In this paper, we examine the role of polarimetry in synthetic aperture radar (SAR) interferometry. We first propose a general formulation for vector wave interferometry that includes conventional scalar interferometry as a special case. Then, we show how polarimetric basis transformations can be introduced into SAR interferometry and applied to form interferograms between all possible linear combinations of polarization states. This allows us to reveal the strong polarization dependency of the interferometric coherence. We then solve the coherence optimization problem involving maximization of interferometric coherence and formulate a new coherent decomposition for polarimetric SAR interferometry that allows the separation of the effective phase centers of different scattering mechanisms. A simplified stochastic scattering model for an elevated forest canopy is introduced to demonstrate the effectiveness of the proposed algorithms. In this way, we demonstrate the importance of wave polarization for the physical interpretation of SAR interferograms. We investigate the potential of polarimetric SAR interferometry using results from the evaluation of fully polarimetric interferometric shuttle imaging radar (SIR)-C/X-SAR data collected during October 8-9, 1994, over the SE Baikal Lake Selenga delta region of Buriatia, Southeast Siberia, Russia.

Polarimetric SAR interferometry

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The Lee sigma filter was developed in 1983 based on the simple concept of two-sigma probability, and it was reasonably effective in speckle filtering. However, deficiencies were discovered in producing biased estimation and in blurring and depressing strong reflected targets. The advancement of synthetic aperture radar (SAR) technology with high-resolution data of large dimensions demands better and efficient speckle filtering algorithms. In this paper, we extend and improve the Lee sigma filter by eliminating these deficiencies. The bias problem is solved by redefining the sigma range based on the speckle probability density functions. To mitigate the problems of blurring and depressing strong reflective scatterers, a target signature preservation technique is developed. In addition, we incorporate the minimum-mean-square-error estimator for adaptive speckle reduction. Simulated SAR data are used to quantitatively evaluate the characteristics of this improved sigma filter and to validate its effectiveness. The proposed algorithm is applied to spaceborne and airborne SAR data to demonstrate its overall speckle filtering characteristics as compared with other algorithms. This improved sigma filter remains simple in concept and is computationally efficient but without the deficiencies of the original Lee sigma filter.

Improved Sigma Filter for Speckle Filtering of SAR Imagery

Speckle reduction is approached as a minimum mean-square error (MMSE) filtering performed in the undecimated wavelet domain by means of an adaptive rescaling of the detail coefficients, whose amplitude is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the variance and autocorrelation of the fading variable, and the wavelet filters only, without resorting to any model to describe the underlying backscatter. On the test image Lena corrupted by synthetic speckle, the proposed method outperforms Kuan's local linear MMSE filtering by almost 3-dB signal-to-noise ratio. When true synthetic aperture radar (SAR) images are concerned, empirical criteria based on distributions of multiscale local coefficient of variation, calculated in the undecimated wavelet domain, are introduced to mitigate the rescaling of coefficients in highly heterogeneous areas where the speckle does not obey a fully developed model, to avoid blurring strong textures and point targets. Experiments carried out on widespread test SAR images and on a speckled mosaic image, comprising synthetic shapes, textures, and details from optical images, demonstrate that the visual quality of the results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the wavelet decomposition avoids typical impairments often introduced by critically subsampled wavelet-based denoising.

Speckle removal from SAR images in the undecimated wavelet domain

Classification of radar images based on the information provided by individual pixels cannot generally produce satisfactory results due to speckle. The classification based on area analysis is therefore expected to be more accurate, as a uniform area, which usually consists of multipixels, provides reliable measurement statistics and texture characteristics. However, the area analysis requires partitions of uniform areas to be performed first. In this paper, an approach to the classification of radar images is developed based on two steps. First an image is partitioned into uniform areas (segments), and then these segments are classified. Both segmentation and classification are achieved by using the Gaussian Markov random field model. Test images are classified to demonstrate the method.

Segmentation and classification of vegetated areas using polarimetric SAR image data

This paper makes two contributions. It first introduces an algorithm for synthetic aperture radar (SAR) speckle reduction and edge sharpening. Existing speckle filtering algorithms can effectively reduce the speckle effect but unfortunately also, to some degree, smear edges and blur images. Even for unfiltered images, there is still a need for edge sharpening; since SAR sensors have limited bandwidths, leading to slow responses to sudden changes (smearing sharp edges). The proposed algorithm functions as an adaptive-mean filter. Edge crossing points are detected by using the second-order derivative of the Gaussian function as a wavelet transform function. A proper dilation scale factor enables the wavelet transform function to detect only edge crossings and ignore the local oscillations. Then in a moving window the mean filter is applied if there is no edge crossing point. Otherwise, averaging is only applied to the part of the window separated by edge crossing points. Consequently, the algorithm smooths uniform areas while it sharpens and enhances edges. Edges of the filtered images are generally sharper than the original. Similarities between the proposed filter and other popular speckle filters, such as the Lee, Kuan, and Frost filters, designated for SAR multiplicative noise, are analyzed. Another contribution of the paper is the evaluation of popular filters from the viewpoint of texture preservation. The evaluation is carried out using the first and second-order histograms. Possible distortions caused by filters are explained.

A.K. Milne

Papers

Segmentation and classification of vegetated areas using polarimetric SAR image data

Toward edge sharpening: a SAR speckle filtering algorithm