Sparsity and morphological diversity for multivalued data analysis

International audienceThe recent development of multi-channel sensors has motivated interest in devising new methods for the coherent processing of multivariate data. An extensive work has already been dedicated to multivariate data processing ranging from blind source separation (BSS) to multi/hyper-spectral data restoration. Previous work1 has emphasized on the fundamental role played by sparsity and morphological diversity to enhance multichannel signal processing. GMCA is a recent algorithm for multichannel data analysis which was used successfully in a variety of applications including multichannel sparse decomposition, blind source separation (BSS), color image restoration and inpainting. Inspired by GMCA, a recently introduced algorithm coined HypGMCA is described for BSS applications in hyperspectral data processing. It assumes the collected data is a linear instantaneous mixture of components exhibiting sparse spectral signatures as well as sparse spatial morphologies, each in specified dictionaries of spectral and spatial waveforms. We report on numerical experiments with synthetic data and application to real observations which demonstrate the validity of the proposed method

Sparsity constraints for hyperspectral data analysis: linear mixture model and beyond

The recent development of multi-channel sensors has motivated interest in devising new methods for the coherent processing of multivariate data. An extensive work has already been dedicated to multivariate data processing ranging from blind source separation (BSS) to multi/hyper-spectral data restoration. Previous work has emphasized on the fundamental role played by sparsity and morphological diversity to enhance multichannel signal processing. GMCA is a recent algorithm for multichannel data analysis which was used successfully in a variety of applications including multichannel sparse decomposition, blind source separation (BSS), color image restoration and inpainting. Inspired by GMCA, a recently introduced algorithm coined HypGMCA is described for BSS applications in hyperspectral data processing. It assumes the collected data is a linear instantaneous mixture of components exhibiting sparse spectral signatures as well as sparse spatial morphologies, each in specified dictionaries of spectral and spatial waveforms. We report on numerical experiments with synthetic data and application to real observations which demonstrate the validity of the proposed method

Spatiotemporal blind source separation using double-sided approximate joint diagonalization

In independent component analysis (ICA) the common task is to achieve either spatial or temporal independence by linearly mapping into a feature space. If the data possesses both spatial and temporal structures such as a sequence of images or 3d-scans taken at fixed time intervals, we can require the transformed data to be as independent as possible in both domains. First introduced by Stone using a joint entropy energy function, spatiotemporal ICA is a promising method for real-world data analysis. We propose a novel algorithm for performing spatiotemporal ICA by jointly diagonalizing various source conditions such as higher-order cumulants of the mixtures, both in time and in space. Similar to algebraic ICA algorithms, this provides a robust method for data analysis, which is confirmed by simulations