Adaptive image estimation based on multiplicative superposition

Abstract

A nonlinear adaptive filtering approach is applied to the problem of estimating images corrupted by multiplicative noise. With a pointwise digital model of multiplicative noise, the problem of obtaining a minimum mean squared error estimate of a true image from an observed noisy image and the statistical properties of the degrading noise field is posed. The approach presented in this paper is to perform image estimation with locally adaptive estimating operators that display the property of multiplicative superposition. Optimal point and multipoint adaptive estimating operators are formulated. Image processing algorithms are developed based on the calculation of local statistics estimates, Taylor series approximations to optimal formulas, and the normalization of data by local multiplicative sample means. Both adaptive and edge-adaptive implementations are investigated. The image processing results of single-point and two-point algorithms are given; the resulting images are noise-smoothed both visually and in mean squared error. The image processing algorithms are compared with other known methods of multiplicative filtering and estimation such as adaptive homomorphic point filtering.