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A hybrid sigma filter for unbiased and edge-preserving speckle reduction

An enhanced version of Lee's sigma filter is derived and proposed for unbiased filtering of images affected by multiplicative noise with speckle statistics. Instead of the plain point value, a more accurate start value is first produced, and then fed to the procedure of conditional average. A robust estimate of the nonstationary mean is defined according to a decision rule borrowed from the FIR-median hybrid filters, thus improving the performance also for impulsive noise. The start value is provided by a nonlinear decision rule aimed at rejecting noise spikes, which is undertaken on the averages computed within four isotropically balanced pixel sets able to capture step edges and thin lines. The level range of pixels to be averaged, adaptively defined as the product of the space-variant mean estimate by the constant noise variance, is also forced to account for the imbalance of the noise distribution, for unbiased processing. Comparison tests performed on images affected by synthetic speckle, simulating both one-look and multi-look statistics, show significant improvements over the basic scheme, as well as over Kuan's and geometric filter, resulting in lower distortion between noise-free and processed images. Also visual comparisons on a true NASA/JPL AIRSAR image, establish the superiority of the novel scheme.