Image smoothing with exponential functions

Noise reduction in images, also known as image smoothing, is an essential a nd first step before further processings of the image. The key to image smo othing is to preserve important features while removing noise from the imag e. Gaussian function is widely used in image smoothing. Recently it has bee n reported that exponential functions (value of the exponent is not equal t o 2) perform substantially better than Gaussian functions in modeling and p reserving image features. In this paper we propose a family of exponential functions, that include Gaussian when the value of the exponent is 2, for i mage smoothing. We experiment with a variety of images, artificial and real , and demonstrate that optimal results are obtained when the value of the e xponent is within a certain range.