# An Edge-Enhancing Nonlinear Filter for Reducing Multiplicative Noise

## Mark A. Schulze

**Perceptive Scientific Instruments, Inc.**

League City, Texas
**San Jose, California**

10-11 February 1997
## Abstract

*Complete reference:*

M. A. Schulze. "An Edge-Enhancing Nonlinear Filter for Reducing Multiplicative Noise." In E. R. Dougherty and J. Astola, editors, Nonlinear
Image Processing VIII, Proc. SPIE, v. 3026, (1997) pp. 46-56.

This paper illustrates the design of a nonlinear filter for edge-enhancing smoothing of multiplicative noise using a morphology-based filter structure. This filter is called the Minimum Coefficient of Variation (MCV) filter. The coefficient of variation is the ratio of the standard deviation of a random process to its mean. For an image corrupted only by stationary multiplicative noise, the coefficient of variation is theoretically constant at every point. Estimates of the coefficient of variation indicate whether a region is approximately constant beneath the multiplicative noise or whether it contains significant image features. Regions containing edges or other image features yield higher estimates of the coefficient of variation than areas that are roughly constant. The MCV filter uses a morphological structure to direct low-pass filtering to act only over regions determined to be most nearly constant by measuring the coefficient of variation.

Examples of the use of the MCV filter are given on synthetic aperture radar (SAR) images of the earth. SAR images are corrupted by speckle, a predominantly multiplicative noise process. Therefore, the MCV filter is a good choice for reducing speckle without blurring edges. The MCV filter is useful for pre-processing in image analysis applications such as coastline detection in SAR images.

*Keywords:*
nonlinear filtering, multiplicative noise, edge enhancement, synthetic aperture radar, mathematical morphology

© Copyright 1997.

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Last Updated: 17 July 2003