A Riemannian manifold optimization strategy is proposed to facilitate the relaxation of the orthonormality constraint in a more natural way in the course of performing independent component analysis (ICA) that employs a mutual information-based source-adaptive contrast function. Despite the extensive development of manifold techniques catering to the orthonormality constraint, only a limited number of works have been dedicated to oblique manifold (OB) algorithms to intrinsically handle the normality constraint, which has been empirically shown to be superior to other Riemannian and Euclidean approaches. Imposing the normality constraint implicitly, in line with the ICA definition, essentially guarantees a substantial improvement in the solution accuracy, by way of increased degrees of freedom while searching for an optimal unmixing ICA matrix, in contrast with the orthonormality constraint. Designs of the steepest descent, conjugate gradient with Hager-Zhang or a hybrid update parameter, quasi-Newton, and cost-effective quasi-Newton methods intended for OB are presented in this paper. Their performance is validated using natural images and systematically compared with the popular state-of-the-art approaches in order to assess the performance effects of the choice of algorithm and the use of a Riemannian rather than Euclidean framework. We surmount the computational challenge associated with the direct estimation of the source densities using the improved fast Gauss transform in the evaluation of the contrast function and its gradient. The proposed OB schemes may find applications in the offline image/signal analysis, wherein, on one hand, the computational overhead can be tolerated, and, on the other, the solution quality holds paramount interest.

The upcoming launch of the next generation of hyperspectral satellites (PRISMA, EnMap, HyspIRI, etc.) will meet the increasing demand for the availability/accessibility of hyperspectral information on agricultural land use from the agriculture community. To this purpose, algorithms for the classification of remotely sensed images are here considered for agricultural monitoring of cultivated area, exploiting remotely sensed high spectral resolution images. Classification is accomplished by procedures based on discriminant analysis tools that well suit hyperspectrality, circumventing what in statistics is called “the curse of dimensionality”. As a byproduct of classification, a full assessment of the spectral bands of the sensor is obtained, ranking them with the purpose of understanding their role in segmentation and classification. The methodology has been validated on two independent image datasets gathered by the MIVIS (Multispectral Infrared and Visible Imaging Spectrometer) sensor for which ground validations were available. A comparison with the popular multiclass SVM (Support Vector Machines) classifier is also presented. Results show that a good classification (minimum global success rate 95% through all experiments) is achieved by using the 10 spectral bands selected as the most discriminant by the proposed procedure; moreover, it also appears that nonparametric techniques generally outperform parametric ones. The present study confirms that the new generation of hyperspectral satellite data like PRISMA can ripen an end-user application for agricultural land-use of cultivated area.

A model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. A related algorithm, based on the Hazard Rate Method, is also devised and described.