curvelet techniques for analyzing radar polarimetric datasar polarimetric data consists of 32-bit...

ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

CURVELET TECHNIQUES FOR ANALYZING RADAR POLARIMETRIC DATA

Edmundo Simental, Mathematician Verner Guthrie, Physical Scientist

U.S. Army Engineer Research and Development Center Topographic Engineering Center

7701 Telegraph Road Alexandria, VA 22315-3864

[email protected] [email protected]

ABSTRACT Synthetic Aperture Radar (SAR) polarimetry data is useful for determining topographic and man-made features. Previous work has shown that polarimetric analysis is superior to using single channel imagery. Addition of extra polarization modes enables better discrimination and recognition of objects on the ground, and improved classification and modeling capability. Multiple bands, namely C, L, and P frequency, in various combinations, can be used to differentiate features that cannot otherwise be differentiated. However, SAR images are sometimes corrupted by noise due to random interference of electromagnetic waves. The noise degrades the quality of the images and makes interpretation, analysis, and classifications of these images difficult. Therefore, some noise reduction is necessary prior to the processing of these images. In this paper, we document initial efforts at image denoising based on a relatively new transform, namely the discrete curvelet transform. This transform is new enough that the fundamental theory is still under development and study. Using in-house, public domain, and commercial software, we develop computer algorithms for a very simple initial curvelet denoising paradigm for polarimetric images. Our effort concentrates on implementing a routine that offers efficient image reconstruction, stability and ease of implementation within our resources, low mathematical complexity, and curvelet theory understanding. Computational speed and denoising optimization are not a major concern in this effort. The curvelet-denoising paradigm has a high degree of promise to produce better quality images than wavelet-based reconstructions, visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Key Words: SAR, polarimetric, curvelets, image denoising, image classification

BACKGROUND

Synthetic Aperture Radar’s all-weather, day/night operation, sensitivity to the terrain environment, and wide area coverage has proven to be an exceptional sensor for terrain remote sensing. Most current operational radar sensors provide single polarization data. Image classification, feature extraction, and categorization is based on the received intensity. Excellent results have been obtained with these radars. However, uncertainties are often present that make reliable and accurate operations a difficult task if no additional data is available (Simental and Damron, 2001). Polarimetric radar data provides much more detailed information about the surface geometry, terrain cover, and subsurface discontinuities than image brightness alone (Elachi et al., 1990). It is known, for example, that the polarization of the incident radar waves and the physical structural characteristics of the illuminated features govern the polarization of the backscatter radar waves (Vander Sanden and Gross, 2001). These radar sets have also aided in vegetation discrimination as revealed by variation in density and structure (Evans, et al., 1986; Ranson and Sun, 1994). This type of information, only available in polarimetry data, is inestimable in remote sensing tasks.

Modern sensors are capable of providing highly accurate, efficient, satisfying, and nearly noise-free data, and sensor technology is continuously improving these sensors. In this era of computer gigabyte random access memory (RAM), gigahertz processing speed and terabyte data storage, software is constantly providing better, faster, and more powerful enhancements for information extraction, cleaner data, analysis, and product generation. One of the newer and more promising enhancements in recent years for promoting cleaner data is multi-resolution analysis, better known as wavelets.


The foregoing seems to indicate that the need for noise reduction research is retreating. However, these improved capabilities are somewhat offset by the constant interest for detection of very small features that may easily be obscured or even lost within very docile speckle image noise (Guthrie and Simental, 2003).

In the past few years, there has been a great interest in wavelet methods for image analysis operations including noise removal in images. The many hundreds of papers published in journals and numerous conference presentations throughout the scientific and engineering communities confirm this interest. Wavelets provide us with mathematical tools to describe object signals and datasets at different levels of resolution. Wavelets, or multi-resolution analysis, are among the greatest accomplishments in digital data analysis in recent years. Wavelets have moved the image and signal analysis field away from classical Fourier analysis. In previous research efforts we have employed wavelets and have obtained excellent results (Simental and Evans, 1997), (Simental et al., 2005). Wavelets, however, are not the optimum tool for all aspects of image analysis.

Wavelets have an inherent limit and on some image processing operations fail to provide adequate results. For example, two-dimensional wavelet transforms of images exhibit large wavelet coefficients along the edges in the image at all scales so that in a map of the large wavelet coefficients, one sees the edges of the image repeated at every scale. This normally leads to a relatively high mean squared error (MSE) in 2D operations. This failure of wavelets in 2D operation is well documented (Starck et al., 2002; Donoho and Duncan, 2000). Also, wavelets manage straight lines very well, but do not adequately manage curved lines in image anlaysis.

The new curvelet and ridgelet transforms were developed over several years in an effort to overcome wavelet limitations. Curvelets are an extension of wavelet technology. In our effort, the curvelet transform consists of a complex representation of an image using a series of backscatter (energy) measurements ranging across scale, orientation, and position. Each curvelet consists of a tight frame constrained over a slice of the Fourier domain. In the spatial domain, the curvelet is a scaled and rotated signal along the width and length. This allows for the curvelet to act like a needle at fine scale resolutions (Candés and Guo, 2001).

In this study, we analyze a multi-frequency, polarimetric SAR dataset to conduct denoising and decomposition techniques to aid in the separation and identification of terrain features. The dataset will be described and then the methods will be discussed. Finally, the results and conclusions will be presented. .

OBJECTIVES

The basic objective of this study is an attempt to remove noise from polarimetric SAR data in order to better exploit a limited polarimetric dataset for segmentation, feature extraction, classification, and terrain analysis. Full SAR polarimetric data consists of 32-bit floating-point complex numbers. Our limited dataset is 8-bit real number data scaled from 0.0 to 1.0 that represents power or intensity values. Tools that are employed for the rigorous analysis of polarimetric data require the complex numbered data, but it is possible to extract some information that is not available in single polarization data from limited polarimetric datasets. Additional objectives are to determine the usefulness of decomposition techniques and other algorithms using the denoised images when trying to characterize terrain features.

METHODOLOGY

Corresponding subimages in the HH, HV, and VV orientation were selected for denoising. The subimages have been pre-processed and are almost noise-free. To these subsets we have added a certain amount of random noise to simulate what one would expect in a noisy image. The HH, HV, and VV subimages are highly correlated, but noise distribution would not be expected to be identical in all three orientations. The noise was generated with a Gaussian distribution, mean zero, and standard deviation of plus/minus one. The noise is slightly different in each of the subimages and is isotropic distributed within the subimages. The figure below shows the noise distribution in the three orientations.


Figure 1. Gaussian Noise Distribution in the HH, HV, and VV orientation.

The curvelet transform of an image consists of splitting the image into three sub-bands, and each curvelet is defined by the parameters J, L, and K representing scale, orientation, and location, J = Scale L = Orientation K = Location The curvelet basis functions are:

γ(x,y) =ψ(x)ϕ(y)

ψ(x) = Gabor(x) Distributionϕ(y) = Gaussian Distribution

The curvelet is defined by;

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Figure 2 below shows the HH subimage in the curvelet domain.

Figure 2. HH subimage in the curvelet domain.

The low frequency or coarse resolution coefficients are stored at the center of figure 2. The concentric rectangles represent the coefficients at different resolutions. The outer rectangles correspond to higher frequencies or finer resolutions. There are four strips associated with each rectangle, hardly visible, corresponding to the four cardinal points; top, bottom, left, right. These are further subdivided in angular panels, but not visible in the figure. Each panel represents coefficients at a specified resolution and along specific orientations.

In our effort, in very simplistic terms, the curvelet transform is applied to the subimage and the denoising takes place in this domain. An inverse transform is applied to the curvelet-transformed image to revert back to the image domain. The result is a denoised image. The figure below is a simplistic diagram of the denoising procedure.

Figure 3. Denoising procedure.

The diagram shows the main steps, but clearly the denoising procedure is much more complex that what is

shown in the diagram. The “Coefficient Filtering” step is mathematically convoluted. Thresholding, cycle spinning, iterations, and tolerances are determined in this step.

The efficiency of the denoising algorithm is highly dependant on image content, the amount of noise, noise distribution, and image resolution. Denoising works best in clear, level areas, void of clutter and anomalies. Our chosen image contains enough noise to simulate an expected noisy image, substantial clutter around man-made features, has an elevation gradient, and contains several other anomalies, thereby giving the algorithm a severe test.


DATASET

The data used in this study is from the airborne synthetic aperture radar (AIRSAR) managed by the Jet Propulsion Laboratory, National Aeronautics and Space Administration (JPL/NASA). The instrument is mounted on a modified NASA DC-8 aircraft. The AIRSAR is a side-looking radar instrument and collects fully polarimetric data (POLSAR) at three radar wavelengths: C-band (5.6 cm), L-band (24.5 cm), and P-band (68 cm) (JPL Website, 2005 and Abundo et al., 1998).

The study area is in the Odenton, Maryland vicinity. This suburb in the Washington, D.C. metropolitan area is characterized by urban structures (residential, commercial buildings and roads), some open fields and rural parkland. The imagery was flown in 1995. Road construction and other man-made features have added to the changes in the area since 1995. Figure 4 shows the study area as recorded in AIRSAR Band C and HH polarization. Features include, but are not limited to, roads, fields, cropland, buildings, forest, bare ground, and powerlines. Previous studies by the authors examined the same data set with an emphasis on terrain feature classification (Simental et al., 2004) and polarimetry band ratios, decompositions and statistics. (Simental et al, 2005). The central part of the image shows open fields and cropland (banded areas) that are part of the U.S. Naval Academy Dairy Farm (not now in operation) in Gambrills, Maryland.

Quarter-quad Digital Orthophoto Quadrangles (DOQQs) were used to assist with ground truth of the area. These images, available from the United States Geological Survey (USGS), are digitized color infrared aerial photographs in GeoTIFF format with embedded geo-referenced information The DOQQs, a USGS Digital Elevation Model (DEM), National Land Cover Data (NLCD) from USGS, EarthSat imagery, and printed 7.5-minute topographic quadrangle maps were the sources of ground truth used for the AIRSAR radar data analysis. A subset of the mosaic of portions of six DOQQ color infrared images depicting the study area is shown in Figure 5. The banded areas are open field crops that represent strip farming where different crops are rotated from year to year.

Figure 4. AIRSAR (Chh) image of the Figure 5. DOQQ colored infrared subset study site of study area

RESULTS

The study area is represented by a 512 x 512 pixel image. The noisy image of the three polarizations are shown

in figures 6, 8, and 10. The denoised images are shown in figures 7, 9, and 11. The improvement in image quality can visually be detected, but the improvement is best illustrated by the Pauli decomposition (Figures 12 and 13).


Figure 6. Noisy Chh image. Figure 7. Denoised Chh image.

Figure 8. Noisy Chv image. Figure 9. Denoised Chv image.


Figure 10. Noisy Cvv image Figure 11. Denoised Cvv image

Figure 12 depicts the study area and shows a Pauli decomposition RGB composite of the noisy images of the C-

band in which the CHH and CVV subtraction is displayed in red, the CHH and CVV addition is displayed in blue and the cross-polarization (CHV) is displayed in green. Figure 13 shows the restored (denoised) image using the same Pauli decomposition techniques. The flat fields and roads in both images appear mostly dark, but differences in texture and tone occur in the fields. Built-up areas are mostly magenta in color, representing a composite of red and blue inputs. This would imply that man-made structures are dominated by single-bounce (CHH minus CVV) and double-bounce (CHH plus CVV) effects. The vegetative canopy appears mostly green in the Pauli decomposition image; we expect that this is mostly due to the depolarizing effect (CHV) of canopy structure. The features in Figure 13 are smoother and show sharper edges than the noisy images. This should allow edge detection algorithms and classification routines to produce better results when performed on the individual denoised images.

Figure 12. Pauli decomposition Figure 13. Pauli decomposition of of noisy images denoised images


CONCLUSIONS

The curvelet transform is a higher dimensional generalization of the well-known wavelet transform. Candés and Donoho first introduced them in 1999 and great progress has been made since with application in several disciplines. One of the main features of curvelets is their ability to approximate very well curve singularities with very few coefficients. Although most of the work is still “beta” and the fundamental theory is still being developed, curvelet theory shows great promise in data analysis operations.

Our effort shows that curvelets are a viable tool for image denoising. We have tried several combinations of denoising methods including, “Box Complex”, “Diagonal Complex”, and “Diagonal Real”. The parameters within the curvelet have been varied in our quest for better image denoising. The C, L, and P radar polarimetry bands have been used in this effort, but only the C-band, “Box Complex” results are shown in this paper. The results are very encouraging. However, it is still not clear if this is the best method or the optimum parameters for our data. As previously stated, several factors determine the success or failure of denoising, and it is not expected that one curvelet method or group of parameters will “fit all” polarimetric data. More needs to be done, including the use of different and larger datasets. Other researchers have already done preliminary work on curvelet denoising. However, these efforts are specific dataset dependant, use synthetic data, or are otherwise not suitable for our data (Saevarsson et al., 2004), (Starck et al., 2003).

ACKNOWLEDGEMENTS

This effort was implemented using MatLab and IDL commercial-off-the-shelf (COTS) software and HyperCube, an in-house software package as well as CurveLab, a public domain package. HyperCube is an application software program directed to the analysis and display of multi and hyperspectral imagery (Pazak, 2004). Robert Pazak of the U.S. Army Engineer Research and Development Center (ERDC), Topographic Engineering Center (TEC), Alexandria, Virginia developed HyperCube. CurveLab is a collection of experimental computer files for the Fast Discrete Curvelet Transform (Candés et al., 2005). After our initial experience with the MatLab version, our reliance on CurveLab increased greatly and we wish to gratefully thank the authors. The authors would also like to thank Robert S.Rand, ERDC-TEC, for advice and consultation on curvelet techniques.

The authors would like to acknowledge the help of Mary Brenke and Peggy Diego of the ERDC-TEC imagery office for assistance in obtaining data for this project. We would also like to acknowledge Rebecca Ragon and Melody Clanton for graphics support.

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Candés, E. J., and F. Guo (2001). New multiscale transforms, minimum total variation synthesis: applications to edge-preserving image reconstruction, IEEE Transactions on Signal Processing, Vol. 82, pp. 1519 – 1543, December, 2001.

Candés, E., L. Demanet, D. Donoho, and L. Ying (2005). CurveLab, http://www.curvelab.org . Donoho, D., and M. Duncan (2000). Digital curvelet transform: strategy, implementation and experiments,

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Saevarsson, B.B., J. R. Sveinsson, and J. A. Bnediktsson (2004). Combined wavelet and curvelet denoising of SAR

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Simental, E.,V.Guthrie,B.Blundell (2005). Polarimetry band ratios, decompositions, and statistics for terrain characterization. Proceedings, Pecora 16 Conference, ASPRS, Sioux Falls, SD-USA October 2005.

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curvelet techniques for analyzing radar polarimetric datasar polarimetric data consists of 32-bit...

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