The Study On Fourth-order Partial Differential Equations Filtering Methods For The Different Types Of Noise And Their Applications

Image signals are often suffered from noise which including Speckle noise,Impulsive noise, Gaussian noise and Poisson noise in acquisition, transmission,conversion or terminal processing, which usually degrades the visual quality of theimages. Image filtering has become an important part of image preprocessing, whoseresult will have an important and direct effect on the validity and reliability of theimage analysis and image recognition. In this paper, the research is mainly focused onthe filtering of the speckle noise of the electronic speckle pattern interferencetechnology (ESPI) fringe patterns and phase patterns and the impulse noise of thestandard image, and it proposed the new fourth-order partial differential equation(PDE), the fourth-order oriented PDE and the fourth-order PDE with the detectiontechniques filtering model.ESPI is a kind of non-destructive, whole-field optical measurement technique,which has been widely used in nondestructive testing, optical rough surfacedisplacement, deformation measurement, vibration analysis, and other fields.However, Speckle become the information carrier while becoming the noise, and theESPI fringe patterns and phase patterns always have strong noises which seriouslyaffect the ESPI phase extraction. For the ESPI fringe patterns and phase patterns withthe strong speckle noise, this paper derived the new fourth-order PDE model availablefor the fringes with low density and the fourth-order oriented PDE model available forthe fringes with high density, and compared with the related PDE models. Theexperimental result showed that the proposed models can suppress impulse noiseeffectively, and keep image edges at the same time.In addition, for the standard image with the impulse noise, this paper also derivedthe fourth-order PDE with the detection techniques filtering model. This method usedthe two-stage iterative method which is first detected and then filtering for imageprocessing, that is, first to use the TSM method to identify pixels which are likely tobe corrupted by noise, and then use the new fourth-order PDE method to remove thenoise. The experimental result showed that the fourth-order PDE with the detectiontechniques filtering model can maintain image details as well as smooth noise.