Comparisons of Speckle Noise Filtering Methods on Interferometric Synthetic Aperture Radar Images

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1 908 JOURNAL OF COMPUTERS, VOL. 9, NO. 4, APRIL 2014 Comparisons of Speckle Noise Filtering Methods on Interferometric Synthetic Aperture Radar Images Yifei Chen Department of Electronic & Information Engineering, Beihang University, Beijing, China Huaping Xu Department of Electronic & Information Engineering, Beihang University, Beijing, China Abstract Speckle noise in interferometric synthetic aperture radar (InSAR) phase images seriously degrades the quality of interferogram, disenables interferogram to reflect accurate phase characteristics of the target and increases the difficulty in extracting DEM information of the target area. Therefore, reducing speckle noise by interferogram filtering is a significant step in InSAR processing. First, a noise-included interferometric SAR phase image is simulated based on a terrain model and geometrical parameters of InSAR system. The phase image can be characterized by multilook phase distribution. Then, three interferogram filtering algorithm are explored to remove speckle noise: Goldstain filter, rotating kernel transformation and Lee filter. Proper implementation of three methods is given. Based on experimental results, performances of three different methods are compared. Two aspects need to be comprehensively considered in noise reduction process: the required accuracy in practical application and the processing duration. And also secondtime or multiple combined noise reduction is highly recommended. Index Terms phase filtering, speckle noise, radar interferometry, synthetic aperture radar (SAR) A. Overview of InSAR I. INTRODUCTION One powerful tool for producing digital elevation maps (DEM) is interferometric synthetic aperture radar (InSAR) technique. This geodetic method uses two or more synthetic aperture radar (SAR) images to generate maps of surface deformation or digital elevation, using differences in the phase of the waves returning to the satellite or aircraft [32]. Manuscript received August 25, 2013; revised September 29, 2013; accepted October 17, Corresponding author: Yifei Chen. There are three types of antenna pattern of InSAR system where two passes of a radar satellite/aircraft, or a single pass if the satellite/ aircraft is equipped with two antennas: the across-track interferometry (XTI), the along-track interferometry (ATI), and the repeat-pass interferometry (RTI). Over the past four decades, various applications of InSAR technique continues to develope in many research areas, such like topographic mapping [1], geophysical monitoring of natural hazards [2], measurement of glacier [3], observation of the forest and classification of vegetation [4], marine surveying [5], 3-D building reconstruction [6], military purpose [7]. Figure 1 shows the InSAR data processing flow aim to obtain DEM information. Due to the good quality of SAR interferogram directly affects the accuracy of phase unwrapping, noise reduction is a significant step in the InSAR data processing to generate high resolution DEM in target area after phase unwrapping. B. Speckle Noise Reduction The application of InSAR encounters problems due to noise appearing in the interferogram phase measurement. There are two types of noises in the interferometric SAR image including the inherent system noise and speckle noise. The speckle noise appearing in interferometric SAR phase images is caused by the coherence interference of waves reflected from many elementary scatters, which degrades the quality of interferogram seriously and makes interferogram reflect the scattering characteristics of the target inaccurately. Therefore, the inhibition of the speckle noise is significant on the SAR imaging process issue. [8, 9] show that the speckle noise reduction processing is necessary for the applications of rapid identification of oil spills and the sea ice segmentation. The quality of DEM can be improved by many methods at different processing levels, and one of them is filtering of the interferometric phase. At the earliest, there are several interferogram filtering methods as demonstrated: Goldstein filter [10], Lee filter [11], doi: /jcp

2 JOURNAL OF COMPUTERS, VOL. 9, NO. 4, APRIL rotating kernel transformation [12], median filtering [13], spatial vector filtering [14], etc. shows that Then, [15] presents a modification to the adaptive Goldstein filter to make parameter alpha dependent on coherence, [16, 17] propose modifications to the Lee adaptive complex filter with adjusted directional windows aim tocut losses of signal and reduce noise. Also, there are numerous improved filters based on new estimation methods of local fringes frequency, such like the maximum likelihood method [18], the modified multiple-signal classification method [19]. Furthermore, in order to improve estimation accuracy, [20] separates the interferogram into two deterministic components corresponding to low frequency fringes and high frequency patterns, and 2-step methods [21] is considering to apply different proper filters into two components. Specially in recent years, various novel methods of speckle noise reduction are developed in terms of many new ideas, such like the sparse representation and dictionary learning method [22], signal subspace technique [23], the partial distribution of noisy image [24], an improved wavelet threshold [25], the alternating minimization algorithm with a shifting technique [26], and comparative studies are also given in [27, 28]. SAR Image (Antenna 1) Noise Reduction Co-Regestration Interferogram Phase Unwrapping DEM Figure 1. Flow chart of InSAR data processing II. FILTERING ALGORITHM SAR Image (Antenna 2) Conjugate Multiplication Flatting Baseline Determination In this section, the paper explores three interferogram filtering algorithm to remove speckle noise: Goldstain filter, rotating kernel transformation and Lee filter. For more detail about three algorithms, see [10-12]. A. Goldstein Filter Goldstein filter is a nonlinear filtering in frequency domain. Goldstein and Werner [10] propose this adaptive radar interferogram filtering based on the concept of multiplication of the Fourier spectrum of a small interferogram patch by its smoothed absolute value to the power of an exponent. Figure 2 is a flow chart to show how Goldstein filtering put into effect. ( x, y) represents the position of a pixel in the interferogram. nxy (, ) represents noise in the position of the pixel ( x, y ). φ( x, y) represents the principal value of the real interference phase. Original Interferogram φ ( x, y) + n( x, y) Filtered Interferogram Vector Space exp{ j[ φ ( x, y) + n( x, y)]} IFFT Frequency Spectrum Weighted Figure 2. Flow chart of Goldstein filtering method FFT Goldstein filter method can be divided into the following steps: 1) Map the interference phase φ( x, y) of the fringe interferogram into a unit vector in the vector space: E( x, y) = exp[ jφ( x, y)] = cos[ φ( x, y)] + jsin[ φ( x, y)]. (1) 2) choose a filtering window ( w E ) ( x, y ) with a certain dimensions. Then apply fast Fourier transform (FFT) to obtain spectrum data ( w F ) ( uv, ), in which u and v represent space frequencies. 3) kernel function K is assumed to get ( w) FK ( uv, ). Then normalize it using the ( w) maximum value max FK ( uv, ). 4) The frequency spectrum data is been processed by weighting function ( w) ( w) ( w) k F ( uv, ) = F ( uv, ) F ( uv, ). (2) Apply two-dimensional Fourier inverse transform (IFFT) to the processed spectrum to ( w obtain the post-filtering result E ) G ( x, y ). k(0 k 1) in Equation (2) represents the exponent sign of the frequency filter weighting function. Various mathematical functions can be used to weight in frequency domain such like power function, sinusoidal function, or exponential function.

3 910 JOURNAL OF COMPUTERS, VOL. 9, NO. 4, APRIL ) Move the filtering window along image E( x, y ) and apply the above filtering at the each pixel. Mark the filtered result as EG ( xy, ). B. Rotating Kernel Transformation The Yim-Kul Lee and William T.Rhodes [12] present a new method for nonlinear image processing to enhance the straight-line features relative to non-straight-line features in the image. Rotating kernel transformation technique is originally used for hybrid optical-electronic implementation, especially applied to cell boundary enhancement with a good performance. This method utilizes directional information contained in a circular neighborhood centered on each point in the input image. Figure 3 shows up the flow chart of rotating kernel transformation (RKT). An input image Iin( x, y ) is convolved with a long, narrow two-dimensional kernel Kθ (, xy) which is rotated through 360 degree. As the kernel rotates, the convolution output Sθ ( x, y) is measured, and the maximum and minimum values at each point ( x, y ), defined in accord with ( x y) S ( x y) { o θ θ } Max, = maximum, : 0 < 360, (3) ( x y) S ( x y) { o θ θ } Min, = minimum, : 0 < 360. (4) are stored. The output image is given by ( ) I x, y = Max( x, y) Min( x, y). (5) out Original Interferogram I in (x,y) Convolution S 0 (x,y)= I in (x,y)* k θ (x,y) Stored Max(x,y) and Min(x,y) for each point New Mapping Max(x,y)-Min(x,y) 2-D Kernel is rotated through 360 o k θ (x,y) Figure 3. Flow chart of RKT method C. Lee Filter Lee filtering algorithm has been developed by Jong-sen Lee [11] aim to adaptively filter the interferometric phase image using either the real or complex phase. This adaptive filtering method emphasizes four valuable factors. First, the interferometric phase can be characterized by an additive noise model φ = φ x + v, (6) Second, the spatial separation of the two antennas leads to decorrelation of the speckle pattern in the two SAR images, producing higher noise level in the interferometric phase images. Coherence value between the two of images is affected by various factors including: 1) geometrical decrrelation 2) temporal decorrelation 3) thermal decorrelation 4) Doppler centroid decorrelation 5) scattering decorrelation 6) data processing decorrelation And the accuracy of interferometric phase is reduced by any of loss in coherence [11]. Third, multilook processing is necessary by averaging neighboring pixels, then a probability density function of the multilook interferometric phase image can be derived by Equation (7) based on the circular Gaussian assumption 2 L (1 γ ) 1 2 ( φγ ; ; ; φ0 ) = ( ;1; ; β ) PDF L F L 2π L Γ ( L + )(1 γ ) β L πγ( L)(1 β ) where β = γ cos( φ φ0 ) ; Γ is the Gamma function; F represents a Gaussian hypergeometric function. Fourth, based on the noise model above, Lee filter is designed according to the local noise level by using sixteen directional dependent windows (masks) aim to adaptively filter noise along the fringes. The flow chart of Lee filtering algorithm is shown in Figure 4. III. IMPLEMENTATION AND RESULTS A. Interferogram with Noise Firstly, the universal multifractal technique [29] is adopted to simulate the DEM. The paper plots a terrain model, a surface with three local maximum (cone) by peaks function in MATLAB, which is a function of two variables, obtained by translating and scaling Gaussian distributions and can be expressed by (7)

4 JOURNAL OF COMPUTERS, VOL. 9, NO. 4, APRIL f( x, y) = 3(1 x) e x ( y+ 1) x 1 10( x y ) e e x y ( x+ 1) y.(8) Figure 5 shows a terrain model sized of 625 by 625 pixels with maximum height m. Secondly, based on the assumed geometrical model of InSAR system, the paper simulates phase map and wrap it [16], which is referred as true phase without noise. The parameters value of InSAR system is assumed in Table I. Thirdly, the interferogram phase image with noise as shown in Figure 6 is simulated by adding an additive noise model into the true phase map, which can be characterized by the multilook phase distribution as shown in Equation (7), where multilook number L is assumed 1. Coherence map γ is synthesized by three factors: geometrical decorrelation γ γ geom, temporal decorrelation temporal, and thermal decorrelation γ thermal. Coherence map can be expressed by an additive noise model γtotal = γ geom γtemporal γthermal. (9) The geometrical decorrelation γ result from the geom difference of look angle between two antennas, which can be calculated with geometrical parameter listed in the Table I [30] by γ = θ λr, (10) 2 geom 1 (2 Bh Rg cos )/ where R g is the resolution of a terrain model. The slope map is derived from the simulated DEM, and the temporal decorrelation γ temporal value is simulated using the fractal technique. Thermal noise in this radar system is ignored in order to simplify calculation. Fourthly, the phase noise simulation is conducted based on Equation (11) using the relationship among phase noise, multilook number and coherence [16] π 2 2 φ = 0 0 π σ ( γ, L) ( φ φ ) PDF( φ; γ; L; φ ) dφ. (11) 2 where σ is phase variance; φ γ is interferometric coherence; L is multilook number; φ is interferometric phase and φ 0 is the expectation of interferometric phase; PDF is the probability density function of interferometric phase, which can be calculated by Equation (7). At last, based on the above equtions, the paper simulates the phase noise map for L=1, and calculate the interferometric phase with noise by adding a simulated phase noise to the true phases. Also, tests are run specifically for different baseline length value vary from 30m to 180m aim to get best wrapped phase image. Normally, A larger baseline length corresponds with a smaller height ambiguity to obtain more fringes and a wrapped phase image. Only one noisy interferometric phase image with longest baseline length is as shown in Figure 6, which is one of the best result. Compute the phase noise standard deviation σ using a v look-up table Original Interferogram Apply adaptive noise filtering φ ' = φ + b( φ φ) Figure 4. Flow chart of Lee filtering method TABLE I. PARAMETERS VALUE IN INSAR SYSTEM Parameters Satellite Height [km] Value Baseline Length [m] 180 Baseline Orientation [ o ] 10 Looking angle [ o ] 19 Slant Range (to the first point) [km] Select a directional window with minimum variance from a set of 16 windows var( φx ) Compute the filtering weight b = var( ) Slant Range (to the last point) [km] Wavelength [cm] 5.7 Doppler [Hz] 0 φ

5 912 JOURNAL OF COMPUTERS, VOL. 9, NO. 4, APRIL 2014 B. Phase Filtering Algorithm As for Goldstein filter, the kernel function K = 0.5 is assumed, setting a local window sized of 15 x 15 pixels. As for Rotation Kernel Transformation, the length of square equals 3 and width of kernel equals 1 are assumed, respectively. As for Lee filter, the center pixel in a 5 x 5 window is to be filtered. Figure 7 shows all filtered interferogram image. As shown in Figure 7, interferogram filtering methods mentioned above can improve the quality of the interferogram, eliminate the phase noises so that improve the accuracy of phase unwrapping to various degrees. Goldstein filtering method can effectively retain edge information and filter the speckle noise out to the greatest extent. Figure 5. A simulated terrain model Figure 6. Interferogram with noise Rotating kernel transformation has the ability to enhance straight-line features relative to non-straight-line features in the image, using directional information contained in a circular neighborhood. At the point lies upon an approximate straight-line segment (a piece of circle with smaller radian), the convolution output will be large when the kernel is oriented with the line segment. On the other hand, in a region containing a curved-line segment (a piece of circle with larger radian), the difference between the maximum value and minimum value at that point will not nearly so large. Therefore, the overall filtered image result is fairly easy to see by eye as shown in Figure 7. RKT method produces significantly enhanced circle boundaries feature while undesirable features are suppressed. Excellent result has been obtained in low contrast area. However, the operation tends to fill in short gaps in approximate straight lines, which produces one more undesirable circle for each cone area. Lee filtering algorithm can reduce speckle noise dramatically and also maintain the structure of an interferogram well, because this method is adaptive and the amount of filtering depends on three factors including the local coherence and the number of looks, and the local variation [31]. Also, Lee filer has a better ability to filter areas with high fringe rates. The fringes patterns are clearer and unbroken in the adaptively filtered images. IV. CONCLUSIONS This paper implemented and compared Goldstein filter, rotating kernel transformation and Lee filter for speckle noise reduction based on a simulated noisy interfermetric SAR phase image. As shown in Figure 7, Goldstein filter and Lee filter have a better ability to maintain the real structure of phase image with clear and unbroken fringes patterns. Furthermore, there are still a few small spot noise left on the edge of circle in Figure 7 (b). Comprehensively, most effective approach to reduce speckle noise as well as preserve the fringe in interferometric SAR image is by using Lee filter based on the experimental results. In general, the effect of noise reduction is better when the algorithm is more complicated led to larger computational complexity, so two aspects need to be comprehensively considered in noise reduction process: the required accuracy in practical application and the processing duration. Choosing a proper method is necessary which depends on the different purposes of application of InSAR. For instance, the relative complicated algorithms such as Lee filtering algorithm that will obtain higher resolution interferometric SAR images with perfect accuracy for military purpose, should be conducted, even though spending much more computation time and more money. On the contrary, finding an easier, more effective solution is a good way to apply the noise reduction algorithms only with simple computations on the interferometric SAR images that aim to observe forest or classify of vegetation. Also, second-time or multiple combined noise reduction is highly recommended, which can preserve edge information well and decrease phase noise dramatically at the cost of adding a little computation. However, more experiments need to be developed for testing repetition times, in order to acquire optimized

6 JOURNAL OF COMPUTERS, VOL. 9, NO. 4, APRIL balance between lower computation and better noise reduction effect. The paper agrees that it is on the list of things worth studying. (a) Noisy interferogram SAR image (b) Goldstein filter result (c) RKT result Figure 7. Filtered interferogram image (d) Lee filter result ACKNOWLEDGMENT We would like to acknowledge and thank Dr. Guang Liu, a research scientist at CEODE, and Dr. Jinghui Fan, a research scientist at AGRS, who are both respectable, responsible and resourceful scholars. Without their enlightening instruction, impressive kindness and patience, We could not have completed the paper. We are grateful to the anonymous referees for the their valuable comments and suggestions to improve the presentation of this paper. We are really appreciated all efforts from them. REFERENCES [1] H. A. Zebker, S. N. Madsen, J. Martin, and K. B. Wheeler, The TOPSAR interferometric radar topographic mapping instrument, Geoscience and Remote Sensing, IEEE Transactions on, vol.30, no.5, pp.933,940, Sep [2] G. Peltzer, K. W. Hudnut, and K. L. Feigl, Analysis of coseismic surface di.splacement gradients using radar interferometry&colon, New insights into the Landers earthquake, J. Geophys. Res., 99: , [3] R. M. Goldstein, Satellite radar interferometry for monitoring ice-sheet motion: application to an Antarctic ice stream, Science, 262: , [4] J. O. Hagberg, L. M. H. Ulander, and J. Askne, Repeat-pass SAR interferometry over forested terrain, Geoscience and Remote Sensing, IEEE Transactions on, vol.33, no.2, pp.331, 340, Mar [5] R. M. Goldstein and H. A. Zebker, Interferometric radar measurement of ocean surface currents, Nature, vol. 328, pp , [6] P. Gamba, B. Houshmand, and M. Saccani, Detection and extraction of buildings from interferometric SAR data, Geoscience and Remote Sensing, IEEE Transactions on, vol.38, no.1, pp.611, 617, Jan [7] R. Bamler and P. Hartl, Synthetic aperture radar interferometry, Inverse Problems, vol. 14, pp. R1-54, [8] Y. Zhang, H. Li, X. Wang, and D. Wu, Edge extraction of marine oil spill in SAR images, Challenges in Environmental Science and Computer

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8 JOURNAL OF COMPUTERS, VOL. 9, NO. 4, APRIL Yifei Chen received her B.S. degree in electrical & information engineering from Beijing University of Technology, Beijing, China in June 2010 and her M.S. degree in electrical engineering from The George Washington University, Washington, DC, U.S in August She is currently working towards her M.S. degree at Beihang University, Beijing, China, majoring electrical & communication engineering. Her primary research interests include synthetic aperture radar images processing and software defined instruments & RF minitransceivers. Huaping Xu received her Ph.D. in the Department of Electronic & Information Engineering from Beihang University, Beijing, China in December She is currently working as an associate professor at Beihang University, Beijing, China, Department of Electronic & Information Engineering. Her primary research interests include interferometric synthetic aperture radar and synthetic aperture radar image processing.