PHASE CALIBRATION OF MULTIBASELINE SAR DATA BASED ON A MINIMUM ENTROPY CRITERION M. Pardini, K. Papathanassiou German Aerospace Center (DLR) Microwave and Radar Institute (HR) Oberpfaffenhofen (Germany) V. Bianco, A. Iodice Universit` a degli Studi di Napoli “Federico II” Naples (Italy) ABSTRACT Prior to any processing of multibaseline (MB) synthetic aperture radar (SAR) data stacks, a MB phase calibration is necessary to compensate for phase contributions due to platform motions and/or atmospheric propagation delays. Classical calibration methods rely on the detection of point-like scatterers. However, especially in nat- ural scenarios, their final calibration performance could be impaired by the nature of the scattering and by the typical low number of base- lines. In this paper, we propose a calibration method based on the minimization of the entropy of the vertical profile of the backscat- tered power. This allows to potentially exploit the MB SAR signal independently of the nature of the scattering. The proposed method has been tested by processing simulated and real airborne datasets of a forest stand. Index Terms— Synthetic aperture radar, tomography, calibra- tion, entropy minimization, adaptive beamforming 1. INTRODUCTION It is well demonstrated that the processing of multibaseline (MB) SAR data allows an improved imaging and characterization of the observed scene. Unfortunately, especially in airborne SAR acquisi- tions, residual non-compensated platform motions result in baseline estimation errors. On the other hand, atmospheric propagation de- lays have to be accounted in the case of multiple space borne acquisi- tions. In both cases, the MB data stack is affected by unknown phase contributions different from track to track [1, 2]. As a consequence, prior to any MB coherent processing, it is necessary to correct the data stack for these phase residuals [3]. From a signal processing perspective, the phase calibration can be carried out by following two different classes of algorithms. A first class makes use of a grid of targets of opportunity (generally point-like) which remain stable during the entire acquisition time span. MB calibration methods based on the detection of the so-called PS (persistent scatterer) and CS (coherent scatterers) have been ex- perimented in [3] and [4], respectively. However, the effectiveness of this class of techniques is scenario-dependent. In fact, in natural scenarios the presence of PS/CS is more reduced than in urban sce- narios. Moreover, as the number of baselines is typically kept low to avoid temporal decorrelation problems, the detection performance worsen and the calibration quality degrades dramatically. As a con- sequence, the MB phase calibration in presence of a few tracks turns out to be a challenging task. To overcome all these problems, a sec- ond class of algorithms has been introduced based on some kind of MB autofocus. With particular reference to forest scenarios, in [5] an approach has been proposed which performs a sort of autofocus on the ground scatterer, after its separation from the canopy scatterer by exploiting a full-pol MB data stack. However, this method could not be effective when calibrating over an area with dense vegeta- tion, where the isolation of the ground scatterer results to be more difficult. A different method has been proposed in [6], which esti- mates the calibration phases by optimizing an ad-hoc measure of the contrast of the vertical profile of the backscattered power (viz. to- mogram) based on the statistics of the profile amplitudes measured on a range-azimuth area around the SAR cell of interest. This work proposes and investigates a new calibration method based on the minimization of the entropy [7] of the adaptive beam- forming (ABF) tomogram in the SAR cell under test. Indeed, in the context of the information theory the minimization of the en- tropy of a functional with respect to some parameters is equivalent to the maximization of its sharpness, as it get reduced when phase miscalibrations corrupt the data [2]. It is worth noting that the pro- posed method exploits the whole MB information, and there is no need to focus on a particular target or on a scatterer in the profile. In this way, the spatial coverage of calibration targets is full and a sin- gle polarimetric channel is sufficient to correct properly the whole MB data stack. Moreover, the proposed technique can be considered alternative to the one in [6], with the advantage that the minimum entropy-based solution can operate with a single cell, thus overcom- ing possible performance limitations due to profile variability in the range-azimuth plane. 2. ENTROPY MINIMIZATION Let {y(n)} N n=1 be the K-dimensional MB complex data vectors col- lected in N adjacent range-azimuth pixels composing the multilook cell under test, being K the number of images in the data stack. As- suming the phase errors very correlated in the range-azimuth plane [3, 5], for each pixel it results: y(n)= y0(n) ⊙ exp{j φ}, n =1,...,N , (1) where {y0(n)} N n=1 are the perfectly calibrated MB data vectors, φ is a K-dimensional vector containing the unknown residual miscali- bration phases φ k with respect to the master image, and “⊙” denotes the Hadamard product. Given {y(n)} N n=1 , it is possible to estimate the ABF vertical profile f (z). It is well-known that f (z) show re- markable height super-resolution, sidelobe rejection and sharpness in absence of miscalibration (φ = 0). However, when φ increases in magnitude, f (z) will look, in general, less sharp with inflated sidelobes and possible mislocations in height of the imaged scatter- ers. In the information theory, the profile sharpness is expressed by resorting to the concept of entropy. In particular, the Renyi entropy