayesian methods.
Spectral estimation from contaminated data: Using an expectation-maximization (EM) type algorithm, the angular spectrum of powers is recovered from images contaminated by other types of unwanted sources.
Statistical study of distributions: Determination of non-Gaussianity. Some of the techniques developed include: wavelets, goodness-of-fit, morphological and topological indicators, Minkowski's functional and n-pdf study.
Adaptation of existing signal processing techniques in the literature under non-ideal conditions (correlated, non-Gaussian, non-stationary noise) to specific problems.
Development of completely new technical solutions, specifically adapted to the type of problem images.
Applications: Human and veterinary health, security and defence, telecommunications and information technology. The experience in signal analysis is easily extrapolated to any problem where images or large data sets appear, from medical images to remote sensing.