Advances and Experiments of Tomographic SAR Imaging for the Analysis of Complex Scenarios

It is expected that the number of synthetic aperture radar (SAR) images available for a same scene will increase exponentially in the future, thanks to the technical developments in this area. In order to fully exploit the information lying in data acquired in looking angle (multibaseline, MB), time, and polarization diversity, developments are underway of processing techniques which constitute an evolution of the mature phase-only SAR interferometry for producing new and/or more accurate measures. In particular, by combining coherently (i.e. amplitude and phase) the SAR data, new opportunities are arising for an improved imaging and information extraction of the observed scene. Among these techniques, a very promising advance is constituted by SAR Tomography, a MB interferometric mode allowing a full 3-D imaging in the range-azimuth-height space, thus separating multiple scatterers in layover at different heights in the same SAR cell in complex scenarios. Recently, a new interferometric mode called Differential SAR Tomography has been conceived at the University of Pisa from the synergic fusion of SAR Tomography and the conventional Differential Interferometry, allowing the estimation of also the possible relative deformations between multiple layover scatterers. In this thesis, theoretical advances and experimental results are presented in the analysis of complex scenarios. In particular, the tomographic imaging problem is addressed by exploring different algorithmic options able to enhance the image contrast and possibly also increase the scatterer resolution in height. Moreover, in order to automate the estimation of the height or height/deformation velocity, a scatterer detection algorithm has been developed, which constitutes also a preliminary step for the extensive validation of the information extracted. With regards to volumetric scatterers (e.g. the scatterer in forest scenarios), tomography-based coherent data combination techniques have been proposed and investigated, in particular for the extraction of the sub-canopy digital terrain model and for deriving in a non-model based fashion a coherent MB dataset with only the signal from the scattering layer of interest. Finally, the differential tomographic framework has been exploited for the robust tomographic analysis of temporal decorrelating volumetric scatterers. For each investigated topic, extensive experiments have been carried out with MB urban and forest SAR data

Array Interpolation Methods for Non-Uniform Multibaseline SAR Interferometers

This work deals with the interferometric phase (IP) estimation from data collected by nonuniform multibaseline InSAR system. The approach proposed aims to recover the uniform linear array (ULA)data by means of a linear transformation of the data collected by the actual sensing geometry. After array interpolation, the IP estimation is carried out by means of the parametric spectral estimator root-MUSIC. Different InSAR scenarios are analized and the estimation accuracy is obtained performing a Monte Carlo analysis. Furthermore, the estimation performance is analyzed also in presence of array miscalibration and robust interpolation techniques are then proposed. As a benchmark, the hybrid Cramér-Rao bound is calculated in the case of interest

Una soluzione di Business Intelligence per l'analisi del budget

Si presenta il problema della stesura di un budget commerciale e della realizzazione di un data warehouse di supporto alle analisi inerenti un caso di studio. Successivamente si presentano le caratteristiche degli strumenti open source utilizzati per produrre la reportistica riguardo le analisi comparative sugli scostamenti e la determinazione del punto di pareggio

TomoSAR Mapping of 3D Forest Structure: Contributions of L-Band Configurations

Synthetic Aperture Radar (SAR) measurements are unique for mapping forest 3D structure and its changes in time. Tomographic SAR (TomoSAR) configurations exploit this potential by reconstructing the 3D radar reflectivity. The frequency of the SAR measurements is one of the main parameters determining the information content of the reconstructed reflectivity in terms of penetration and sensitivity to the individual vegetation elements. This paper attempts to review and characterize the structural information content of L-band TomoSAR reflectivity reconstructions, and their potential to forest structure mapping. First, the challenges in the accurate TomoSAR reflectivity reconstruction of volume scatterers (which are expected to dominate at L-band) and to extract physical structure information from the reconstructed reflectivity is addressed. Then, the L-band penetration capability is directly evaluated by means of the estimation performance of the sub-canopy ground topography. The information content of the reconstructed reflectivity is then evaluated in terms of complementary structure indices. Finally, the dependency of the TomoSAR reconstruction and of its structural information to both the TomoSAR acquisition geometry and the temporal change of the reflectivity that may occur in the time between the TomoSAR measurements in repeat-pass or bistatic configurations is evaluated. The analysis is supported by experimental results obtained by processing airborne acquisitions performed over temperate forest sites close to the city of Traunstein in the south of Germany

Addressing Forest Change by means of Pol-InSAR Measurements at L- and P-band

By coherently combining interferometric SAR acquisitions at different polarization states, Polarimetric SAR Interferometry (Pol-InSAR) [1] allows to locate in height different scattering mechanisms present in the resolution cell. Together with the use of scattering models of the vegetation, as the well-known two-layer Random Volume over Ground (RVoG) model [2], Pol-InSAR has demonstrated its potential in forest monitoring applications. While the potential and limitations of Pol-InSAR measurements for reconstructing forest structure (parameters) are today well understood, the question of how to qualitatively and quantitatively characterize forest (structure) change using Pol-InSAR measurements is – besides first attempts [3, 4] – far from answered. This is primarily because of our incomplete understanding of how to parameterize forest change(s) and on how to resolve ambiguities arising from the superposition of structural and weather / seasonal changes. Both terms can be attributed to the lack of appropriate experimental “change” data sets as well as the absence of an established change processing methodology. In this sense, this paper constitutes a first step into the characterization of forest change by exploring and analyzing new Pol-InSAR data sets. Experimental SAR data acquired at low frequency bands, i.e. L- and P-band, capable of penetrating through the forest canopy until the underlying ground, are evaluated. In particular, data acquired by the DLR’s airborne F-SAR sensor in the frame of the TempoSAR22 campaign are available. The campaign is carried out over the temperate forest of Traunstein, in the South-East of Germany. The data set includes fully polarimetric multi-baseline data acquired at two different dates. In each date, different flights, each with different tracks (spatial / temporal baselines), were acquired. Therefore, this data set allows the study of dielectric changes throughout the daily cycle of the forest. Possible changes in the daily cycle of the forest are evaluated by exploiting the geometrical representation of Pol-InSAR data on the complex plane, the so-called coherence region [5]. According to the RVoG model, the coherence region follows a line segment that models the vertical profile of the forest canopy at pixel level. Under this assumption, a Pol-InSAR technique that is able to separate the scattering response from the underlying ground and the volume of the forest canopy [6] is applied. The obtained ground and volume coherences are the extremes that define the RVoG model line segment. A first evaluation is carried out over pixels corresponding to forest areas of data acquired at zero baseline, thus avoiding possible residual geometrical decorrelation effects. Under such conditions, a change in the ground and volume contributions translates into a change in the coherence region, and thus, into a change in the RVoG model line. The changes are as well analyzed in terms of the different observations of the master and slave covariance matrices of the interferometric pair. This provides a link between possible interferometric and polarimetric [7] changes. The analysis of such changes will be extended to non-zero spatial baselines. Further results of this study aim to help devise new strategies for the exploitation of future SAR missions, as the upcoming ESA BIOMASS

Understanding Forest Change from P-band Polarimetric and Interferometric SAR Data

Understanding the changes taking place in the forest structure is key for the correct assessment of forest biomass and productivity. By exploiting polarimetric SAR acquisitions [1], different techniques have been proposed in the past to address changes [2, 3]. These techniques, however, are limited to the detection of changes in terms of radiometric information, i.e. amount of change. In [4], a polarimetric change analysis methodology which takes a step further into the interpretation of the changes between different SAR acquisitions is introduced. This methodology provides a representation of the changes based on the type of change (type of scattering mechanisms) weighted by the amount of change (increasing or decreasing radiometric intensity). From the radar point of view, forest are complex scenarios. As a result, the polarimetric change analysis [4] over forest scenes at P-band applies on a relatively high entropy scenario. This means that only with polarimetric acquisitions, many ambiguities and uncertainties arise from the superposition of dielectric, phenological and/or structural changes. A way to provide sensitivity to the vertical structure of the forest, and thus break down (some) of these ambiguities, is to incorporate interferometry. By exploiting both polarimetric and interferometric SAR (Pol-InSAR) acquisitions, the radar return from the forest canopy can be decomposed into ground and volume scattering components [5]. This allows to increase the observation space by applying the polarimetric change analysis over the two separated radar components. In this contribution, we evaluate forest change following the described Pol-InSAR methodology over different P-band datasets. To this end, data acquired by DLR’s airborne F-SAR sensor in the framework of the TMPSAR campaign are used. This campaign covers several years. In particular, multi-baseline fully polarimetric P-band data are available for years 2021, 2022 and, very recently, also for 2023. The test site is located around the temperate forest of Traunstein, in the south-east of Germany. It can be divided into two main forest areas, known as Traunstein and Froschham, for which reference lidar data are available. The first results of applying the polarimetric change analysis over the separated ground and volume components have proven to be sensitive to forest structural changes. As the most recent works also corroborate [6, 7], the challenge still remains in the interpretation of the nature of such changes. The large wavelength (around 70 cm) of P-band SAR data allows the signal to penetrate into the forest canopy and reach the ground. This leads to a slightly lower entropy scenario when compared to other higher frequencies, as L-band, which makes P-band particularly suitable for the interpretation of forest changes. Different forest change scenarios will be targeted and analyzed in detail, comparing the complementary information between their polarimetric and interferometric signatures. Further results of this study will support the development of strategies to exploit data from the upcoming ESA BIOMASS mission. REFERENCES [1] S. Cloude, Polarisation: Applications in Remote Sensing.New York, NY, USA: Oxford Univ. Press, 2009. [2] K. Conradsen, A. A. Nielsen, J. Schou, and H. Skriver, “A test statistic in the complex wishart distribution and its application to change detection in polarimetric SAR data,” IEEE Trans. Geosci. Remote Sens., vol. 41, no. 1, pp. 4–19, Jan. 2003. [3] A. Marino, S. R. Cloude, and J. M. Lopez-Sanchez, “A new polarimetric change detector in radar imagery,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 5, pp. 2986–3000, May 2013. [4] A. Alonso-González, C. López-Martínez, K. P. Papathanassiou and I. Hajnsek, “Polarimetric SAR Time Series Change Analysis Over Agricultural Areas,” in IEEE Trans. Geosci. and Remote Sens., vol. 58, no. 10, pp. 7317-7330, Oct. 2020. [5] A. Alonso-Gonzalez and K. P. Papathanassiou, “Multibaseline Two Layer Model PolInSAR Ground and Volume Separation,” in EUSAR 2018; 12th European Conference on Synthetic Aperture Radar, pp. 1-5. VDE, June 2018. [6] S. Cloude, “A Physical Approach to POLSAR Time Series Change Analysis,” IEEE Geosci. Remote Sens. Letters, vol. 19, pp. 1-4, 2022. [7] A. Marino and M. Nannini, “Signal Models for Changes in Polarimetric SAR Data,” IEEE Trans, Geosci. and Remote Sens., vol. 60, pp. 1-18, 2022

A new family of surfaces with pg=q=2p_g=q=2 and K2=6K^2=6 whose Albanese map has degree 44

We construct a new family of minimal surfaces of general type with $p_g=q=2$ and $K^2=6$, whose Albanese map is a quadruple cover of an abelian surface with polarization of type $(1,3)$. We also show that this family provides an irreducible component of the moduli space of surfaces with $p_g=q=2$ and $K^2=6$. Finally, we prove that such a component is generically smooth of dimension 4 and that it contains the 2-dimensional family of product-quotient examples previously constructed by the first author. The main tools we use are the Fourier-Mukai transform and the Schr\"odinger representation of the finite Heisenberg group $\mathscr{H}_3$.Comment: 23 pages. To appear in the Journal of the London Mathematical Society. This is a preprint version, slightly different from the published versio