PAPER SAR Image Enhancement based on Phase-Extension Inverse Filtering

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1 PAPER SAR Image Enhancement based on Phase-Extension Inverse Filtering Dae-Won Do and Woo-Jin Song, Nonmembers SUMMARY In this paper we present a new post enhancement method for single look complex (SLC) SAR imagery, which is based on phase-extension inverse filtering. To obtain a highquality SAR image, the proposed method improves the mainlobe resolution as well as efficiently suppresses the sidelobes with low computational complexity. The proposed method extends the effective signal band up to the maximum-bandwidth allowed by a SAR system. The band-extension is achieved by adjusting the magnitude level of matched filtered SAR spectrum. Because the proposed method preserves the phase components of the spectrum unlike other super-resolution techniques and deconvolution techniques, it enhances a SAR image without causing any displacement. To verify the efficacy of the proposed method we apply it to a simulated SAR image and a real ERS- SAR image. The result images show that the proposed method improves the mainlobe resolution with low sidelobe levels. key words: SAR image, high-resolution, deconvolution, enhancement, ERS-.. Introduction Due to the capability of producing high-resolution imagery from echoed signals collected by a relatively small antenna, synthetic aperture radars (SAR) have been used for various purposes []. Conventionally, SAR images are reconstructed from the echoed signals by the matched filtering approach [][], where onedimensional processing is applied twice on the raw data arranged in two dimensions, that is, the range and the azimuth directions. Although the matched filtering approach provides the best achievable signal-to-noise ratio, it produces spurious ringings due to high sidelobe levels in the output image. To reduce the sidelobes, amplitude-weighting functions, such as Hamming or Hann weighting functions, have been applied to the data prior to the final FFT []. This weighting method, however, can achieve the lower sidelobes at the expense of the wider mainlobe width, which results in degradation of the spatial resolution [][]. To control sidelobes more effec- Manuscript received February,. Manuscript revised January 9, 3. The authors are with Microwave Application Research Center, Division of Electronics and Computer Engineering, Pohang University of Science and Technology (POSTECH), Pohang, Kyungbuk, , Republic of Korea ( wjsong@postech.ac.kr). This work was presented in part at the International Workshop on Intelligent Signal Processing and Communication Systems (ISPACS), Hawaii, USA, November. tively, such techniques as spatially variant apodization (SVA) [3] and adaptive sidelobe reduction (ASR) [4] have been introduced. However, these sidelobe control techniques are not effective in reducing the mainlobe width which determines the spatial resolution. Recently super-resolution techniques [5] [8] have been proposed to reduce sidelobes with improved mainlobe resolution. But the super-resolution techniques are restricted to problems where a priori knowledge of scene contents is available. Furthermore they require high computational complexity. To overcome these shortcomings of the conventional methods, the idea of band-extension with preserved phase components in the frequency domain has been presented by us in [9]. Extending this concept, we propose phase-extension inverse filtering as a new post enhancement method for single look complex (SLC) SAR imagery. The analysis of the characteristics of the chirp signal used in a SAR imaging system is given with detailed discussions on the characteristics of matched filtered SAR images. We mathematically analyze how the phase components can provide valuable information even beyond the limited bandwidth of the chirp signal in the frequency domain. Furthermore, it will be shown that the characteristics of the magnitude level of the matched filtered SAR images can give us an idea of how to control the magnitude level in the new algorithm. To obtain a high-quality SAR image, the proposed method improves the mainlobe resolution as well as efficiently suppresses the sidelobes with low computational complexity. To improve the mainlobe resolution with low sidelobe levels, the proposed method extends the effective signal band of matched filtered SAR spectrum up to the maximum-bandwidth, which is allowed by a SAR system. Some of super-resolution techniques also extend the signal band to improve the mainlobe resolution. For example, bandwidth extrapolation is used in the super-sva algorithm [6] to extend the signal band. Despite the bandwidth extrapolation extends the frequency band greater than the original bandwidth, it has a difficulty in providing additional information beyond the original limited bandwidth. So, the original signal data must be embedded in the extrapolated data and further iterations are required to improve the fidelity of the processed image [6]. On the other hand, the

2 proposed method extends the effective signal band by using the phase information beyond the original limited bandwidth. The band-extension is accomplished by adjusting the magnitude level of the matched filtered SAR spectrum without disturbing the phase of the spectrum. There are no needs to embed the original data in the extrapolated data and to perform further iterations to improve the the quality of images. Hence, the proposed method requires low computational complexity. This paper is organized as follows. Section reviews the conventional matched filtering approach and describes the characteristics of its output signal in a SAR imaging system. In Section 3, we formulate the phase-extension inverse filtering and show an example. In Section 4, by applying the proposed method to both a simulated image and a real ERS- SAR image, we present experimental results that proves its efficacy. Finally, Section 5 gives a summary and conclusions. Phase (radian) Frequency index Analysis of matched filtering in a SAR imaging system Matched filtering approach is used to reconstruct SAR images from echoed signals. We review the matched filtering approach used in a general SAR imaging system. We also describe the characteristics of matched filtered SAR spectrum, which are related to the proposed method.. Matched Filtering in a SAR imaging system When a radar signal s(t) is transmitted, a matched filter used at a receiver has h(t) = s ( t) for target detection and its spectrum is H(f) = S (f), where S(f) is the spectrum of s(t). For simplicity of explanation, we consider the one-dimensional geometry shown in Fig.. An antenna located at the origin illuminates a point scatterer located at x = R, which has reflectivity of q(x) = δ(r), where δ( ) means Dirac impulse function. For the point scatterer, ignoring the scale factor, the received signal becomes the transmitted signal delayed by R/c. Thus the spectrum of the matched filtered data for the received signal will be given by [] G(f) = H(f)S(f) exp ( j4πfr/c) = S (f)s(f) exp ( j4πfr/c) Frequency index Fig. FFT plots of the transmitted signal : magnitude components phase components. = S(f) exp ( j4πfr/c), () where denotes the complex conjugate operation. This is equivalent to the overall transfer function of the SAR imaging system. When S(f) is constant over a finite frequency band, it is obvious from () that G(f) has a rectangular magnitude spectrum with bandwidth B. The overall impulse response function (IRF) is described as g(t) = B/ B/ exp ( j4πfr/c) exp (jπft) df = Bsinc [πb (t R/c)], () where sinc(t) denotes sin t/t []. The envelope of g(t) has a form of sinc(t) with nominal time-width /B, centered at the time delay R/c.. Characteristics of the Matched Filtered Signal Fig. Simplified SAR geometry. In a general SAR system, the transmitted signal s(t) has usually gone through a linear frequency modulation, i.e., a chirp signal. Assume that s(t) is continuous and the scale factor is ignored. Then s(t) is represented by s(t) = exp ( jπkt ), t < τ p /, (3) where K is a modulation rate of the transmitted signal and τ p is a pulse duration. The signal bandwidth for

3 DO and SONG: SAR IMAGE ENHANCEMENT BASED ON PHASE-EXTENSION INVERSE FILTERING 3 Phase (radian) Frequency index Frequency index Fig. 3 Overall transfer function of a SAR imaging system : magnitude components phase components. Fig Spatial index (8m/pixel) Overall impulse response of a SAR imaging system. this chirp signal is B = K τ p. If the time-bandwidth product Bτ p is large enough, the spectrum of s(t) can be approximated as the following equation by the principle of stationary phase []: S(f) = K / exp [j(π/4)sgn(k)] exp ( jπf /K ), f < B/, (4) where the magnitude component is constant within the chirp signal bandwidth B. With this approximated S(f), the overall IRF is supposed to have an ideal sinc function as in () []. Because the real spectrum of a chirp signal doesn t have the closed form as in (4), the practical S(f), the FFT of (3), doesn t have constant magnitude within the bandwidth B. Fig. shows magnitude and phase components of the practical S(f) with the parameters taken from the ERS- mission. With this practical S(f), Fig. 3 shows the plot of the overall transfer function G(f) in a noise-free situation. Its IRF, the inverse FFT of G(f), is plotted in Fig. 4. From (), both the practical S(f) and G(f) have the same signal bandwidth B. Due to the fact that G(f) has a finite bandwidth, the IRF is not a Dirac impulse function but a sinc-like function as shown in Fig. 4. The IRF is not even an ideal sinc function, because G(f) with the practical S(f) doesn t have a rectangular magnitude spectrum as shown in Fig. 3. Also we can see that the higher frequency components of G(f) are greater than the lower ones. From these observations, it is obvious that the effective signal band of G(f) should be extended up to the entire frequency band and the magnitudes of G(f) should be constant in order to obtain a Dirac impulse function as an IRF of a SAR imaging system. In other words, because the chirp signal bandwidth B has smaller value than the sampling frequency, the mainlobe resolution of the IRF can be improved by extending the effective signal band. To extend the effective signal band, it is required to use information beyond the chirp signal bandwidth. The phase components of the practical S(f), as shown in Fig. 3, have information of the target beyond the chirp signal bandwidth up to the sampling frequency, despite the magnitude components are small. This fact shows that the phase information can be used to extend the effective signal band. If we consider additive noise, the spectrum of a returned baseband signal is described by V r (f) = S(f)X(f) + N(f), (5) where X(f) is the spectrum of general target reflectivities and N(f) is the spectrum of additive noise. Then the spectrum of the matched filtered SAR data is given by Y (f) = S (f)v r (f) = S (f)s(f)x(f) + S (f)n(f) = S(f) exp( jωr/c)x(f) exp(jωr/c) +S (f)n(f), (6) where ω = πf. From (), (6) can be rewritten as Y (f) = G(f)X(f) exp (jωr/c) + S (f)n(f). (7) Let the first term in (7) be X (f) = G(f)X(f) exp(jωr/c) = S(f) X(f), (8) and the second term be N (f) = S (f)n(f). (9) As shown in (7), the phase component of Y (f) is related to the slant-range R. And the phase of X(f) is equal to that of X (f) as in (8). Using X (f) and N (f), the phase component of Y (f) is calculated by the equation:

4 4 ( X Q Y (f) = arctan (f) + N Q (f) ) X I (f) + N I (f), () where the subscript I, Q mean the inphase and the quadrature component of a complex signal, respectively. In a general SAR system with a high signal to noise ratio (SNR), we can assume that the magnitude of X (f) is much greater than that of N (f). From this assumption, the phase component can be approximated by ( X Q Y (f) arctan (f) ) X I (f) = X (f). () This fact shows that the phase component of the matched filtered SAR spectrum contains more information related to the target reflectivities rather than noise. It means that the phase component has the information of the target reflectivities beyond the finite chirp signal bandwidth B, though the magnitude component is relatively small. So, the extension of the effective signal band can be accomplished by exploiting the phase components of the matched filtered SAR spectrum. This band-extension results in the improvement of the spatial resolution. 3. Phase-Extension Inverse Filtering Before introducing the phase-extension inverse filtering, we review conventional image enhancement methods and their problems when they are to be applied to SAR images. Firstly, a traditional -D inverse filtering [] can be considered as a deconvolution method, whose output spectrum is formulated as ˆX(u, v) = Y (u, v), if G(u, v) > T, G(u, v)., otherwise, () where Y (u, v) is the -D spectrum of the matched filtered output, G(u, v) is the -D transfer function of a SAR imaging system and T is a threshold which is determined by the chirp signal bandwidth B. There is a similarity between the inverse filtering and the ideal filtering concept [] in providing an ideal sinc funtion for a point target. However, we have a serious problem in using this traditional inverse filtering to extend the effective signal band, because G(u, v) are relatively small beyond the chirp signal bandwidth, that is, the division by G(u, v) causes noise enhancement. Secondly, root filtering [] can be used to improve the spatial resolution, which is described as ˆX(u, v) = Y (u, v) α exp [ jθ Y (u,v) ], < = α < =,(3) Fig. 5 Partition of the transfer function. where the α-root of the magnitude component is taken while the phase component being preserved. The effect of α-rooting is to emphasize higher spatial frequency components relative to lower ones. This filtering has the merit of not requiring the knowledge of the transfer function. This filtering extends the effective signal band while preserving the phase component of Y (u, v), which leads to the enhancement of image quality. Because the magnitude component of a matched filtered SAR spectrum is usually too small beyond the chirp signal bandwidth B, the effect of root filtering is not so good at extending the effective signal band of a SAR image. To overcome the shortcomings of the conventional enhancement methods, the phase-extension inverse filtering has the goal of obtaining a more improved mainlobe resolution with low sidelobe levels. To reach this goal, the proposed method extends the effective signal band up to the maximum bandwidth allowed by a SAR system. Because the phase components of Y (u, v) have information of target reflectivities beyond the chirp signal bandwidth, band-extension can be accomplished by preserving the phase components of Y (u, v) like root filtering. And deconvolution by G(u, v) is applied within the chirp signal bandwidth like the traditional inverse filtering method. This processing eliminate the undesirable effect of G(u, v) in the chirp signal bandwidth, which is that the higher frequency components of G(u, v) are greater than the lower ones as mentioned in Section.. Now, we describe the proposed method in detail. First, we divide the frequency domain of G(u, v) into the chirp signal bandwidth B and the extended band. For convenience, we use a threshold T to divide the frequency domain, whose value is determined by E{ G(u, v) }/. The E{ G(u, v) } means the average magnitude level of the transfer function in the whole frequency domain. Φ and Φ are the divided frequency domains, which are defined by Φ = {(u, v) G(u, v) > T }, Φ = {(u, v) G(u, v) < T }. (4)

5 DO and SONG: SAR IMAGE ENHANCEMENT BASED ON PHASE-EXTENSION INVERSE FILTERING 5.5 Spectrum before processing.9 Uniform Weighting.9 Hamming Weighting Range index (8m/pixel) Range index (8m/pixel) Range frequency index.5 Spectrum after processing SVA Proposed method Range index (8m/pixel) (c) Range index (8m/pixel) (d) Range frequency index Fig. 7 Impulse response functions : no processing Hamming weighting (coefficient=.75) (c) SVA (d) proposed method. Fig. 6 Spectrum for a point target (σ n =.) : matched filtered spectrum Processed spectrum. For example, Fig. 5 shows the -D profile of G(u, v) in the range direction. The Φ in Fig. 5 represents the frequency domain of the chirp signal bandwidth B. In Φ, Y (u, v) is divided by G(u, v) to eliminate the undesirable effect of G(u, v), where G(u, v) in () is replaced by G(u, v) to preserve the phase of Y (u, v). To get a more improved mainlobe resolution with lower sidelobes, we extend the effective signal band greater than the chirp signal bandwidth B. The Φ represents the extended band. In Φ, we adjust the magnitude level while preserving the phase component. The magnitude level is generally increased for better effect of bandextension. Since the exact magnitude values, which are related to the target reflectivities, are unknown in Φ, a magnitude level too high may cause noise enhancement. So, the magnitude level is determined by considering the average spectrum level and the standard deviation of added noise. Incorporating these facts, the phase-extension inverse filtering is formulated as Y (u, v) G(u, v), if (u, v) Φ, ˆX(u, v) = Y (u, v) (5) ηe{ Y (u, v) } Y (u, v), if (u, v) Φ. As mentioned before, the magnitude level in Φ is adjusted to get a desirable effect of band-extension. In the proposed method E{ Y (u, v) } and a system parameter η are used to adjust the magnitude level. The E{ Y (u, v) } means the average magnitude level of Y (u, v) in the whole frequency domain. The parameter η is set to be inversely proportional to the standard deviation of added noise at the receiver, σ n, which prevents noise amplification. In choosing the value of η, it is not desirable that the value is either too large or too small. If the value of η is too large, noise amplification is inevitable. And if the value of η is too small, the improvement through the band-extension would be poor. The adequate value of η can be chosen empirically. Fig. 6 shows the spectrum when the proposed method is applied: Fig. 6 is the matched filtered spectrum for a point target, where each inphase and quadrature component of echoed signals is corrupted by additive white Gaussian noise with σ n =.. Fig. 6 shows the spectrum processed by the proposed method, where T is.7 and the η is. Fig. 7 shows the -D IRFs in the range direction with no processing, Hamming weighting method, the SVA algorithm and the proposed method. The IRF in shows that the Hamming weighting method provides lower sidelobe levels at the expense of wider mainlobe width. As shown in Fig. 7 (c), the SVA algorithm eliminates the sidelobes effectively but it doesn t reduce the mainlobe width: in other words, it can t improve the mainlobe resolution. The IRF in (d) is processed by the proposed method, which shows that the proposed method provides improved mainlobe resolution with much lower sidelobe levels. Also, we can see that the proposed method enhances the SAR data without causing any displacement, because it extends the effective signal band of the magnitude components with the phase components being preserved.

6 6 Fig. 8 Simulated images : reflectivity map echoed signals. 4. Experimental Results To demonstrate the efficacy of the proposed method, a simulation of the ERS- mission whose general parameters are given in Table was carried out. Fig. 8 is a reflectivity map used in the simulation, where all magnitudes of 77 targets are set to be. Fig. 8 is the image of the echoed signals, whose I and Q raw signals were corrupted by additive white Gaussian noise with σ n =.5, respectively. Each image shown in Fig. 8 is scaled to take 55 its maximum pixel value. To analyze the effect of additive noise at the receiver, the mean power of the -D echoed signals v r (i, j) without noise is calculated by ε t = A p E { v r (i, j) }, (6) (c) Fig. 9 Result images for the simulated image. The SNR raw is 8.dB : no processing Hamming weighting (coefficient=.75) (c) SVA (d) proposed method. (d) where each i, j means the range and the azimuth index, respectively, and A p represents an area in which the echoed signals exist. The mean power of receiver noise is estimated by Table ERS- parameters uses in the simulation runs Orbital altitude Look angle Incidence angle Azimuth antenna dimension Range antenna dimension Frequency Chirp bandwidth A/D sampling rate Pulse Repetition Frequency (PRF) Pulse duration Azimuth image pixel spacing Range image pixel spacing 785 (km).3 (degrees) 3. (degrees) (m) (m) 5.3 (GHz) 5.5 (MHz) 8.96 (Msamples/sec) 68. (Hz) 37. (µsec) 3.98 (m) 7.94 (m) ε n = A n E { n(i, j) }, (7) where n(i, j) is -D additive noise at the receiver and A n is an area where the mean power of receiver noise is estimated. In general, ε n is estimated in a large area without transmitting a pulse. Then the signal-to-noise ratio (SNR) at the receiver is defined as SNR raw = log ε t ε n (db). (8) The SNR raw is 8.dB in the simulation. This value of SNR raw is appropriate for performance evaluation through the simulation [8]. Fig. 9 shows the original image with the matched filtering approach only and the result images processed by Hamming weighting method, the SVA algorithm, and the propose method, respectively. The threshold T

7 DO and SONG: SAR IMAGE ENHANCEMENT BASED ON PHASE-EXTENSION INVERSE FILTERING 7 is.7, the system parameter η is. The zoomed images of the top area in Fig. 9 are shown in Fig.. Each image displayed in Fig. 9 and Fig. is scaled to make its maximum pixel value 55. As shown in Fig. 9 and Fig., the proposed method improves the mainlobe resolution with much lower sidelobe levels. Fig. shows a part of result images where each method is applied to a real SAR image. A real ERS- SAR image around Asan Bay in Korea is used. The SNR raw is about.7db, which is about 5.4dB lower than that of the previous simulated image. Fig. (d) is the result image processed by the proposed method, where the threshold T is.7 and the system parameter η is. As shown in the result image, the proposed method provides thinner lines than any other methods, although there still remain some sidelobes. These thinner lines imply that the spatial resolution is improved by the proposed method. With a larger value of SNR raw, we expect that the sidelobes will be more suppressed and also the performance will be more improved. (c) Fig. Zoomed images : no processing Hamming weighting (c) SVA (d) proposed method. (c) Fig. Result images for a real SAR image : no processing Hamming weighting (c) SVA (d) proposed method. (d) (d) 5. Summary and Conclusions In this paper the phase-extension inverse filtering has been introduced. As a post processing, the proposed method enhances the quality of SAR images. To obtain high-quality SAR images, the proposed method improves the mainlobe resolution with much lower sidelobe levels by extending the effective signal band. The band-extension is achieved by adjusting the magnitude level of the matched filtered SAR spectrum. The proposed method exploits the phase components based on the characteristics of the chirp signal. And it doesn t disturb the phase components unlike other super-resolution techniques. Furthermore, the computational complexity of the proposed method is much lower than other super-resolution techniques, because it adjusts the magnitude level in the frequency domain and requires no iterations. We have tested the proposed method with a simulated SAR image and a real ERS- SAR image to verify the efficacy of the proposed method. With the proposed method, the results showed that the mainlobe resolution is much improved with low sidelobe levels. Since noise can be somewhat amplified by increasing the magnitude level in the proposed method, the performance may be degraded in the low SNR raw environment. Hence, to get better performance through the proposed method, it is desirable that SNR raw is high enough for the phase component to contain more information related to the target reflectivities rather than noise. Acknowledgments The authors wish to acknowledge that this work has been partially supported by Ministry of National Defense through the Agency for Defense Development, Republic of Korea, and also the authors have been partially supported by BK program of Ministry of Education, Republic of Korea. References [] J. C. Curlander and R. N. Mcdonough,Synthetic Aperture Radar Systems and Signal Processing, Wiley-Interscience publication, 99. [] D. C. JR. Munson and R. L. Visentin, A signal processing view of strip-mapping synthetic aperture radar, IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no., pp. 3-47, Dec. 989.

8 8 [3] H. C. Stankwitz, R. J. Dallaire, and J. R. Fienup, Nonlinear apodization sidelobe control in SAR imagery, IEEE Trans. Aerosp. & Electron. Syst., vol. 3, no., pp , Jan [4] S. R. DEGRAAF, Sidelobe reduction via adaptive FIR filtering in SAR imagery, IEEE Trans. Image Processing, vol. 3, no. 3, pp. 9-3, May 994. [5] S. R. Degraaf, SAR imaging via modern -D spectral estimation methods, IEEE Trans. Image Processing, vol. 7, no. 5, pp , May 998. [6] H. C. Stankwitz and M. R. Kosek, Super-resolution for SAR/ISAR RCS measurement using spatially variant apodization, Proc. AMTA Symp., Williamsburg, VA, pp. 5-56, Nov [7] Jian Li and P. Sroica, An adaptive filtering approach to spectral estimation and SAR imaging, IEEE Trans. Signal Processing, vol. 44, no. 6, pp , Jun [8] V. Gaulielmi, F. Castanie and P. Piau, Super-resolution algorithm for SAR images, Proc. SPIE - The International Soc. for Opt. Engineering, 37, pp. 95-, 997. [9] Dae-Won Do, Woo-Jin Song, SAR image enhancement based on the phase extension inverse filtering, Proc. the ISPACS, vol., pp , November. [] Anil K. Jain, Fundamentals of Digital Image Processing, Prentice-Hall Inc., pp , 989. [] A. Moreira and T. Misra, On the use of the ideal filter concept for improving SAR image quality, J. Electro. Waves & Application, vol. 9, no. 3, pp. 47-4, 995. of digital signal processing, in particular, radar signal processing, signal processing for digital television and multimedia products, and adaptive signal processing. Dae-Won Do was born in Seoul, Korea, on February 4, 974. He received the B.S. and M.S. degrees in electronic and electrical engineering from Pohang University of Science and Technology (POSTECH) in 996 and 998, respectively. Since 996, he has been a Research Assistant at the Department of Electronic and Electrical Engineering, POSTECH where he is currently working toward the Ph.D. degree. His research interests include SAR imaging systems and digital image processing, in particular, SAR image compression. Woo-Jin Song was born in Seoul, Korea, on October 8, 956. He received the B.S. and M.S. degrees in electronics engineering from Seoul National University in 979 and 98, respectively and the Ph.D. degree in electrical engineering from Rensselaer Polytechnic Institute in 986. During 98 98, he worked at Electronics and Telecommunication research Institute (ETRI), Korea. In 986, he was employed by Polaroid Corporation as a senior engineer, working on digital image processing. In 989, he was promoted to a principal engineer at Polaroid. In 989, he joined the faculty at Pohang University of Science and Technology (POSTECH), Korea, where he is a professor of electronic and electrical engineering. His current research interest are in the area