The application of partial differential equation in interferogram denoising

Abstract

The presence of noise in interferograms is unavoidable, it may be introduced in acquisition and transmission. These random distortions make it difficult to perform any required processing. Removing noise is often the first step in interferograms analysis. In recent yeas, partial differential equations(PDEs) method in image processing have received extensive concern. compared with traditional approaches such as median filter, average filter, low pass filter etc, PDEs method can not only remove noise but also keep much more details without blurring or changing the location of the edges. In this paper, a fourth-order partial differential equation was applied to optimize the trade-off between noise removal and edges preservation. The time evolution of these PDEs seeks to minimize a cost function which is an increasing function of the absolute value of the Laplacian of the image intensity function. Since the Laplacian of an image at a pixel is zero if the image is planar in its neighborhood. these PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image .piecewise planar images look more nature than step images which anisotropic diffusion (second order PDEs)uses to approximate an observed image .The simulation results make it clear that the fourth-order partial differential equatoin can effectively remove noise and preserve interferogram edges.