PDE-Based Research On Image Filtering Methods

With the development of multi-media technology, image has become one of the major sources of information throughout peoples’daily life, and obtaining high definition pic-tures is intensely desired by many fields. However, the reality is the image is quite vul-nerable to noise during the process of acquisition and transportation. Consequently, im-proving the performance of smoothing methods has significant meanings to high quality images. Recent years, image filtering model based on partial differential equations has been among the most important approaches by its unique advantages. Though some achievements have been made, there are still some shortcomings needed to be overcome, such as edge blur, the birth of "blob" and other problems. Therefore, it is necessary to improve the models.The paper focuses on research of image filtering methodologies based on partial dif-ferential equations, in which a self-adaptive forward-and-backward divergent diffusion model is proposed from the procedure-oriented view. The model selects an S-curve function that possesses both positive and negative values as the diffusion coefficient in order to enhance image edges. Then the second-order mixed partial derivative is intro-duced to extract more information from the adjacent area to protect sharp jump discon-tinuities. Besides the measures mentioned above, the adaptive fidelity term and gradient threshold are set up to avoid the isolated noise being intensified due to a magnifying gradient value.Secondly, from the procedure-oriented angle, a self-adaptive TV model based on lo-cal information is created. To protect the image edges, the second-order mixed partial derivative is brought into gradient of energy function, and at the same time, the noise visibility function based on local information is designed as the control parameter to enhance visual effects. Additionally, adaptive weight coefficient is set up to weaken the level of which the isolated noise is intensified. Numerical simulation results reveal that the improved models have better perfor-mance in terms of visual effects and SNR, PSNR when comparing with traditional ones, are validated to be rational and effective, which could be applied to remove noise in most cases.