Speaker
Description
Abstract
The mapping of the global forest structure by means of synthetic aperture radar (SAR) tomography (TomoSAR) [1] – [4] is an important motivated issue for the upcoming Tandem-L and BIOMASS space missions. In recent works [5], it has been demonstrated that the forest structure can be characterized from the vegetation layers that compose it, reflected as local maxima in the tomographic profiles. For each pixel of the already focused TomoSAR data, the horizontal and vertical structure measurements are recovered from the peaks of the corresponding reflectivity profiles. The presence or absence of multiple maxima in certain zones, within the illuminated forested scene, has a direct influence (meaning) in the retrieval of the forest structure measurements [5], by instance, it could represent a forest with an undisturbed growth or a forest after a fire event. Such characterization of the forest structure entails several challenges on the retrieval of the needed tomographic slices, specifically: (i) the number of baselines is constrained to the revisit time that avoids temporal decorrelation issues; (ii) enhanced resolution is expected, since the forest structure is characterized from the multiple maxima present in the vertical profiles; (iii) suppression of artifacts and ambiguity levels reduction is desired to avoid false detections.
The TomoSAR problem at hand is conventionally treated as an ill-conditioned non-linear inverse problem [2] – [4], and is commonly tackled within the direction-of-arrival (DOA) estimation framework. The DOA-inspired non-parametric techniques, as the celebrated matched spatial filter (MSF) and minimum variance distortionless response (MVDR) beamformers [2] – [4], are well suited to cope with distributed targets, since these techniques recover an estimate of the continuous power spectrum pattern (PSP); nonetheless, the achievable resolution highly depends on the span of the tomographic aperture. Alternatively, super-resolved parametric approaches, as multiple signal classification (MUSIC) [3], have the main drawback related to the white noise model assumption that guaranties the separation of the signal and noise sub-spaces. On the other hand, taking advantage of the sparse representations of the cross-range profiles in the wavelet domain, super-resolved compressed sensing (CS) based approaches [6], [7], are also employed to solve the TomoSAR inverse problem. However, CS-based techniques often imply a considerable computational burden, due to their iterative nature and due to the non-availability of adapted efficient convex optimization algorithms.
To overcome such drawbacks and as an alternative to the aforementioned commonly performed TomoSAR-adapted focusing techniques, we suggest to apply instead statistical regularization approaches, in the context of the statistical decision-making theory. In the statistical regularization methodology, the inference is made in terms of probabilistic statements, where the Bayes minimum risk (BMR) estimation strategy plays a key role [8], [9]. Therefore, we first present the Bayes strategy, which makes use of probabilistic models to quantify the uncertainty of the unknowns. Later on, the addressed BMR methodology is extended to the maximum-likelihood (ML) approach, by imposing no constrain on linearity and by assuming no a priori knowledge about the statistical distribution of the desired PSP, to be retrieved. To guarantee well-conditioned solutions (in the Hadamard sense) of the TomoSAR nonlinear inverse problem, the derived ML-based technique is implemented in a closed fixed-point iterative manner, yielding what we define as the MARIA (ML-inspired Adaptive Robust Iterative Approach) technique [9].
The MARIA technique presents particular advantages in comparison to the previously discussed TomoSAR-adapted focusing methods: (i) it provides resolution-enhanced tomographic profiles with a reduced (limited) number of baselines, performing suppression of artifacts and reduction of the ambiguity levels; (ii) allows the separation of multiple scattering contributions within each resolution cell, retrieving an accurate location of the corresponding arbitrarily close phase-centers; (iii) as a non-parametric technique, it does not require any a priory knowledge about the number of backscattering sources that constitute the illuminated area; (iv) it incurs less computation time in comparison to the other CS-based competing methods.
The latter mentioned properties of MARIA facilitate the characterization of the forest structure, to be recovered from the 3D distribution of peaks of the reconstructed reflectivity profiles [5].
References
[1] A. Reigber and A. Moreira, “First demonstration of airborne SAR tomography using multibaseline L-band data”, IEEE Trans. Geosc. Remote Sens., vol. 38, no. 5, pp. 2142–2152, Sep. 2000.
[2] F. Gini, F. Lombardini and M. Montanari, “Layover solution in multibaseline SAR interferometry”, IEEE Trans. Aerosp. Electron. Syst., vol. 38, no.4, pp. 1344-1356, Oct. 2002.
[3] M. Nannini, R. Scheiber, and A. Moreira, “Estimation of the minimum number of tracks for SAR tomography”, IEEE Trans. Geosc. Remote Sens., vol. 47, no. 2, pp. 531-543, Jan. 2009.
[4] M. Nannini, R. Scheiber, R. Horn, and A. Moreira, “First 3-D reconstructions of targets hidden beneath foliage by means of polarimetric SAR tomography”, IEEE Geoscience and Remote Sensing Letters, vol. 9, no.1, pp. 60-64, Jan. 2012.
[5] V. Cazcarra-Bes, M. Tello-Alonso, R. Fischer, M. Heym and K. Papathanassiou, “Monitoring of Forest Structure Dynamics by Means of L-Band SAR Tomography. Remote Sensing, vol. 9, no.12, pp. 1229–1250, Nov. 2017.
[6] E. Aguilera, M. Nannini and A. Reigber, “A Data-Adaptive Compressed Sensing Approach to Polarimetric SAR Tomography of Forested Areas”, IEEE Geoscience and Remote Sensing Letters, vol. 10, no.3, pp. 543–547, Sept. 2012.
[7] E. Aguilera, M. Nannini and A. Reigber, “Wavelet-Based Compressed Sensing for SAR Tomography of Forested Areas”, IEEE Trans. Geosc. Remote Sens., vol. 51, no.12, pp. 5283–5295, Dec. 2013.
[8] Y. V. Shkvarko, “Unifying regularization and Bayesian estimation methods for enhanced imaging with remotely sensed data––Part I and Part II”, IEEE Trans. Geosc. Remote Sens., vol. 42, no. 5, pp. 923–940, May 2004.
[9] G. D. Martín del Campo, M. Nannini, and A. Reigber, “Towards Feature Enhanced SAR Tomography: A Maximum-Likelihood Inspired Approach”, IEEE Geoscience and Remote Sensing Letters, pp. 1–5, August 2018.
Summary
The mapping of the global forest structure by means of synthetic aperture radar (SAR) tomography (TomoSAR) is an important motivated issue for the upcoming Tandem-L and BIOMASS space missions. In recent works, it has been demonstrated that the forest structure can be characterized from the vegetation layers that compose it, reflected as local maxima in the tomographic profiles. For each pixel of the already focused TomoSAR data, the horizontal and vertical structure measurements are recovered from the peaks of the corresponding reflectivity profiles. The presence or absence of multiple maxima in certain zones, within the illuminated forested scene, has a direct influence (meaning) in the retrieval of the forest structure measurements, by instance, it could represent a forest with an undisturbed growth or a forest after a fire event. Such characterization of the forest structure entails several challenges on the retrieval of the needed tomographic slices, specifically: (i) the number of baselines is constrained to the revisit time that avoids temporal decorrelation issues; (ii) enhanced resolution is expected, since the forest structure is characterized from the multiple maxima present in the vertical profiles; (iii) suppression of artifacts and ambiguity levels reduction is desired to avoid false detections.
The TomoSAR problem at hand is conventionally treated as an ill-conditioned non-linear inverse problem, and is commonly tackled within the direction-of-arrival (DOA) estimation framework. The DOA-inspired non-parametric techniques, as the celebrated matched spatial filter (MSF) and minimum variance distortionless response (MVDR) beamformers, are well suited to cope with distributed targets, since these techniques recover an estimate of the continuous power spectrum pattern (PSP); nonetheless, the achievable resolution highly depends on the span of the tomographic aperture. Alternatively, super-resolved parametric approaches, as multiple signal classification (MUSIC), have the main drawback related to the white noise model assumption that guaranties the separation of the signal and noise sub-spaces. On the other hand, taking advantage of the sparse representations of the cross-range profiles in the wavelet domain, super-resolved compressed sensing (CS) based approaches, are also employed to solve the TomoSAR inverse problem. However, CS-based techniques often imply a considerable computational burden, due to their iterative nature and due to the non-availability of adapted efficient convex optimization algorithms.
To overcome such drawbacks and as an alternative to the aforementioned commonly performed TomoSAR-adapted focusing techniques, we suggest to apply instead statistical regularization approaches, in the context of the statistical decision-making theory. In the statistical regularization methodology, the inference is made in terms of probabilistic statements, where the Bayes minimum risk (BMR) estimation strategy plays a key role. Therefore, we first present the Bayes strategy, which makes use of probabilistic models to quantify the uncertainty of the unknowns. Later on, the addressed BMR methodology is extended to the maximum-likelihood (ML) approach, by imposing no constrain on linearity and by assuming no a priori knowledge about the statistical distribution of the desired PSP, to be retrieved. To guarantee well-conditioned solutions (in the Hadamard sense) of the TomoSAR nonlinear inverse problem, the derived ML-based technique is implemented in a closed fixed-point iterative manner, yielding what we define as the MARIA (ML-inspired Adaptive Robust Iterative Approach) technique.
The MARIA technique presents particular advantages in comparison to the previously discussed TomoSAR-adapted focusing methods: (i) it provides resolution-enhanced tomographic profiles with a reduced (limited) number of baselines, performing suppression of artifacts and reduction of the ambiguity levels; (ii) allows the separation of multiple scattering contributions within each resolution cell, retrieving an accurate location of the corresponding arbitrarily close phase-centers; (iii) as a non-parametric technique, it does not require any a priory knowledge about the number of backscattering sources that constitute the illuminated area; (iv) it incurs less computation time in comparison to the other CS-based competing methods.
The latter mentioned properties of MARIA facilitate the characterization of the forest structure, to be recovered from the 3D distribution of peaks of the reconstructed reflectivity profiles.
