Wavelet-Based Compressed Sensing for SAR Tomography of Forested Areas

Abstract

Synthetic aperture radar (SAR) tomography is a 3-D imaging modality that is commonly tackled by spectral estimation techniques. Thus, the backscattered power along the cross-range direction can be readily obtained by computing the Fourier spectrum of a stack of multibaseline measurements. In addition, recent work has addressed the tomographic inversion under the framework of compressed sensing, thereby recovering sparse cross-range profiles from a reduced set of measurements. This paper differs from previous publications, in that it focuses on sparse expansions in the wavelet domain while working with the second-order statistics of the corresponding multibaseline measurements. In this regard, we elaborate on the conditions under which this perspective is applicable to forested areas and discuss the possibility of optimizing the acquisition geometry. Finally, we compare this approach with traditional nonparametric ones and validate it by using fully polarimetric L-band data acquired by the Experimental SAR (E-SAR) sensor of the German Aerospace Center (DLR).

Multibaseline polarimetric synthetic aperture radar tomography of forested areas using wavelet-based distribution compressive sensing

“…Here, we use the wavelet basis as a sparse basis in which the profile p has an approximately sparse representation. 15,16 However, for all possible practical observed forested terrains, it is very complicated to find a theory providing analysis on the performance of sparsity of the reflectivity profile in the wavelet basis. Thus, the FP-WDCS TomoSAR method may not be suitable in almost all cases.…”

“…[11][12][13][14] However, in the analysis of forest scenes, it is difficult to use the CS technique in the retrieval of the vertical distribution of the backscattered power, mainly because the reflectivity signal of the distributed media is rarely sparse in the object domain and the optimal sparse representations of the reflectivity signal of the distributed media must be exploited in forested areas. A good solution may be found in the work by Aguilera et al 15,16 The authors exploited suitable sparse representations of forested areas in the wavelet domain. In order to further discriminate and characterize the objects under analysis using their polarimetric responses, they extended this method to the FP case.…”

Urban Area Tomography Using a Sparse Representation Based Two-Dimensional Spectral Analysis Technique

“…Several TomoSAR methods exist: nonparametric spectral analysis methods, like Fourier beamforming and Capon [4,5], are fast and robust in focusing artifacts, whereas parametric spectral analysis methods such as multiple signal classification (MUSIC) [6], truncated singular value decomposition (TSVD) [7], and weighted subspace fitting (WSF) estimators [8] obtain better vertical resolution. The compressive sensing-based method not only provides a good compromise between the parametric and nonparametric spectral analysis methods, but can achieve superior resolution with a small number of acquisitions and unevenly spaced orbits [9][10][11][12][13][14][15][16][17][18].…”

Monitoring of Forest Structure Dynamics by Means of L-Band SAR Tomography

“…In order to reconstruct more detailed vertical distribution of scatterers, multi-baseline interferometric acquisitions have been used [10]. More recently, tomographic acquisitions (TomoSAR), that can be seen as an extension of multi-baseline interferometric acquisitions, have been used to reconstruct the 3D radar reflectivity of forests, to explore for mapping 3D forest structure, and to improve biomass estimators [11][12][13][14][15][16]. These activities were complemented by a number of ground-based [17][18][19][20] and airborne SAR experiments [21] aiming to quantify the impact of temporal decorrelation on the effect of weather and seasonal conditions on a temporal series of TomoSAR data rather than to analyse forest structure dynamics [22][23][24].…”