Trainable fourth-order partial differential equations for image noise removal

Iranian Journal of Numerical Analysis and Optimization

مقاله 1، دوره 11، شماره 2 - شماره پیاپی 20، آذر 2021، صفحه 235-260   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.67760.1002

نویسندگان

N. Khoeiniha^* ؛ S.M. Hosseini؛ R. Davoudi

Department of Applied athematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran.

چکیده

Image processing by partial differential equations (PDEs) has been an active topic in the area of image denoising, which is an important task in computer vision. In PDE-based methods for unprocessed image process ing, the original image is considered as the initial value for the PDE and the solution of the equation is the outcome of the model. Despite the advan tages of using PDEs in image processing, designing and modeling different equations for various types of applications have always been a challenging and interesting problem. In this article, we aim to tackle this problem by introducing a fourth-order equation with flexible and trainable coefficients, and with the help of an optimal control problem, the coefficients are determined; therefore the proposed model adapts itself to each particular application. At the final stage, the image enhancement is performed on the noisy test image and the performance of our proposed method is compared to other PDE-based models.

کلیدواژه‌ها

Partial Differential Equations؛ Image Processing؛ Image Denoising؛ Optimal Control

مراجع