PDEs are very good candidates for image denoising. One of the most commonly used PDE based denoising technique is the second order non linear PDE proposed by Perona and Malik in 90s and its various versions. One probelm with the second order PDEs is the it may arise blocky effects in the image. This can be avoided by using fourth order PDEs.
Ref : Yu-Li You, M. Kaveh, Fourth Order Partial Differential Equations for Noise Removal?, IEEE Trans. Image Processing, vol. 9, no. 10, pp 1723-1730, October 2000
Jeny Rajan (2022). Image Denoising using Fourth Order PDE (https://www.mathworks.com/matlabcentral/fileexchange/7683-image-denoising-using-fourth-order-pde), MATLAB Central File Exchange. Retrieved .
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