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Last Update: 2006.09.14
Derive a novel edge detector, the instantaneous coefficient of variation (ICOV), for speckle edge detection; and based on the ICOV, design and implement speckle reducing anisotropic diffusion (SRAD) algorithm for ultrasounic (radar) imagery.
Speckle, a form of multiplicative, locally correlated noise, plagues imaging applications such as medical ultrasound image interpretation. For images that contain speckle, a goal of enhancement is to remove the speckle without destroying important image features. Applications where speckle removal is desired include region-based object detection, segmentation, and classification. The reducing filters have originated mainly in the synthetic aperture radar (SAR) community. The most widely cited and applied filters in this category include the Lee, Frost, Kuan, and Gamma MAP filters. The Lee and Kuan filters have the same formation, although the signal model assumptions and the derivations are different. Essentially, both the Lee and Kuan filters form an output image by computing a linear combination of the center pixel intensity in a filter window with the average intensity of the window. So, the filter achieves a balance between straightforward averaging (in homogeneous regions) and the identity filter (where edges and point features exist). This balance depends on the coefficient of variation inside the moving window.
The Frost filter also strikes a balance between averaging and the all-pass filter. In this case, the balance is achieved by forming an exponentially shaped filter kernel that can vary from a basic average filter to an identity filter on a pointwise, adaptive basis. Again, the response of the filter varies locally with the coefficient of variation. In case of low coefficient of variation, the filter is more average-like, and in cases of high coefficient of variation, the filter attempts to preserve sharp features by not averaging.
More recently, the Gamma maximum a posterior (MAP) and extended versions of the Lee filter and the Frost filter have been introduced to alter performance locally according to three cases. In the first case, pure averaging is induced when the local coefficient of variation is below a lower threshold. Above a higher threshold, the filter performs as a strict all-pass (identity) filter. When the coefficient of variation exists in between the two thresholds, a balance between averaging and the identity is computed (as with the standard Lee and Frost filters).
Although the existing despeckle filters are termed as "edge preserving" and "feature preserving," there exist major limitations of the filtering approach. First, the filters are sensitive to the size and shape of the filter window. Given a filter window that is too large (compared to the scale of interest), over-smoothing will occur and edges will be blurred. A small window will decrease the smoothing capability of the filter and will leave speckle. In terms of window shape, a square window (as is typically applied) will lead to corner rounding of rectangular features that are not oriented at perfect 90 degrees rotations, for example. Second, the existing filters do not enhance edges -- they only inhibit smoothing near edges. When any portion of the filter window contains an edge, the coefficient of variation will be high and smoothing will be inhibited. Therefore, noise/speckle in the neighborhood of an edge (or in the neighborhood of a point feature with high contrast) will remain after filtering. Third, the despeckle filters are not directional. In the vicinity of an edge, all smoothing is precluded, instead of inhibiting smoothing in directions perpendicular to the edge and encouraging smoothing in directions parallel to the edge. Last, the thresholds used in the enhanced filters, although motivated by statistical arguments, are ad hoc improvements that only demonstrate the insufficiency of the window-based approaches. The hard thresholds that enact neighborhood averaging and identity filtering in the extreme cases lead to blotching artifacts from averaging filtering and noisy boundaries from leaving the sharp features unfiltered.
In this project, we have outlined a partial differential equation (PDE) approach to speckle removal that we call speckle reducing anisotropic diffusion (SRAD). The PDE-based speckle removal approach allows the generation of an image scale space (a set of filtered images that vary from fine to coarse) without bias due to filter window size and shape. SRAD not only preserves edges but also enhances edges by inhibiting diffusion across edges and allowing diffusion on either side of the edge. SRAD is adaptive and does not utilize hard thresholds to alter performance in homogeneous regions or in regions near edges and small features. The new diffusion technique is based on the same minimum mean square error (MMSE) approach to filtering as the Lee (Kuan) and Frost filters. In fact, we show that the SRAD can be related directly to the Lee and Frost window-based filters. So, SRAD is the edge sensitive extension of conventional adaptive speckle filter, in the same manner that the original Perona and Malik anisotropic diffusion is the edge sensitive extension of the average filter. In this sense, we extend the application of anisotropic diffusion to applications such as radar and medical ultrasound in which signal-dependent, spatially correlated multiplicative noise is present.
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