Research On Image Denoising Based On L₀ Norm And Kernel Regression Model

With the rapid development of the computer technology,digital image has become one of the most important media for message exchange.However, in the process of image acquisition and transmission, because of various reasons, noise interference is inevitable, which could have massive impact on the subsequent image analysis and the spread of the image information. So to solve this problem, using image denoising is one of the most foundational and crucial treatment technology in the field of image processing and computer vision.As a foundamental mathematical tool the L0 gradient minimization model has been used for image smoothing successfully. The most impressive advantage of L0 gradient minimization is protecting the salient edges in the image processing. As an improvement of the total variation(TV) model which employs the L1 norm of the gradient, the LGM model performs better when processing images with the feature of piecewise constant. However, just like the TV model, the LGM model suffers, even more seriously, from the staircase effect and it fails to well preserve the texture in image.In recent decades, an image denoising method using the non-parameter data fitting approach based on the localized least squares has been proposed and has attracts lots of attention from image processing researchers. The kernel regression(KR) model, the most representative one, has been proved to present better visual effect and more accurate texture memory. But this method has the probability of serious flow-like effects and the image edges often blur because of their excessive smooth boundary.According to the analysis, the two methods just play complementary roles in the process of image denoising, so this paper proposes two novel schemes by combining above two models. The proposed models successfully avoid the disadvantages of both methods.First, this paper introduces an new effective fidelity term(KR) into the LGM model(L0 gradient minimization-kernel regression, LGM-KR). It is demonstrated that the proposed method presents the promising ability to remove the noise by numbers of experiments, meanwhile, the edges and texture information is well preserved.Second, we extend the LGM-KR model by replacing L0 gradient minimization by L0 two-order partial derivative minimization, and the extended model is used for image denoising combined with KR model. As a result, this scheme has more predominant performance due to the high-order feature.