The Wishart distribution is a well-established statistical model for characterizing the density of random variables in Polarimetric SAR (PolSAR) data, particularly within homogeneous regions where Gaussian assumptions hold. However, as PolSAR applications expand into heterogeneous environments, alternative statistical models have been developed to better capture the complexity of such areas, playing an important role in tasks such as classification. In this study, we examine the effectiveness of covariance matrix estimation using the median matrix, a technique grounded in optimal transport theory and validated in prior research for its effectiveness. Building on this foundation, we propose the application of a statistical model tailored for heterogeneous regions, i.e., following theG0Pdistribution, addressing the limitations of traditional assumptions. This method is particularly suitable for high-resolution PolSAR datasets, where the homogeneity hypothesis often does not hold. The experimental results obtained using L-band PolSAR images acquired over Foulum in Denmark demonstrate the robustness of our proposed variant.

A polarimetric synthetic aperture radar (PolSAR) system, which uses multiple images acquired with different polarizations in both transmission and reception, has the potential to improve the description and interpretation of the observed scene. This is typically achieved by exploiting the polarimetric covariance or coherence matrix associated with each pixel, which is processed to meet a specific goal in Earth observation. This paper presents a design framework for selecting the structure of the polarimetric covariance matrix that accurately reflects the symmetry associated with the analyzed pixels. The proposed methodology leverages both polarimetric and temporal information from multipass PolSAR images to enhance the retrieval of information from the acquired data. To accomplish this, it is assumed that the covariance matrix (of the overall acquired data) is given as the Kronecker product of the temporal and polarimetric covariances. An alternating maximization algorithm, known as the flip-flop method, is then developed to estimate both matrices while enforcing the symmetry constraint on the polarimetric covariance. Subsequently, the symmetry structure classification is formulated as a multiple hypothesis testing problem, which is solved using model order selection techniques. The proposed approach is quantitatively assessed on simulated data, showing its advantages over its competitor, which does not exploit temporal correlations. For example, it reaches accuracies of 94.6% and 92.0% for the reflection and azimuth symmetry classes, respectively, while the competitor achieves 72.5% and 72.6% under the same simulation conditions. Moreover, the proposed method can realize a Cohen’s kappa coefficient of 0.95, which significantly exceeds that of its counterpart equal to 0.78. Finally, the effectiveness of the proposed framework is further demonstrated using measured RADARSAT-2 data, corroborating the results obtained from the simulations. Specifically, tests conducted applying the Freeman-Durden Wishart classification have proved that the new approach greatly enhances the accuracy of pixel classification. For instance, in areas dominated by surface scattering, it boosts the percentage of correctly classified pixels from 68.23%, achieved using the classic method, to 91.65%.

Next generation space-terrestrial-ocean integrated mobile networks providing global internet access that extend to the undersea are based on heterogeneous networks. In underwater applications, a key role is played by the acoustic positioning. In particular, this task can be accomplished making use of multiple passive sensors that estimate the differential signal delays employed for positioning. This paper exploits a methodology aimed at improving delay estimation by means of cross-cross-correlation, i.e., the cross-correlation between all the multi-sensor cross-correlations. The resulting equation system is formulated as a least squares (LS) minimization problem, whose solution is efficiently found resorting to the pseudo-inverse technique, ensuring a fast execution of the algorithm, without using statistical information on random signal spectra. The performance of the devised method is numerically analyzed for an extensive range of operating parameters to demonstrate the validity of the proposed approach in comparison with classic counterparts and theoretical optimum bounds.

This letter proposes a robust framework for polarimetric covariance symmetries classification in Synthetic Aperture Radar (SAR) images applying a pre-screening on the data looks before they are used to perform inferences. More specifically, the devised method improves the performance of a previous work based on the exploitation of the special structures assumed by the covariance/coherence matrix when symmetric scattering mechanisms dominate the polarimetric returns. To do this, the algorithm selects first the most homogeneous data through the cancellation of those sharing the highest Generalized Inner Product (GIP) values computed with the use of the geometric barycenters. Then, the procedure based on Model Order Selection (MOS) developed in the homogeneous case is applied on the filtered data. The conducted tests show the potentiality of the proposed method in correctly classifying the observed scene of L-band real-recorded SAR data with respect to its standard counterpart.

This letter exploits the intrinsic selectivity properties of the median to enhance the covariance symmetry classification in polarimetric synthetic aperture radar (PolSAR) images. More in detail, the median matrices are utilized to properly detect and remove outliers in the data belonging to a reference window, in turn used to estimate the covariance structure of the pixel under test. Hence, the scene is classified in terms of the structures assumed by the covariance under specific symmetric scattering mechanisms. To do this, for each pixel under test, the data in a reference window are filtered through the application of a generalized inner product (GIP)-based procedure involving the median matrix in its computation. The filtered data are then used as input to a model order selection (MOS)-based procedure for the final scene classification. Tests conducted on L-band real-recorded SAR data show the effectiveness of the devised framework.

This paper tests a SAR image coregistration method, developed to account for a joint rotation and range/azimuth shift effect in absence of zooming, on foliage penetrating (FOPEN) data. In particular, the method is referred as a constrained Least Squares (CLS) optimization method and, in its basic form, it sharply extracts all patches composing the entire image. Differently, in next developments it applies a detection stage to identify extended areas in the images where patches are then selected. Moreover, it also performs a refinement of the equations in the CLS problem through an iterative cancellation procedure. The performance of this enhanced version of the CLS are made on the challenging Carabas-II VHF-band FOPEN SAR data to demonstrate its effectiveness also in high-resolution SAR images.

In this letter, an automatic method to validate the reciprocity theorem on full-polarimetric heterogeneous synthetic aperture radar (SAR) data is derived. The study extends, to the more general heterogeneous scenario, the work of[1], where the conformity with the reciprocity is studied in the homogeneous case. At the design stage, it is assumed that the pixels in the polarimetric image share the same covariance structure but different power levels. Then, the dependence on nuisance parameters is removed resorting to the Principle of Invariance. The resulting problem is formalized as a binary hypothesis test and is solved through the generalized likelihood ratio test (GLRT). Tests are conducted both on simulated and real-recorded data to show the superiority of the proposed GLRT with respect to its homogeneous counterpart.

This letter extends the constrained least-squares (CLS) optimization method developed to coregister multitemporal synthetic aperture radar (SAR) images affected by a joint rotation effect and range/azimuth shifts enforcing the absence of zooming effects. To take advantage of the structural information extracted from the scene, the method starts with a detection stage that identifies extended targets/areas in the images. The selected tie-points allow the CLS problem to be reformulated to find its (initial) solution based on a robust subset of image blocks. Then, the mean square error (MSE) of each equation evaluated from the initial solution allows to implement an iterative cancellation procedure to further skim the CLS equation set. The effectiveness of the proposed procedure is validated on real SAR data in comparison with the standard CLS.

This letter proposes a coregistration algorithm to compensate for the possible inaccuracy of trajectory sensor during the synthetic aperture radar (SAR) image acquisition process. Such a misalignment can be modeled as a pure displacement in range and azimuth directions and a rotation effect due to different angles of sight. The approach is formalized as a constrained least squares (CLS) optimization problem enforcing a constraint of the absence of a zooming effect between the two SAR images. Moreover, the system equations can optionally be weighted according to local properties between the extracted patches within the quoted couple. Interestingly, the solution can be obtained in closed form, therefore, with a low computational cost. The results of the tests conducted on the 9.6-GHz Gotcha SAR data demonstrate the capability of the strategy to properly register the imagery.

This letter considers the design of a two-stage direction of arrival (DOA) scheme for radar systems. Precisely, at the first stage a sparse recovery approach is used to obtain both DOA and complex amplitude estimates of the incoming signal. Since the DOA is evaluated on a predefined grid of bins sampling the antenna azimuth mainbeam, at the second stage, a closed-form complex-valued parabolic interpolation is performed to refine it. By doing so, the angle accuracy is improved, but at the same time maintaining fixed the overall computational complexity. Numerical results show the enhancement provided by the proposed procedure to the initial sparse recovery method.

Entropy concept is related to uncertainty and predictability of random time series. The estimated trend of such a parameter can provide useful information and possibly predict future behavior of a number of non-stationary noisy signals. The goal of this paper consists of analyzing the Covid19 signal made by the number of registered infections in Italy during the first four months of the pandemic epidemy (March-June 2020). Finally, some considerations are drawn after matching historical dates of some Covid-19 related Acts made by the Italian Government (i.e., lockdown and unlockdowns). Based on the obtained results, we could conjecture that the provisions have inducted people to a common behavior concerning local mobility during the lockdowns and the progressive unlockdowns of the quarantine period in Italy.

Magnetic resonance (MR) images can play a very important role to evaluate patients' diagnosis. In particular, there is an increasing interest in image processing and advanced texture analysis methods able to extract features from MR images that are not easily to percept by the human eye. Among many, Haralick's features have been strongly exploited referring to texture analysis of medical images. Therefore, in this paper, we have investigated Haralick's features computed from MR T2-weighted acquisitions in order to differentiate benign to malignant salivary gland tumors. The study has involved a total of 6 patients affected by salivary gland cancer: from the followup exams performed by radiologists, 3 patients have been identified as benign tumor affected while 3 patients as malignant one. Haralick's textural features are computed from normalized gray level co-occurrence matrix (GLCM) considering four different spatial relationships. In this preliminary study all the 14 Haralick's textural features are investigated in our attempt to differentiate benign from malignant salivary gland tumors: the obtained results reveal that these textural features may be useful to point out the differences between the tumor's nature, helping the clinicians with the diagnosis routine of the disease.

This letter studies the conformity with the reciprocity theorem on the measured polarimetric synthetic aperture radar (SAR) data. The problem is formalized via a binary hypothesis test where the reciprocity assumption is tested versus its alternative (absence of reciprocity). The generalized likelihood ratio (GLR) is used as design criterion and the resulting decision rule ensures the constant false alarm rate (CFAR) property. At the analysis stage, the performance of the GLR statistic is analyzed on the simulated data as well as on two different measured data sets (collected by two systems) thus highlighting the effectiveness of the approach.

In this article, the problem of synthetic aperture radar (SAR) images coregistration is considered. In particular, a novel algorithm aimed at achieving a fine subpixel coregistration accuracy is developed. The procedure is based on the parabolic interpolation of the 2-D cross correlation computed between the two SAR images to be aligned. More precisely, from the 2-D cross correlation, a neighborhood of its peak value is extracted and the interpolation of both the 2-D paraboloid and the two alternative 1-D parabolas is computed to provide the finer misregistration estimation with subpixel accuracy. The main advantage of the proposed framework is that the overall computational burden is only due to the 2-D cross correlation estimation since the parabolic interpolation is calculated with a closed-form expression. The results obtained on real recorded unmanned aerial vehicle (UAV) SAR data highlight the effectiveness of the proposed approach as well as its capabilities to provide some benefits with respect to other available strategies.

This letter proposes a novel technique for automatic classification of the dominant scattering mechanisms associated with the pixels of polarimetric SAR images. Focusing on the heterogeneous scenario wherein the polarimetric image pixels share the same covariance but different power levels, the original data are replaced by a maximal invariant statistic in order to remove the dependence on the scaling factors. Then, the classification problem is formulated as a multiple hypothesis test which is addressed by applying the model order selection rules. The performance analysis is conducted on both simulated and measured data and points out the effectiveness of the proposed approach.

In this paper, an automatic classification approach for polarimetric covariance structure is derived and assessed. It extends the framework of Pallotta et al. “Detecting Covariance Symmetries in Polarimetric SAR Images” to the heterogeneous environment, where the pixels of the polarimetric image share the same covariance structure but different power levels. The Principle of Invariance is exploited to replace the original data with a suitable statistic whose distribution is independent of the scale factors. Then, the classification problem is formulated in terms of a multiple hypotheses test and solved by means of model order selection rules. The behavior of the newly devised classifiers is first assessed over simulated data also in comparison with the analogous counterparts for a homogeneous environment. Next, the classification performances are evaluated on real measured data corroborating the satisfactory results highlighted in the simulations.

In the last two decades, the use of synthetic aperture radar (SAR) for remote sensing purposes has significantly developed due to improvements in the quality and the availability of the images. Two powerful SAR techniques, namely, polarimetry and interferometry, have further increased the range of applications of the sensed data. Using polarimetry, geometrical properties and geophysical parameters, such as shape, roughness, texture, and moisture content, can be retrieved with considerable accuracy, while interferometric information may be used to extract vertical information with accuracy less than 1 cm. In this paper, the potential of using joint polarimetry and interferometry techniques in SAR data (PolInSAR) for the purpose of SAR image classification is investigated. To achieve this goal, we extend a covariance symmetry detection framework to the PolInSAR scenario. The proposed approach will be shown to be able to exploit the peculiar structures of the covariance matrices of PolInSAR images to discriminate structures within the image. Results using real-SAR data are presented to validate the effectiveness of the proposed approach.

This paper deals with detection of oil spills from multipolarization synthetic aperture radar images. The problem is cast in terms of a composite hypothesis test aimed at discriminating between the polarimetric covariance matrix (PCM) equality (absence of oil spills in the tested region) and the situation where the region under test exhibits a PCM with at least an ordered eigenvalue smaller than that of a reference covariance. This last setup reflects the physical condition where the backscattering associated with the oil spills leads to a signal, in some eigendirections, weaker than the one gathered from a reference area where the absence of any oil slicks is a priori known. A multifamily generalized likelihood ratio test approach is pursued to come up with an adaptive detector ensuring the constant false alarm rate property. At the analysis stage, the behavior of the new architecture is investigated in comparison with a benchmark (but nonimplementable) structure and some other suboptimum adaptive detectors available in the open literature. This study, which is conducted in the presence of both simulated and real data, confirms the practical effectiveness of the new approach.

The availability of multiple images of the same scene acquired with the same radar but with different polarizations, both in transmission and reception, has the potential to enhance the classification, detection, and/or recognition capabilities of a remote sensing system. A way to take advantage of the full-polarimetric data is to extract, for each pixel of the considered scene, the polarimetric covariance matrix, the coherence matrix, and the Muller matrix and to exploit them in order to achieve a specific objective. A framework for detecting covariance symmetries within polarimetric synthetic aperture radar (SAR) images is here proposed. The considered algorithm is based on the exploitation of special structures assumed by the polarimetric coherence matrix under symmetrical properties of the returns associated with the pixels under test. The performance analysis of the technique is evaluated on both simulated and real L-band SAR data, showing a good classification level of the different areas within the image.

This letter deals with the problem of adaptive signal detection in partially homogeneous and persymmetric Gaussian disturbance within the framework of invariance theory. First, a suitable group of transformations leaving the problem invariant is introduced and the maximal invariant statistic (MIS) is derived. Then, it is shown that the (two-step) generalized-likelihood ratio test, Rao, and Wald tests can be all expressed in terms of the MIS, thus proving that they all ensure a constant false-alarm rate.

A high-contrast inpainting scheme based on the Complex Ginzburg-Landau equation recently applied successfully to image restoration is applied to SAR interferograms to improve their quality and therefore final quality of Digital Elevation Models (DEMs). The new technique attempts to recover the phase values in low coherence regions through diffusion and inpainting. After phase unwrapping low coherence regions are masked and discarded and a Complex Ginzburg-Landau (CGL) inpainting scheme is applied to regions where phase values are missing. We demonstrate that the residues reduce and the proposed algorithm leads to a higher Signal-to-Noise Ratio (SNR) if compared with MCF algorithm. The restoration technique has been applied to ERS-1 and ERS-2 data sets acquired on July 1995. Results appear to be very promising: the proposed algorithm provides good performances especially in presence of strong noise level and low coherence areas with relatively small dimensions.