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The generalized Rényi image entropy as a noise indicator

Typically, entropy is used as a number indicating the amount of uncertainty or information of a source. That means that noise can not be distinguished from information by simply measuring entropy. Nevertheless, the Rényi entropy can be used to calculate the entropy in a pixel-wise basis. When the source of information is a digital image, a value of entropy can be assigned to each pixel of the image. Consequently, entropy histograms of images can be obtained. Entropy histograms give information about the image information contents in a similar way as image histograms give information about the distribution of gray-levels. Hence, histograms of entropy can be used to quantify differences in the information contents of images. In this paper, the behavior of entropy histograms of noisy images has been analyzed and results have been applied to define an index that measures the noise contents of natural images. The pixel-wise entropy of digital images has been calculated through the use of a spatial/spatial-frequency distribution. The generalized Rényi entropy and a normalized windowed pseudo-Wigner distribution (PWD) have been selected to define particular pixel-wise entropy. In this way, a histogram of entropy values has been derived. The shape of such a distribution of entropy indicates the amount of noise present in the image. Some examples are presented and discussed.