IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 3, NO. 1, JANUARY 2006

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Range Resolution Improvement of Airborne SAR Images Stéphane Guillaso, Member, IEEE, Andreas Reigber, Member, IEEE, Laurent Ferro-Famil, Member, IEEE, and Eric Pottier, Member, IEEE

Abstract—This letter proposes an algorithm to improve the range resolution in airborne synthetic aperture radar (SAR) data by coherently combining an interferometric image pair, i.e., two images acquired with slightly different viewing angles. This algorithm is based on the wavenumber shift principle. In contrast to other methods, developed for application to spaceborne SAR data, the proposed algorithm takes the nonlinear effects due the strong variations in incidence angle in airborne SAR data into account. The proposed method is applied to SAR data of German Aerospace Center (DLR)’s E-SAR sensor. Quantitative verification results are obtained by measuring the resolution of several corner reflectors placed in the area under study, as well as the resolution of speckle of different areas. It is demonstrated that a resolution improvement of almost a factor of two can be achieved by incorporating a second interferometric image, which can be acquired easily with an airborne sensor. Index Terms—Interferometry, range resolution improvement, synthetic aperture radar (SAR) imaging.

where the topography does not include steep gradients, a constant wavenumber shift can be assumed for the whole scene. However, in the airborne case, the wavenumber shift between two interferometric images varies strongly due to variations in incidence angle over the scene. The purpose of this letter is to present an algorithm to increase the range bandwidth in airborne SAR data, demonstrating, using real data, that this approach is useful in practice. The principle of the wavenumber shift, the range resolution principle, and the adaptation to the airborne case, where local variations in wavenumber shift must be accounted for, are discussed in Section II. Section III shows quantitative results using the impulse response resolution measurement of corner reflectors and a measure of the resolution of speckle for diverse areas. Section IV contains conclusions about this work. II. RANGE RESOLUTION IMPROVEMENT

I. INTRODUCTION

R

ESOLUTION enhancement is achieved by combining two images acquired in an interferometric imaging mode, and is based on the observation that the spectra of two synthetic aperture radar (SAR) images, obtained from slightly different look angles, contain different parts of the ground reflectivity spectrum. This effect is known as the “wavenumber shift” in SAR interferometry [1]. The basic principle of range resolution improvement is to coherently combine different parts of the measured spectra, in order to increase the total range bandwidth. The spectra in both images partially overlap and can be combined to obtain the new image spectrum, if continuity is ensured. In this way, an image with enhanced range resolution can be computed. Up to now, this idea was applied only to spaceborne data [1]–[3]. In [4] and [5], an enhanced approach has been presented, which accomodates for the atmospheric phase screen, present in spaceborne imagery. With airborne sensors it is a relatively simple task to acquire, in addition to a single dataset, a second dataset by using an interferometric imaging geometry with a larger baseline. This makes the method of range resolution improvement highly attractive for airborne sensors. In cases Manuscript received November 19, 2004; revised August 8, 2005. This work was supported in part by the German Science Foundation DFG under Project RE 1698/1. S. Guillaso and A. Reigber are with the Berlin University of Technology, Computer Vision and Remote Sensing Group, D-10587 Berlin, Germany (e-mail: [email protected]; [email protected]). L. Ferro-Famil and E. Pottier are with the University of Rennes 1, Institute of Electronic and Telecommunication of Rennes, F-35042 Rennes, France (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/LGRS.2005.859943

A. Spectral Shift In order to achieve a high range resolution, SAR sensors transmit signals with a wide bandwidth, either by using short pulses or by using frequency modulation. Thus, the transmit signal of the radar cannot be considered as monochromatic; it has a certain bandwidth , located around the carrier freof the system. The slant range resolution of a quency SAR system is given by (1) where denotes the speed of light. Depending on the incidence angle, the received SAR image contains a certain part of the ground reflectivity spectrum [1]. The relation between a radar signal frequency , and the ground wavenumber is given by (2) where is the wavelength of the signal, and represents the off-nadir angle. For the sake of simplicity, the terrain is assumed of a SAR to be flat in this case. The ground range resolution system can then be expressed as (3) being the bandwidth of the measured ground with wavenumber spectrum. In order to improve the ground range resolution it is necessary to increase this bandwidth.

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Fig. 1. Spectral shift principle in the frequency domain. Due to the slightly change in the look angle, different parts of the ground object spectrum are measured by the sensor. This is exploited to increase the bandwidth and improve the resolution of the final image.

In the case of an interferometric data acquisition, the slight difference in look angle means that the two images contain different parts of the ground reflectivity spectrum. This principle is illustrated in Fig. 1. By changing the look angle, the part of the ground wavenumber seen by the sensor is shifted by (4) This relation is obtained from (2) using the Taylor expansion series. The formation of an interferogram corresponds to the convolution of the two image spectra. Thus, only the common part of the two spectra contains useful interferometric information. To optimize interferogram quality, it is useful to apply a spectral filtering to the range spectra to eliminate parts of the ground reflectivity spectrum that are not common to both images [1]. B. Improvement of the Range Resolution Another application of the spectral shift principle is to use the joined spectra to increase the ground range bandwidth in order to generate a new image with increased ground resolution. In the literature, several experiments using multiple surveys of spaceborne sensors to improve the ground range resolution of SAR data are described [1]–[3]. The principle of the range resolution improvement can be stated in three steps. The first step is a precise estimation of the spectral shift based, in this case, on geometric estimates of pa, the slant range distance rameters like the normal baseline , and the incidence angle . In the monostatic case, and assuming flat terrain, it can be shown that the spectral shift corresponds to the range frequency of the phase fringes [6] (5) Then, as shown in Fig. 2, the two spectra are shifted symmetrically to align the common part. Finally, a new image is formed by combining both spectra. The new spectrum has a higher bandwidth than the original ones. The new resolution is then given by (6)

Fig. 2. Three-step range resolution improvement principle using spectral shift. (A) Estimation of the spectral shift using the local fringe frequency. (B) Symmetric spectral alignment in order to link the common part of both spectra. (C) A new image with a higher bandwidth is formed using a spectral combination.

A necessary condition for this approach is that the two spectra must overlap. In order to obtain the best possible improvement, the overlap part should be close to zero. The point at which no overlap remains is known as critical baseline [6]. Above this limit, no interferogram can be formed. An improvement of the range resolution is then only possible using additional data acquisition with smaller baseline to fill the gap between the two spectra [3]. C. Airborne Range Resolution Improvement Algorithm In the spaceborne case, over flat areas, local variations in the incidence anglemay be neglected. As an example, the incidence angle for the European Remote Sensing (ERS) satellite system varies from 19 to 26 . In this case, the spectral shift is almost constant over the entire image. In the airborne case, variations in the local incidence angle always have to be taken into account: within the E-SAR dataset used for this study, the incidence angle varies from 15 to 60 . In the first part of the algorithm, the topography is ignored, and is then accounted for in the second part. Before the two image spectra can be joined, all target spectra have to be aligned according to their local spectral shift, which is dependent on the range position of the respective target. The amount of spectral shift in the frequency domain corresponds to the range frequency of the interferometric phase in the time domain [1], [6]. In the case of a flat area, this is equivalent to the frequency of the flat-Earth phase (7) where denotes the range position of the target in the data. In the airborne case, its shape is strongly curved as follows: (8) where is the flat-Earth phase and and denote the slant-range distances, one for each acquisition, between the sensor and a target located at the respective range in a flat terrain without topography. The curvature of the flat-Earth phase therefore corresponds exactly to the range dependence of the spectral shift. In focused data, the impulse responses are well localized and it becomes approximately correct to associate a local spectral shift given by the deviation of the flat-Earth phase with every

GUILLASO et al.: RANGE RESOLUTION IMPROVEMENT OF AIRBORNE SAR IMAGES

range-bin. This deviation can be assumed to be constant locally as the flat-Earth phase varies slowly. By multiplying each range and the line in one of the complex SAR images by other by , a compensation in the form of a spatially varying frequency shift is applied symmetrically to both images. After this operation, all target spectra are aligned around the center frequency, independent of their range position [7]. By using the flat-Earth phase, instead of the real interferometric phase, to compensate for the spectral shift, the effect of the topography on the local incidence angle and, therefore, on the local spectral shift is neglected. The symmetrical spectral shift should use the total interferometric phase, which is the sum of the flat-Earth phase and the unwrapped topographic phase. However, the interferometric phase is normally known only in the “wrapped” form. Since very high baselines are required to obtain a reasonable resolution improvement, the unwrapping process can be very difficult. To compensate for topography induced errors, a smoothed version of the topographic phase , whose “wrapped” form can be estimated by forming the interferogram between both images and removing the flat-Earth is removed from the second image, as phase, is used. an additional phase correction. To be able to estimate the topographic phase, the spectra must overlap. This means that the area around the critical baseline has to be removed. This smoothed version of the “wrapped” topographic phase is necessary in order to remove the noise, which corrupts the spectral shift. This correction introduces a nonsymmetric spectral shift to the slave image, which correctly aligns the two spectra, but does not yield the correct center location. This is acceptable, as long as only slight topography is involved. In case of more pronounced topography, it might be necessary to proceed as in the case of the flat-Earth phase, i.e., by multiplying half of unwrapped form of the topographic phase to each of the images. The topographic phase can then be estimated by applying a phase unwrapping process or by using a digital elevation model (DEM). Another solution would be to estimate the transition frequencies by applying a local fringe frequency estimator. The second part of the algorithm is the combination of the two image spectra. To avoid abrupt phase changes at the boundary between the two aligned input spectra, it is helpful and for each image. An to use weighting filters example weighting filter is proposed in Fig. 3. The shapes of the and , can be calculated as follows: filter curves,

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Fig. 3. Smoothed spectral combination using a weighting filter. The filter is applied in order to avoid discontinuities in the final spectrum, after the spectral combination. The curves shape over the common part can be calculated using a half part of a Hanning function, for example. The parameters indicated are used to calculate the filter.

to calculate all parameters of the filter, represented by . and are the minimum and maximum frequency of the common part respectively. The filters weight only the common parts and ensure a smooth transition from one spectrum to the other, while the information coming from the uncorrelated parts is not affected. The new image is generated from both original images and , after range spectral shift and topographic compensation, using the following relation: FT

FT

FT

(10)

where FT denotes a linewise Fourier transform in range. To summarize the airborne range resolution improvement algorithm, a schematic overview is shown in Fig. 4. III. EXPERIMENTAL RESULTS

otherwise otherwise

(9)

where and are the limits of the distinct parts of the range image spectra after the symmetric spectral shift, as shown in denotes the length of the Fig. 3. overlap of the two ground reflectivity spectra. Due to the nonlinearity of the airborne case, the spectral overlap is range dependent. To keep intact all information given by the noncommon part of both spectra, the minimal value of the overlap is chosen

The validation of the proposed range resolution improvement procedure is carried out using interferometric SAR data acquired over the Oberpfaffenhofen test site (Germany) by the DLR E-SAR sensor at L-band (0.23 m wavelength) in repeat-pass mode. The area under study is relatively flat without significant topography. Data have been processed using the extended chirp scaling algorithm [8], at squint 0 . The chirp bandwidth is 85 MHz, which gives a nominal range resolution of 2.0 m, calculated at 6 dB. The processed azimuth bandwidth is 100 Hz, which gives a nominal azimuth resolution of about 1.0 m. To improve the performance of the proposed algorithm, an image coregistration method with residual motion error detection has been applied [9]. The aircraft altitude is

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TABLE I SUMMARY OF THE RANGE RESOLUTION OVER THE 11 CORNER REFLECTORS

Fig. 4. Block diagram of the proposed range resolution improvement algorithm. FT denotes a linewise Fourier transform in range.

Fig. 5. Amplitude SAR image of the Oberpfaffenhofen test site. The locations of 11 corner reflectors, as well as the range and azimuth directions, are indicated. Regions A and B are homogeneous areas without texture, used to measure the speckle resolution. Region C illustrates the effect of range resolution improvement in the presence of texture. The dark area on the left represents the part of the data that is over the critical baseline.

around 3215 m. The two passes have an average horizontal and vertical baseline of 240.8 and 0.5 m, respectively. The data acquisition interval was approximately 15 min. Fig. 5 shows an amplitude SAR image over the scene under study. The area around the critical baseline (located in near range and represented by a dark area on Fig. 5) has been removed in order to be able to estimate the topographic phase. The performance of the proposed method is studied using 11 trihedral corner reflectors (CR), numbered 1 to 11 in Fig. 5, placed in the test site along the range direction. In addition, two homogeneous areas (without texture), Regions A and B in Fig. 5, have been defined to quantify the resolution improvement over distributed targets. Region A is located in the near range part, while region B is in the far range position. Region C is used to

visualize the effect of the range resolution improvement over different textured distributed targets. The quantification of the resolution improvement is firstly performed by measuring the resolution over the impulse redB for sponse of different corner reflectors, calculated at the experimental results, without range windowing during the process. Table I is a summary of the different resolution obtained from 11 trihedral corner reflectors (CR). The original resolution is about 2.0 m, and the new resolution varies from 1.2 m in near range to 1.5 in far range. The experimental value of the resolution is identically to the expected theoretical value. This difference in resolution improvement results directly from the variais much longer tion of the spectral shift in the airborne case: quantifies the in near than in far range. The quotient resolution improvement that can be expected depending the position on the image. Point targets, however, are not sufficient to analyze the proposed algorithm: the resolution of point targets would improve even if the fringe frequency estimate were wrong, as long as the phase matches at the target. Another measure to quantify the improvement in range resolution is to calculate the resolution of speckle over a homogeneous area without texture as a spatial autocorrelation (11) where represents complex values of the area under study, is the pixel under study, depicts the area around the pixel , and is the expectation operator. If the resolution is improved, (11) should show a function that tends more toward the -function. Fig. 6 shows the normalized spatial correlation function of the two regions A and B, respectively, without range windowing dB. during the process. Again, the resolution is calculated at An enhancement of the resolution of the speckle is observed in both cases. The initial resolution is around 2.6 m for both areas. The obtained resolution, after applying the proposed method, is 1.5 m for region A and 2.0 m for region B, corresponding to the . expected theoretical value The effect of the airborne range resolution improvement can be also observed by inspecting the amplitude of the SAR data

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Fig. 7(a) and (b) depicts the region C of the two original images used. Fig. 7(c) shows an improvement of the radiometric resolution, obtained by combining the intensity of both images. Fig. 7(d) shows the same area with improved resolution. In both original images, the path, indicated in Fig. 7, is not visible and the texture of different types of distributed target is blurred. By using a radiometric resolution improvement (multilook), the path becomes better visible but the texture stays blurred, whereas using the proposed method, the path and the texture are better defined.

IV. CONCLUSION

Fig. 6. Normalized spatial autocorrelation. (a) Region A. The area is located in near range. The resolution is calculated at 6 dB. The resolution changes from 2.75 to 1.5 m. (b) Region B. The area is located in the far range. The resolution is calculated at 6 dB. The resolution changes from 2.5 to 2.0 m.

0

0

This letter presents a range resolution improvement technique for airborne SAR data. The idea is to enhance the resolution of a SAR image using interferometric SAR data, with an acquisition geometry that differs slightly from the standard interferometry processing, in that it uses a large baseline. The proposed algorithm is based on the wavenumber shift principle, in which all the information in a pair of images is used to increase the range bandwidth. The proposed algorithm takes into account the range and topographic slope dependency of the wavenumber shift, which is inevitably significant in the case of airborne SAR data. Some experimental results are presented. They clearly demonstrate the effectiveness of the proposed approach for point and distributed targets. The range resolution can increase by up to a factor of two using only a single additional image.

REFERENCES

Fig. 7. Amplitude SAR images of the region C, distributed target. (a), (b) Original resolution of both images used. (c) Same area with improvement of radiometric resolution. (d) New image with better resolution.

before and after applying the proposed method. The results are shown in Fig. 7, corresponding to the region C indicated in Fig. 5. A hamming window has been applied to all images.

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