Generalized Statistical Complexity of SAR Imagery

Abstract

Abstract.A new generalized Statistical Complexity Measure (SCM) was proposed by Rosso et al in 2010. It is a functional that captures the notions of order/disorder and of distance to an equilibrium distribution. The former is computed by a measure of entropy, while the latter depends on the definition of a stochastic divergence. When the scene is illuminated by coherent radiation, image data is corrupted by speckle noise, as is the case of ultrasound-B, sonar, laser and Synthetic Aperture Radar (SAR) sensors. In the amplitude and intensity formats, this noise is multiplicative and non-Gaussian requiring, thus, specialized techniques for image processing and understanding. One of the most successful family of models for describing these images is the Multiplicative Model which leads, among other probability distributions, to the G 0 law. This distribution has been validated in the literature as an expressive and tractable model, deserving the "universal" denomination for its ability to describe most types of targets. In order to compute the statistical complexity of a site in an image corrupted by speckle noise, we assume that the equilibrium distribution is that of fully developed speckle, namely the Gamma law in intensity format, which appears in areas with little or no texture. We use the Shannon entropy along with the Hellinger distance to measure the statistical complexity of intensity SAR images, and we show that it is an expressive feature capable of identifying many types of targets.

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

“…where h : (0, ∞) → [0, ∞) is a strictly increasing function with h(0) = 0 and φ : (0, ∞) → [0, ∞) is a convex function such that 0 φ(0/0) = 0 and 0 φ(x/0) = lim x→ ∞ φ(x)/x. Following Almeida et al [2], we will only employ the Hellinger divergence which is also a distance, for which h(y) = y/2, 0 ≤ y < 2 and φ(x) = ( √ x − 1) 2 , and we define the Statistical Complexity of coordinate (i, j) in an intensity SAR image as the product…”

“…Almeida et al [2] employed this idea to the analysis of intensity SAR data. They used the Shannon entropy along with the Hellinger distance between a G 0 and a gamma distribution.…”