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In this paper, a fractional calculus operator for image denoising is constructed based on the characteristic of local entropy and the gradient feature, and an adaptive fractional calculus image denoising algorithm is proposed. First, the effects on the entropy and gradient by noise are analyzed, respectively. Second, the noise points are regarded as small probability events in an image, and the noise points, edges, texture regions, and smooth regions are divided combining with the local structure. Finally, for improving the image denoising effect, we consider employing different fractional orders to deal with different pixels and a piecewise function is constructed to make the differential order to be adaptive. The function is with respect to the local entropy and gradient on the pixel. The experimental results show that the peak signal-to-noise ratio and the entropy (ENTROPY) of the proposed adaptive fractional calculus image denoising algorithm are higher than that of the other algorithms compared in this paper. The proposed algorithm can not only preserve image edges and texture information while removing the noise, but also obtain a good visual effect.

Image Denoising Algorithm Based on Entropy and Adaptive Fractional Order Calculus Operator