Image processing using quadratic volterra filters

Linear image processing algorithms have received considerable attention during the last several decades. These algorithms are attractive in many applications as they are easy to analyze and computationally less intensive. Unfortunately, the basic hypotheses of stationarity and Gaussianity for the development of the linear signal processing algorithms do not hold for images. For example, linear filtering methods applied to an impulse-corrupted image tend to blur sharp edges and remove fine details. In addition, linear algorithms are unable to remove signal-dependent or multiplicative noise in images. Thus, to provide improved performance, image processing algorithms should take into account the nonlinear effects in the human visual system and the nonlinear behavior of the image acquisition systems. As a result there has been an increasing interest in the development of nonlinear image processing algorithms in recent years. In addition, due to a rapid decrease in the costs of computing, image storage, image acquisition, and image display, it has been more practical to implement complicated nonlinear image processing algorithms.