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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.

Abstract: Some empirical localized discriminant analysis methods for classifying images are introduced. They use spatial correlation of images in order to improve classification reducing the ‘pseudo-nuisance’ present in pixel-wise discriminant analysis. The result is obtained through an empirical (data driven) and local (pixel-wise) choice of the prior class probabilities. Local empirical discriminant analysis is formalized in a framework that focuses on the concept of visibility of a class that is introduced. Numerical experiments are performed on synthetic and real data. In particular, methods are applied to the problem of retrieving the cloud mask from remotely sensed images. In both cases classical and new local discriminant methods are compared to the ICM method. [Copyright &y& Elsevier]

Abstract: Two dimensional reduction regression methods to predict a scalar response from a discretized sample path of a continuous time covariate process are presented. The methods take into account the functional nature of the predictor and are both based on appropriate wavelet decompositions. Using such decompositions, prediction methods are devised that are similar to minimum average variance estimation (MAVE) or functional sliced inverse regression (FSIR). Their practical implementation is described, together with their application both to simulated and on real data analyzing three calibration examples of near infrared spectra. [Copyright &y& Elsevier]

The performance of the Infrared Atmospheric Sounding Inteferometer (IASI), which is under development at the laboratories of the French National Space Agency, has been evaluated on the basis of new radiometric noise data. An error analysis has been performed for the direct and simultaneous estimation of temperature, water vapour, and ozone profiles.

Abstract: The modified moment problem is little studied in the literature with respect to the classical moment problem due to the lacking of experiments measuring modified moments. The modified moment problem is analyzed in this paper, when noise affects the modified moments themselves. A numerical method for solving the problem, based on regularization, is given, together with a full theoretical analysis, convergence results and an optimized algorithm. The modified moment problem reveals strongly superior to the classical moment problem in terms of the amplification of the error, conditioning of the matrices involved and ease of computation.

Measurements of aerosol optical depth are presented in the spectral interval 0.40-1.10 μm, which includes the most transparent region of the solar spectrum and the near infrared. The measurements were obtained by a grating spectrometer with a resolution ≈ 0.5 nm during the 1994 summer season at a mountain site (about 850 m above sea level) in the South of Italy. Spectral regions free from gas absorption features have been singled out and used to retrieve the aerosol columnar size distribution. Inversions have been performed by using the Phillips-Twomey inversion method along with a χ2 criterion which allows one to choose a suitable value for the regularization parameter. The result of the inversions are presented in the particle radius range 0.1 ÷ 3 μm and indicate the presence of a bimodal aerosol with the second mode radius at about 1.0 μm undergoing transformations which are well correlated with relative humidity.

In this paper we discuss in detail the long-term maximum yield of photochemical conversion for devices working in realistic weather conditions. In our analysis we take into account both the devices with one photosystem, and those with two photosystems working in parallel. We analyse the dependence of limit efficiency on the main features of devices as threshold frequency and working temperature. Our results show that the limit efficiency of conversion of collected radiation is slightly higher in the case of concentrating devices with respect to nonconcentrating ones. This increase balances the lower collection efficiency of concentrating devices which in fact collect only direct radiation. At last we give some evaluations about economic competitiveness of concentrating devices.

The performances of the Infrared Atmospheric Sounding Interferometer (IASI) which is under development at the aboratories of the French National Space Agency and Italian National Space Agency have been evaluated. An error analysis has been carried out on the basis of the expected radiometric noise. To this end, a linear form of the radiative transfer equation has been formulated for the direct and simultaneous estimation of temperature, water vapour and ozone profiles.

A procedure to recover high resolution spectra without any intervening window from infrared Fourier spectrometer data is presented. The technique relies on the maximum entropy principle in information theory. A parametric autoregressive modelling approach is used. Numerical examples are carried using synthetic spectra computed by an high resolution radiative transfer code. The effect of additive noise is also analysed. The application of the technique to remote sensing of the atmosphere is discussed.