This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and test data differ, presenting additional challenges for learning. Although kernel methods have optimal statistical properties, their high computational demands in terms of time and, particularly, memory, limit their scalability to large datasets. To address this limitation, the main focus of this paper is to explore the trade-off between computational efficiency and statistical accuracy under covariate shift. We investigate the use of random projections where the hypothesis space consists of a random subspace within a given RKHS. Our results show that, even in the presence of covariate shift, significant computational savings can be achieved without compromising learning performance.

We investigate an extension of classical empirical risk minimization, where the hypothesis space consists of a random subspace within a given Hilbert space. Specifically, we examine the Nyström method where the subspaces are defined by a random subset of the data. This approach recovers Nyström approximations used in kernel methods as a specific case. Using random subspaces naturally leads to computational advantages, but a key question is whether it compromises the learning accuracy. Recently, the tradeoffs between statistics and computation have been explored for the square loss and self-concordant losses, such as the logistic loss. In this paper, we extend these analyses to general convex Lipschitz losses, which may lack smoothness, such as the hinge loss used in support vector machines. Our main results show the existence of various scenarios where computational gains can be achieved without sacrificing learning performance. When specialized to smooth loss functions, our analysis recovers most previous results. Moreover, it allows to consider classification problems and translate the surrogate risk bounds into classification error bounds. Indeed, this gives the opportunity to compare the effect of Nyström approximations when combined with different loss functions such as the hinge or the square loss.

We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data, recovering as a special case Nyström approaches for kernel methods. Considering random subspaces naturally leads to computational savings, but the question is whether the corresponding learning accuracy is degraded. These statistical-computational tradeoffs have been recently explored for the least squares loss and self-concordant loss functions, such as the logistic loss. Here, we work to ex- tend these results to convex Lipschitz loss functions, that might not be smooth, such as the hinge loss used in support vector ma- chines. This extension requires developing new proofs, that use different technical tools. Our main results show the existence of different settings, depending on how hard the learning problem is, for which computational efficiency can be improved with no loss in performance. Theoretical results are illustrated with simple numerical experiments.

A discrete scattering model, based on the radiative-transfer theory, is used to simulate the backscattering of burned pine canopies at C-band. The model is first parameterized either with direct field measurements on a selected burned area in Greece or with proper estimations of the required variables, for which direct measurements were not possible. The simulated backscatter at VV polarization was compared against European Remote Sensing 2 (ERS-2) observations. The comparison was based on the observed backscattering of nine burned plots, during four different postfire acquisitions $(n=36)$ . In general, the model provides satisfying estimations of the backscattering with a root-mean-square error of 1.01 dB. The copolar signal for both HH and VV showed a mild decrease with increasing fire impacts and was considerably affected by the incidence angle. From the experiments performed in the simulated environment, it is concluded that the SAR copolar (C-band) backscatter varies with respect to certain fire impact levels. Other important acquisition- or stand-dependent variables (such as incidence angle and snag age) were also found to impact the relationship between backscatter and fire impacts. Finally, the backscattering variability on increasing volumetric soil moisture (VSM) and snag moisture was examined. The increase of VSM from 20% to 30% amplified the signal in both copolarized bands by 1.2–1.5 dB. This amplification was more apparent on VV polarization than in HH polarization. Instead, the HH signal proved to be more sensitive on the increase of snag moisture, which was tested under a stable dry soil.

This paper shows a model study about the emissivity of forests. Model outputs are compared with multifrequency airborne measurements carried out over five broadleaf forests in Italy. Two flights took place, in summer 1999 and winter 2002. Available ground truth included important variables, such as biomass, tree density, and average trunk diameter. This data set, in conjunction with allometric equations and information taken from the literature, is used to give inputs to the model. A general agreement between simulated and measured data is observed at L-, C-, and X-bands. The same model is used to investigate the sensitivity of forest emissivity to soil moisture, woody volume, and average diameter. As expected, a moderate effect of soil moisture is observed only at L-band and for forests with a lower woody volume. At L-band, the model predicts a general increase of emissivity with woody volume but indicates that also the trunk diameter exerts an important influence, since it is a variable which controls several geometrical properties. These results allow us to single out the influence of soil moisture, woody volume, and geometrical properties at L-band. The increase of emissivity with frequency, observed in experimental data, is interpreted by means of electromagnetic considerations about branch scattering.

This paper shows model simulations of forest emissivity at L-band and at global scale. The electromagnetic model developed at Tor Vergata University has been combined with information available from forest literature. Using allometric equations and auxiliary information, the geometric and dielectric inputs required by the model have been related to global variables available at large scale, such as Leaf Area Index. Simulations indicate that, at L-band, leaves are almost transparent, attenuation is mostly due to branches, and soil contribution can be still appreciable, unless the forest is dense. The model is being refined, to consider seasonal variations of foliage cover, subdivided into arboreous foliage and understory contribution. Parametric simulations, as well as comparisons with experimental data, are shown.

This paper describes a microwave model which simulates the emissivity of forests, including litter effects. Detailed input data about forest geometry are obtained by direct measurements and/or by allometric equations. Model outputs have been compared with multifrequency measurements carried out over five broadleaf forests in Italy. Fundamental information about forest properties was available. A general agreement between simulated and measured data is observed. Some discrepancies require further investigation. Also a component analysis has been done. The contribution of soil emission is very low for higher forest volumes, but is appreciable for lower forest volumes.

The objective of this paper is to carry out a systematic investigation about the sensitivity of radar to maize crop growth and soil moisture by considering a wide range of frequencies and angles and all linear polarizations. We show the results of a correlation study carried out on the data collected on a maize field at Suberg, in the Swiss region named Central Plain, by the multifrequency RAdio ScAtteroMeter (RASAM). This agricultural field was monitored over a long period of time at a wide range of frequencies and observation angles so that the correlation between the backscattering and crop height and the biomass and soil moisture was studied under several plant and observation conditions. Moreover, we describe some recent refinements applied to the vegetation scattering model developed at Tor Vergata University, Rome, Italy, and we evaluate the accuracy of extended comparisons between model outputs and RASAM signatures. The Tor Vergata model is finally applied to give a theoretical basis to the experimental correlation findings.

Polarimetric SAR interferometric data can provide estimates of forest biomass density. There are different approaches to deal with the inversion problem, such as neural networks and the traditional optimal estimation approach. This paper presents a study to evaluate their performance by means of quantitative indexes addressing both the computation time and the retrieval accuracy. Better forest parameters estimates have been obtained when neural networks algorithms were used.

In this work, we show the correlation study carried out on the data collected on a maize field in the Swiss region named Central Plain, by the multifrequency RASAM scatterometer. This agricultural field was monitored over long periods, at a wide range of frequencies and observation angles, so that the correlation between backscattering and crop height, biomass and soil moisture could have been studied under several plant and observation conditions. Moreover, we describe some recent refinements applied to the vegetation scattering model developed at Tor Vergata University, and we evaluate the accuracy of extended comparisons between model outputs and RASAM signatures. The Tor Vergata model is finally applied to give a theoretical basis to the experimental correlation findings.

To retrieve soil moisture at vegetated surface by microwave radiometry data, vegetation effect is important to remove. Usually the zero-order model, ω — τ model, is often used where vegetation is treated as an uniform layer. Values of both scattering and attenuation characteristics of vegetation are assigned from experience which there’re slight change at different frequencies or polarizations. As frequencies go higher than L-band, multiple-scattering effect inside vegetation layer and that between vegetation and soil surface is necessary to account for. In this paper, to accurately evaluate vegetation effect at C and X bands, a Matrix-Doubling algorithm is used to retrieve ω and τ of corn. The surface emission model is AIEM that could work well at large roughness and wider frequency range. The preliminary simulation results are presented in this paper.

This letter describes recent advances in modeling forest emissivity at L-band. The formulation is based on a previously developed discrete model and includes a new representation of forest litter. Comparisons with multitemporal radiometric data collected in the framework of the ldquoBray 2004rdquo experiment, which was carried out within Les Landes forest, are shown and discussed. Input variables are given by using detailed ground measurements. In general, the model reproduces both absolute values and temporal variations of measured brightness temperature. The contribution of the litter to overall emission was found to be important.

Bistatic radars have been recently proposed as an alternative to conventional monostatic radars since they can provide additional information in many fields of remote sensing applications. However, up to now, no bistatic radar campaigns, nor laboratory experiments, having vegetation as the target have been set up. This paper presents theoretical simulations of the bistatic scattering coefficient of crop and forest canopies. The electromagnetic model developed at Tor Vergata has been used to analyse scattering as a function of the observation angle, both in azimuth and elevation, and it will be shown that biomass monitoring can be optimized at out-of-incidence scattering planes.

This paper describes a model which simulates the emission of forests at L band. In particular, the problem of soil emission attenuated by vegetation is considered. Results of comparisons with experimental data collected by the upward looking ELBARA radiometer are presented and discussed.

A discrete model, based on the radiative transfer theory, is used to simulate coniferous forest emissivity at L-band. Inputs to the model are given by using a detailed geometrical representation of Les Landes forest. Simulated emissivities are compared against EuroSTARRS campaign measurements, which were made over the same forest at nominally vertical polarization and several angles. The model has also been used to investigate the sensitivity of L-band radiometers to soil moisture under forests. Results of this investigation indicate that the soil contribution to emission is potentially appreciable, even under developed forests. This may be a useful result, in view of future satellite missions, such as SMOS and HYDROS

This paper assess the possibilities of the synthetic aperture radar (SAR) sensors currently in orbit for the maize monitoring defining the configurations (polarization and incidence angles at C-band) maximizing the sensitivity to plant growth and reducing the impact of the soil moisture on the signal. Temporal evolution of the signal was simulated in all the possible configurations using the radiative transfer model developed by the University of Rome "Tor Vergata." The input parameters came from an intensive field campaign providing a detailed description of maize crop over the Belgian Loamy site all along the 2003 growing season. The model was validated for vertical (VV) and horizontal (HH) polarization using ERS, ENVISAT, and RADARSAT observations. The C-band SAR signal in single polarization was found to be sensitive to crop growth till the leaf area index (LAI) reached 4.6 m/sup 2//m/sup 2/, while the soil moisture influenced the signal for sparsely vegetated fields (LAI<2.7 m/sup 2//m/sup 2/). Dual-polarizations indexes were found sensitive to maize growth and less sensitive to soil moisture variations. The VV/VH polarization ratios computed from signal recorded at high incidence angle (35/spl deg/ to 45/spl deg/) could be considered to assess the crop growth till LAI reached 4.9 m/sup 2//m/sup 2/ with low sensitivity to soil moisture. At the beginning of growth, the emergence of maize plants could be detected using the copolarized ratio (VV/HH) computed at low incidence angle. These indexes allow discriminating various crop conditions at a given date between fields of a same region.

Several efforts, aimed at developing and refining crop backscattering models, have been done during the last years. Although important advances have been achieved, it is recognized that further work is required, both in the electromagnetic characterization of single scatterers and in the combination of contributions. This work is focused on the description of leaf geometry and of the internal structure of stems. Recently developed routines, able to model the scattering cross sections of curved sheets and hollow cylinders, are adopted for this purpose and run within the multiple-scattering model developed at the University of Rome "Tor Vergata". Input parameters are taken from experimental campaigns. In particular, ground data collected over a maize field at the Central Plain site in 1988, over wheat and maize fields at the Loamy site in 2003, and over wheat fields at the Matera site in 2001 and 2003 are considered. The multitemporal backscattering coefficients at C-band are simulated. The results obtained under different assumptions are compared to each other, and with C-band radar signatures collected over the same fields. The influence of some critical factors, affecting crop backscattering, is discussed. It is demonstrated that a more detailed scatterer characterization may improve the model accuracy, especially in the case of hollow stems.

Currently, there is a strong interest in studying the L-band emission of forests to exploit the sensitivity of the microwave signature to surface soil moisture and forest biophysical parameters such as biomass or LAI. In this paper we contribute to the understanding of the forest emission problem through simulations of the L-band brightness temperature based on a discrete radiative transfer model. Prior to L-band simulations, a geometric model of a maritime pine tree forest has been developed to get a close description of a real forest. L-band simulations are then analysed and compared to airborne radiometric data over the Les Landes (SW France) Maritime pine tree forest.

This paper shows some recent advances acquired in the crop backscattering model developed at Tor Vergata University. In particular, new routines, able to compute cross sections of curved leaves and hollow cylinders, are described

This article describes a model based on radiative transfer theory, where the leaves geometry is represented by a curved rectangular dielectric sheet.