This work describes the minimum volume enclosing simplex problem, which is known to be a multimodal Global Optimization problem. The problem has been used as a basis to estimate so-called endmember and abundance data in unmixing spectral data of hyperspectral sensors. This estimation problem is a big challenge. We explore the possibility of a new estimation algorithm using the minimum volume en...

Recently, many sparse approximation methods have been applied to solve spectral unmixing problems. These methods in contrast to traditional methods for spectral unmixing are designed to work with large a-prori given spectral dictionaries containing hundreds of labelled material spectra enabling to skip the expensive endmember extraction and labelling step. However, it has been shown that sparse...

This paper reports on the results from ordinary least squares and ridge regression as statistical methods, and is compared to numerical optimization methods such as the stochastic method for global optimization, simulated annealing, particle swarm optimization and limited memory Broyden-Fletcher-Goldfard-Sharon bound optimization method. We used each of the above mentioned methods in estimating...

Integrating spatial information into hyperspectral unmixing procedures has been shown to have a positive effect on the estimation of fractional abundances due to the inherent spatial–spectral duality in hyperspectral scenes. However, current research works that take spatial information into account are mainly focused on the linear mixing model. In this paper, we investigate how to incorporate s...

Nonnegative Matrix Factorization (NMF) is an unsupervised learning method that has been already applied to many applications of spectral signal unmixing. However, its efficiency in some applications strongly depends on optimization algorithms used for estimating the underlying nonnegatively constrained subproblems. In this paper, we attempt to tackle the optimization tasks with the inexact Inte...

We describe the minimum volume simplex enclosure problem (MVSEP), which is known to be a global optimization problem, and further investigate its multimodality. The problem is a basis for several (unmixing) methods that estimate so-called endmembers and fractional values in a linear mixing model. We describe one of the estimation methods based on MVSEP. We show numerically that using nonlinear ...

Hyperspectral images represent an important source of information to assess ecosystem biodiversity. In particular, plant species richness is a primary indicator of biodiversity. This paper uses spectral variance to predict vegetation richness, known as Spectral Variation Hypothesis. Hierarchical agglomerative clustering is our primary tool to retrieve clusters whose Shannon entropy should refle...

Recently, several blind signal separation algorithms have been developed which are based on second order statistics. Little has been published however on whether second order statistics are sufficient to obtain a unique solution. Especially for applications that involve convolutive mixing and unmixing of signals that are correlated in time, there is a lack of knowledge on why and in what cases ...

Chromophore quantification in optoacoustic tomography is challenging due to signal contributions from strongly absorbing background tissue chromophores and the depth-dependent light attenuation. Herein we present a procedure capable of correcting for wavelength-dependent light fluence variations using a logarithmic representation of the images taken at different wavelengths assisted with a blin...

In hyperspectral imagery one pixel typically consists of a mixture of the re ectance spectra of several materials, where the mixture coe cients correspond to the abundances of the constituting materials. We assume linear combinations of re ectance spectra with some additive normal sensor noise and derive a probabilistic MAP framework for analyzing hyperspectral data. As the material reectance c...