We report some results of an experiment to detect early occurrence of Xylella fastidiosa (Xf) in olive trees in the Apulia Region (southern Italy), performed in the framework of a project to assess the feasibility of a service addressed to agricultural authorities. An acquisition campaign was performed in September 2022, over a Xf-affected test area, using UAVborne hyperspectral and thermal sensors. Ground data were also collected through qPCR. Results of classification through SVM provide overall accuracy values ranging from 0.76 to 0.84.

Xylella fastidiosa (Xf) is a plant pathogen affecting olives trees, which has been identified as the bacterium responsible of a devastating landscape transformation in Apulia Region (Italy) from 2013. Actually, it has been found to affect 679 plant species worldwide, such as almond, vine and citrus.In this paper, experimental results concerning the automatic detection of trees infected by Xf from very high resolution hyperspectral and thermal images are shown. First of all, a set of vegetation indices and plant physiological traits related to rapid changes in photosynthetic pigments and leaf processes were computed from hyperspectral data. This information together with thermal data has been used as input to a RUSBoost classifier. Trees in training and test data set were labelled by performing quantitative real time-Polymerase-Chain-Reaction (qPCR) assays.Encouraging experimental results have been obtained, with Overall Accuracies greater than 90%, also when a reduced set of features is used as input for RUSBoost.

This research aims to exploit the potentialities of multi-mission SAR data at X-, C- and L-band for the monitoring of snowpack and alpine soils. The snow parameters as snow water equivalent, snow liquid water content and snow metamorphism have been monitored and different methods are proposed for their retrieval. In order to gather consistent datasets, experimental activities have been conducted in two selected sites in Northern Italy, which are covered by alpine snow during winter and spring periods and are in some cases characterized by the presence of permafrost. Microwave responses of snow and soil have been then simulated by using electromagnetic (i.e., AIEM, Oh, SFT and DMRT-QCA), and physical models (SNOWPACK). Finally, machine learning approaches, as Artificial Neural Networks and Random Forest, were implemented for retrieving snow parameters; whereas interferometric techniques were used in case of snow and soil displacement as rock glaciers. Preliminary and consistent results have been obtained in terms of estimate of snow parameters and soil displacement. This multi-frequency/multi-mission approach enhances the ability of SAR sensors to monitor and analyze snow dynamics, contributing to improved decision-making in various domains.

Multi-temporal remotely sensed data are a precious source of information for high spatial and temporal resolution flood mapping. We present a methodology for flood mapping through processing of long time series of Sentinel-l SAR data, as well as ancillary information. A Bayesian framework is adopted to derive probabilistic maps of the presence of flood waters, through modeling of backscatter time series, based on the as-sumption that floods represent impulsive temporal anomalies. We illustrate some results on a time series of Sentinel-l data acquired from 2015 to 2021 over a test area on the Basento river watershed, Basilicata Region, in Southern Italy, recurrently subject to floods.

We observe relatively high InSAR mean coherence levels over badlands, i.e. clayey bare soil areas, on a test site in the Basilicata region, in southern Italy. Time series of InSAR coherences on cascaded short-baseline image pairs, obtained from stacks of Sentinel-1 SAR images, exhibit oscillating behaviour, with significant correlation with cumulated rainfall levels on bad-land areas, while on other areas with crops or spontaneous vegetation the correlation is lower, and a seasonal trend is instead statistically significant. These observations seem to point to the possibility of investigating erosion phenomena over badland areas through InSAR time series, which involves a significant step forward, in terms of spatial and temporal resolution, with respect to traditional measurements which require repeated topographic surveys at long intervals, or sparse in-field point measurements.

Multitemporal interferometric synthetic aperture radar (MTI) displacement time series are usually characterized by the model-dependent temporal phase coherence as a quality measure. Additional tests have to be performed to recognize other “interesting” but nonmodeled trends, and several automated approaches to this task have been proposed to date. We introduce here the fuzzy entropy ($F_{E}$), a measure introduced in medical data analysis, as a viable parameter to characterize MTI time series. Being a measure of disorder in a time series,$F_{E}$exhibits homogeneously low values for a large class of displacement models, such as seasonal, parabolic, or piecewise linear signals, while increasing for more chaotic trends, dominated by noise. It appears therefore suited as a discriminative parameter to isolate meaningful MTI time series within large data sets, without specifying a predefined model. The calculation of$F_{E}$has low computational cost and can thus be easily performed as a prescreening filter. In this letter, results over simulated data and some examples on a real data set are shown with interesting performances which hint to possible large-scale implementations.

This paper investigates the sensitivity of Sentinel-1 (S-1) interferometric coherence to crop structure and near surface soil moisture (SSM) content. The study analyzes a data set collected in 2017 over the Apulian Tavoliere agricultural site (Southern Italy). The data set includes: i) in situ data over more than 600 agricultural fields monitored during the 2017 winter and spring growing seasons; ii) time-series of S-1 IW VV & VH backscatter & interferometric coherence; iii) time series of S-1 SSM maps. The temporal behavior of S-1 coherence and VH backscatter has been assessed over the monitored agricultural fields. Initial results indicate a stronger sensitivity of S-1 coherence than VH backscatter to crop geometric structure. In addition, an analysis at site scale, conducted before and after an important rain event, indicates a change of SSM from 0.18 to 0.30 m3/m3along with a change of S-1 coherence from 0.61 to 0.53.

Indonesia is periodically affected by severe volcanic eruptions and earthquakes, which are geologically coupled to the convergence of the Australian tectonic plate beneath the Sunda Plate. Multi-temporal SAR interferometry (MTI) can be used to support studying and modelling of terrain movements. This work is aimed at performing an analysis of ground displacements over Indonesian sites through MTI techniques. Two test sites in Sumatra and Java have been selected according to the availability of archived SAR data, GNSS networks, and geological data. Both COSMO-SkyMed (CSK) and Senitnel-1 data-sets have been processed through MTI algorithms. The derived displacement maps have been interpreted according to the available geological and geophysical information.

The Rheticus® cloud-based platform provides continuous monitoring services of the Earth's surface. One of the services provided by Rheticus® is the Displacement Geoinformation Service, which offers monthly monitoring of millimetric displacements of the ground surface, landslide areas, the stability of infrastructures, and subsidence due to groundwater withdrawal/entry or from the excavation of mines and tunnels. To provide this information, the Rheticus® platform processes a large amount of Geospatial Big Data. In particular, Rheticus® is capable to process Synthetic Aperture Radar images acquired by the X-band COSMO-SkyMed constellation, as well as satellite Open Data provided by Copernicus Sentinels, and it is capable to integrate local INSPIRE data sources. In this paper, we summarize the main features of the Rheticus® services and we provide examples of the detection and monitoring of geohazard and infrastructure instabilities through Multitemporal InSAR techniques. Furthermore, we outline the porting activity and the efficient implementation of the most time-consuming algorithmic kernels in the GPGPU environment.

Marina di Lesina is a peculiar geological site, affected by sinkhole phenomena, causing instabilities and failures of infrastructures. This tourist village, lying not far from Punta delle Pietre Nere, the only outcrop of magmatic rock in the Mediterranean basin, sits on a diapir made of Triassic gypsum, mantled by Quaternary sandy deposits. The cutting of the artificial Acquarotta canal in 1930, connecting the nearby Lesina lagoon to the Mediterranean Sea, exposed this grey micro and meso-crystalline gypsum with intercalations of black limestones and marls. This event is a likely cause for the formation of dissolutional conduits and cavities, found in the area, leading to the formation of the sinkholes which have been plaguing the site in the last years [1]. This peculiar geological setting, coupled with its relatively high value as a local touristic resort, led to its selection as a test site for precise InSAR displacement monitoring techniques. The monitoring, started with legacy ERS and ENVISAT sensors, is continuing through analysis of higher-resolution data.

Thanks to the technological maturity as well as to the wide availability of SAR data, Multi-temporal SAR Interferometry (MTInSAR) can be used to support systems devoted to environmental monitoring and risk management. In particular, high resolution X-band MTInSAR applications are also suitable for monitoring single man-made structures (buildings, bridges, railways and highways). The paper presents examples concerning the application of MTInSAR techniques and COSMO-SkyMed constellation for instability monitoring of infrastructures and, in particular, harbor docks and railways.

We apply a Bayesian Network (BN) paradigm to the problem of monitoring flood events through synthetic aperture radar (SAR) and interferometric SAR (InSAR) data. BNs are well-founded statistical tools which help formalizing the information coming from heterogeneous sources, such as remotely sensed images, LiDAR data, and topography. The approach is tested on the fluvial floodplains of the Basilicata region (southern Italy), which have been subject to recurrent flooding events in the last years. Results show maps efficiently representing the different scattering/coherence classes with high accuracy, and also allowing separating the multitemporal dimension of the data, where available. The BN approach proves thus helpful to gain insight into the complex phenomena related to floods, possibly also with respect to comparisons with modeling data.

The multichromatic analysis (MCA) can be applied to interferometric pairs of synthetic aperture radar (SAR) images processed at range subbands and consists of exploring the phase trend of each pixel as a function of the different central carrier frequencies. The phase of stable scatterers linearly evolves with the subband central frequency, with a slope proportional to the absolute electromagnetic path difference that can be estimated and used for both phase unwrapping and height computation. MCA has been theoretically evaluated and tested on airborne wideband SAR data, appearing optimally suited for the new generation of satellite sensors, which operate with larger bandwidths than previously available instruments, generally limited to few tens of megahertzs. In this letter, we illustrate MCA application to satellite SAR data acquired in spotlight mode over the Uluru monolith in Australia. The topographic measurements derived through MCA on the monolith are compared with those provided by a high-resolution digital elevation model from optical stereo imagery. The theoretical parametric model describing the MCA performances according to the processing parameters is also validated.

The Multi-Chromatic Analysis (MCA) uses interferometric pairs of SAR images processed at range sub-bands and explores the phase trend of each pixel as a function of the different central carrier frequencies. The MCA technique introduces the concept of targets exhibiting stable radar returns across the frequency domain (PSfd). In this work we compare this stability along frequencies with the temporal stability which is at the base of persistent scatterers interferometry (PSI) techniques. Different populations of PSfdand “temporal” PS were derived by using COSMO-SkyMed SAR data. An ad hoc processing scheme was developed to derive PSI products by processing the same range sub-bandwidth used by the MCA in order to guarantee the same scattering conditions. The populations of PSfdand “temporal” PS were compared and preliminary considerations provided concerning the scattering properties of the targets selected by the two criteria.

We apply high-resolution, X-band, stripmap COSMO/SkyMed data to the monitoring of a flood event in Southern Basilicata region (Italy), where a multi-temporal dataset is available, allowing interferometric processing. We show how the use of the interferometric phase information can actually help to detect precisely the areas affected by the flood, using e.g. RGB composites of various information layers derived from the data. We also present results of unsupervised clustering of the multi-temporal data, which allow to shed some light on the physical interpretation of some of the identified clusters.

The multichromatic analysis (MCA) uses interferometric pairs of SAR images processed at range subbands and explores the phase trend of each pixel as a function of the different central carrier frequencies to infer absolute optical path difference. This approach allows retrieving unambiguous height information on selected pixels, potentially solving the problem of spatial phase unwrapping, which is instead critical in the standard monochromatic processing. The method, based on concepts originally introduced by Madsen and Zebker, has been developed in previous work both theoretically and through simulations. This paper presents the first MCA experimental validation of the procedure, through application to a wideband SAR single-pass interferometric data set acquired by the AES-1 airborne sensor. An evaluation of the impact of the MCA processing parameters on the height estimation performances is obtained through a parametric analysis. The results confirm the indications derived by the theoretical analysis, demonstrating the feasibility of the MCA absolute phase measurement, provided that a sufficient bandwidth is available.

The Multi-Chromatic Analysis can be applied to interferometric pairs of SAR images processed at range sub-bands, and consists of exploring the phase trend of each pixel as a function of the different central carrier frequencies. The phase of stable scatterers evolves linearly with the sub-band central wavelength, with a slope proportional to the absolute e.m. path difference. The technique appears optimally suited for the new generation of satellite sensors, which operate with larger bandwidths than previously available instruments, generally limited to few tens of MHz. A first experiment on satellite data was carried out by processing a spotlight interferometric pair of images acquired by TerraSAR-X on the well-known Uluru monolith in Australia. In the present work, we illustrate MCA processing on SAR data acquired over the same site by the COSMO-SkyMed constellation. The topographic profile of the monolith is successfully reconstructed. Furthermore, the results are also compared with those previously derived by processing TerraSAR-X data.

The present study is aimed at investigating the potentialities of the COSMO/SkyMed (CSK) constellation for ground elevation measurement with particular attention devoted to the impact of the improved spatial resolution wrt the previous SAR sensors. Assuming no movement and successful orbital error removal, the main problem in height computation through InSAR techniques derives from the interferometric phase artifacts related to the interaction between microwave and the lower layers of the atmosphere (APS, Atmospheric Phase Screen). Different strategies can be adopted to filter out this signal, ranging from the exploitation of the well-known spatial and temporal statistics of the APS to the estimation of independent APS measurements through Numerical Weather Prediction (NWP) models. Their feasibility and the achievable accuracies are discussed here.

COSMO/SKYMED is currently the unique constellation of synthetic aperture radar (SAR) sensors operative, which is also for civilian use. On April 6, 2009, an Mw 6.3 earthquake struck the city of l'Aquila in Central Italy. The constellation acquired data stacks over the hit area at an unprecedented temporal rate. In this letter, the results obtained by processing several data set via two independent multitemporal differential interferometric SAR techniques are presented to demonstrate the capability of this constellation in postseismic deformations monitoring.

Stochastic models are often used to describe the spatial structure of atmospheric phase delays in differential interferometric synthetic aperture radar (DInSAR) data. Synthetic aperture radar interferograms often exhibit anisotropic atmospheric signals. In view of this, the use of anisotropic models for atmospheric phase estimation is increasingly advocated. However, anisotropic models lead to increased computational complexity in estimating the correlation function parameters with respect to the isotropic case. Moreover, the performance is degraded when dealing with DInSAR techniques involving only a few sparse points usable for computations, as in the case of persistent scatterer interferometry applications, particularly when this estimation has to be done in an automated way on many interferograms. In the present work, we propose some observations about the actual advantage given by anisotropic modeling of atmospheric phase in the case of sparse-grid point-target DInSAR applications. Through analysis of simulated data, we observe that an improvement in the performances of kriging reconstruction approaches can be obtained only when sufficient sampling densities are available. In critical sampling conditions, automated methods with reasonable computational cost may improve their performance if external information on the atmospheric phase screen field is available.

Image alignment is a crucial step in synthetic aperture radar (SAR) interferometry. Interferogram formation requires images to be coregistered with an accuracy of better than a few tenths of a resolution cell to avoid significant loss of phase coherence. In conventional interferometric precise coregistration methods for full-resolution SAR data, a 2-D polynomial of low degree is usually chosen as warp function, and the polynomial parameters are estimated through least squares fit from the shifts measured on image windows. In case of rough topography or long baselines, the polynomial approximation may become inaccurate, leading to local misregistrations. These effects increase with spatial resolution of the sensor. An improved elevation-assisted image-coregistration procedure can be adopted to provide better prediction of the offset vectors. This approach computes pixel by pixel the correspondence between master and slave acquisitions by using the orbital data and a reference digital elevation model (DEM). This paper aims to assess the performance of this procedure w.r.t. the “standard” one based on polynomial approximation. Analytical relationships and simulations are used to evaluate the improvement of the DEM-assisted procedure w.r.t. the polynomial approximation as well as the impact of the finite vertical accuracy of the DEM on the final coregistration precision for different resolutions and baselines. The two approaches are then evaluated experimentally by processing high-resolution SAR data provided by the COnstellation of small Satellites for the Mediterranean basin Observation (COSMO/SkyMed) and TerraSAR-X missions, acquired over mountainous areas in Italy and Tanzania, respectively. Residual-range pixel offsets and interferometric coherence are used as quality figure.

On April 6th2009 a Mw=6.3 earthquake struck the area around the city of L'Aquila in Italy. SAR systems have been proven to be valuable sensors for analyzing the effect of earthquakes and monitoring post-seismic displacements. Due to the low deformation rate, the study of post-seismic events requires the use of a multi-temporal InSAR approach. COSMO/SKYMED is a constellation of SAR sensors of 4 X-band sensors operative also for the civilian use. Thanks to the availability of a stack of ascending acquisitions, ad hoc programmed by ASI on the area stricken by the earthquake, it was possible to provide post-seismic deformation maps by using two different multi-temporal interferometric approaches: the SPINUA and SBAS techniques. The work is carried out in the framework of the MORFEO project dedicated to the monitoring of the landslides risk by means of Earth Observation data. The displacement maps related to the post-seismic activity are presented and commented. The results clearly show the potentiality of the COSMO/SKYMED constellation use for emergency monitoring.

The Multi-Chromatic Analysis uses interferometric pairs of SAR images processed at range sub-bands and explores the phase trend of each pixel as a function of the different central carrier frequencies to perform absolute topographic measurements. The previous work on the subject has started demonstrating the practical feasibility of the technique by using a set of SAR data collected by the airborne AES-1 radar-interferometer and by focusing the sensor raw data. The present work verifies the reliability of MCA procedures starting from SLC images, tests the robustness of MCA methods with respect to the total processed bandwidth and, provides first indications on the use of TerraSAR-X satellite data.

This work is focused on the phase validation of interferograms obtained by combining COSMO-SkyMed SAR images acquired by a single satellite (temporal baseline coincident with the orbital repeat cycle) or even by two satellites of the SAR constellation in equi-phased configuration on the orbital plane (temporal baseline: 8 days), thus minimizing the temporal decorrelation. Both qualitative and quantitative analyses have been therefore carried out for HI (HIMAGE: stripmap, single polarization) and S2 (enhanced spotlight) imaging modes, in order to proof whether or not COSMO-SkyMed constellation is well suited for SAR interferometry.

In recent years, attention has been devoted to the possibility of retrieving accurate phase information from stable targets in long SAR data series through Permanent Scatterers Interferometry (PSI), SBAS approach or equivalent methods. Recently, alternative methods for detecting stable targets on single images have been investigated. In particular, the availability of new SAR sensors provided with innovative features, including a wider transmitted bandwidth, allows to explore backscatter stability in the new dimension given by spectral diversity. The Multi-Chromatic Phase (MCP) approach, introduced in [2], uses images processed at range sub-bands and explores the phase trend of each pixel as a function of the different central carrier frequencies. In this paper we present the results of the application of this technique to point target detection. We compare the results with an alternative method proposed in [5] which identifies scatterers with stable spectral behavior.

The detectability of the deformation pattern produced by the June 15, 1995 Aigion earthquake with DInSAR techniques is ensured by its magnitude (Mw=6.3), shallow depth and dip-slip mechanism. In this paper, stacking procedures are applied to a series of ERS interferograms in order to filter out from the differential phase field the atmospheric signal, and an a posteriori test is used to check the statistical properties of the atmospheric signal both in time and space. Based on the DlnSAR-derived deformation pattern, a new fault model is proposed that takes into account the crustal layering of the western part of the Gulf of Corinth.

This paper proposes a unified framework for predicting optimized pairing strategies for interferometric processing of multipass synthetic aperture radar data. The approach consists in a minimum spanning tree (MST) structure based on a distance function encoding an a priori model for the interferometric quality of each image pair. Using a distance function modeled after the interferometric coherence allows reproducing many "small baseline" strategies presented in the recent literature. A novel application of the method to the processing steps of image coregistration and equalization is illustrated, using a test European Remote Sensing Satellite dataset. Widespread methods used for these two operations rely on the computation of the amplitude cross correlation over a large number of corresponding tie patches distributed over the scene. Geometric shift and radiometric equalization parameters are estimated over the patches and used, respectively, within a polynomial warp model and a radiometric correction scheme. The number of reliable patches available behaves similarly to the interferometric synthetic aperture radar (InSAR) coherence with respect to the baselines, and can be assimilated to a quality figure for the derivation of the MST. Results show an improvement in the quality of the stepwise (SW)-processed image stack with respect to the classical single-master procedure, confirming that the SW approach is able to provide better conditions for the estimation of correlation-related InSAR parameters

We illustrate, through a sample application to a difficult landslide test site, the use of a novel method to detect potentially stable objects in Persistent Scatterers SAR Interferometry (PSI). Conventional PSI processing involves selecting first-guess potential stable objects, called PS Candidates (PSC), through thresholding of the amplitude dispersion index. This method can lead, in applications to scenes characterized by scarce urbanization, to very low PSC numbers, insufficient for a successful subsequent phase analysis if their spatial distribution is very sparse. Our classification-based approach relies on the proven fact that urban areas are more likely to contain PS pixels than any other land-cover class. Therefore, using pixels belonging to the urban land-cover class as PSC is a convenient way of increasing the number of initial fiducial points while keeping false alarm probabilities to reasonable levels. Results show that PSC belonging to the urban class, selected through simple external classification algorithms, lead to more consistent results for the final PS, both in terms of spatial density, and of reliability of displacement series.

We present an assessment of stepwise co-registration procedures applied to multitemporal SAR datasets. Images are connected in pairs through a minimum spanning tree structure, obtained by adopting a distance measure which is a function of the expected co-registration quality. Experiments have been performed on a test dataset by a) directly estimating the (a posteriori) co-registration quality over all possible image combinations, b) using an a priori model inspired by similar models for the multitemporal InSAR coherence, with parameters obtained experimentally, c) using the same a priori model with first-guess parameters. Performances were evaluated by analyzing the amplitude inverse coefficient of variation distribution over the co-registered image stacks obtained by the three procedures above. Results show that, although the best coupling strategy depends on the particular dataset and is thus difficult to model via general rules, a nonnegligible improvement in the performance of persistent scatterers interferometry techniques can be obtained by adopting stepwise approaches based on a priori models for the expected co-registration quality, rather than using a single acquisition as master

In SAR interferometry a new approach to height retrieval has been defined, with the aim to obtain the elevation of selected targets in the scene without performing phase unwrapping procedures in the space domain. Following our preliminary simulations, in the paper the results of a first experimentation of this approach with actual SAR data will be introduced

The analysis of multi-temporal SAR data-sets encountered large interest in the remote sensing community during the past few years.The main effort goes toward the extraction of ground displacements signals by means of differential interferometric techniques.In this opera- tional framework an important processing step concerns the estimation and subtraction of signals due to atmospheric artifacts and processing errors.In the present work we apply the technique of Blind Source Separation (BSS) by using the algorithm of Independent Component Analysis (ICA) to Permanent Scatterer processing in order to perform the separation of different signal components.Preliminary investigations are carried out both on simulated and real ERS-1/2 data and results are reported and commented. I. INTRODUCTION The permanent scatterers (PS) technique (1) allows the analysis of the phase information over single objects and thus typically on man-made structures, characterized by a high temporal phase stability. Where such object are present, even when surrounded by low-coherence condi- tions, a non-conventional spatio-temporal phase analysis can be performed, together with an accurate atmospheric phase screen estimation and removal. This new technique, although very promising as an operational tool for the analysis of long series of SAR images, represents still a challenge in termsof computational burden and exhibits modelling aspects not yet fully understood. The main problemsencountered when dealing with data on moun- tainous, un-urbanised areas involve the steep topography causing considerable DEM errors (∆h(x, y)), increased atmospheric effects compared to flat areas, and increased geometric distortions; also, the scarcity of man-made structures lowers considerably the number of detectable stable points, further complicating the processing (5). Many as pectsof the complicationsintroduced in the

Quantitative analysis of multi-temporal SAR datasets requires accurate radiometric calibration. This can usually be achieved by considering a number of multiplicative factors, to be applied to statistically-homogeneous areas on each image to be calibrated. We propose an automated procedure to easily obtain a relative radiometric calibration of a stack of an arbitrary number of ERS SAR images, all coregistered to a unique master. The procedure relies upon the theoretical invariance of both system and scene parameters for targets whose amplitude values are statistically correlated with each other. In practice, with the above-mentioned assumptions, the only varying quantity to take into account is the temporal variation of the calibration factor. We show, based on experiments on two multi-temporal datasets, that the ERS-1 calibration constant exhibits practically no variations except for the expected statistical fluctuations of about /spl plusmn/1 dB. This observation is consistent with the reports on the operations of the ERS-2 satellite, published by ESA. The proposed procedure then consists in applying the full absolute calibration procedure only to the master image, and then relatively correct all other images in the stack by the method described.

The first basic step in the permanent scatterers analysis technique is the location of the stable reflectors. For this purpose, an inter-image amplitude analysis, on a pixel-by-pixel basis, is performed, and the scatterers showing stable amplitude response are named Permanent Scatterer Candidates (PSC). The effects of the interpolation of the SLC (Single Look Complex) images are considered, with particular attention to the oversampling factor and to the interpolation kernels. Finally, experimental results are shown to confirm the PSC theory and the interpolation analysis.

Scaling information is an important tool for the description of natural processes. Many applications of SAR (differential) interferometry lead to a set of sparse phase measurements, e.g. the monitoring of permanent scatterers. In this case, the atmospheric phase screen component of a given SAR image can be estimated over the PS sparse grid. Usually such data have to be unwrapped and then interpolated on a regular grid. We investigate the utility of the scaling information, valid for atmospheric phase screen data, in the process of unwrapping a set of sparse measurements. We show how the power-law behaviour of the data variogram can be used as an a priori constraint for optimization through techniques such as simulated annealing. The results are interpreted in view of operational applications to real data.