The College of Education for Pure Sciences, Department of Mathematics, discussed a master's thesis on (Numerical solution of second-order and higher-order partial differential equations based on image noise reduction methods)
The thesis presented by the researcher (Zahraa Raad Jawad)
Included that image noise reduction is a computer vision task whose primary goal is to remove unwanted noise from a given image while preserving all necessary details and relevant information. Edge detection during the generation of a smooth image is one of the required criteria for measuring the quality of the noise remover. Image noise reduction has been widely used in digital imaging, medical imaging, and document processing. Researchers have studied many different models based on second-order and higher-order PDE.
The aim of the thesis
To address the defect of obtaining a blurry image during noise removal and edge loss using TV- and TV- models, respectively. A new total variation model (NTV) is presented to remove noise in images based on a combination of total variation regularization that combines standard and total variation regularization. The (NTV) model is a second-order PDE. Another new model (YK-I) based on the equal operator direction and fourth-order partial differential equations is proposed to reduce the edge loss problem and preserve important image details. Fourth-order equations are effective in high-frequency regions, so the equal operator can regulate the propagation direction. Therefore, our proposed model can remove noise in the region while preserving important edges and details of the image. The thesis concludes that the efficiency and superiority of the proposed models are proven by applying them to a set of images and solving them numerically using the finite difference method (FDM). Image quality assessment (IQA) is used to compare the results obtained using the proposed models with those obtained using other models. Finally, the proposed models were powerful tools in achieving a balance between image smoothing and preserving edges and fine details, which reflects our goal of this study.