Shannon-Cosine Wavelet Precision Integration Method for Image Enhancement Based on Fractional Partial Differential Equations

Fractional order partial differential equations have a wide range of applications in image processing. The solution of partial differential equations is generally obtained using the finite difference method, which still requires improvement in terms of efficiency and effectiveness. In this work, a multi-scale interpolative wavelet operator is constructed by means of Shannon-Cosine wavelets with interpolation, smoothness, compact support and other excellent properties. We use the wavelet operator instead of the finite difference operator to solve fractional-order partial differential equations. The proposed method can limit the artefacts and remove the noises appeared in the processed images effectively. In addition, for the loss of texture in the denoised image, we enhance the image by employing fractional order differential equations to improve the quality of the image. Finally, the biological sections images are taken as the examples to illustrate the effectiveness of the proposed method.