Statistical model of the noise in speckle pattern and suboptimal digital image filtering method

A statistical analysis of the noise and mathematical model of speckle pattern are presented and an adaptive suboptimal digital image filtering method in space domain in view of the noise is proposed in this paper. A local variable -- parameter exponential transformation and normalization are first used to reduce the serious inhomogeneity of the grey level distribution caused by speckle diffraction halo. Then, the statistical characteristics of the noises in speckle pattern are analyzed and the mathematical model of speckle pattern is established. On the basis of the analysis and modelling, an adaptive suboptimal image filtering method that can simultaneously remove various noises in speckle pattern is described, in which, the characteristics of linear optimal filter and non-linear adaptive filter are combined and the local fringe direction is taken as an adaptive parameter to ensure that neighborhood statistics and filtering proceed within the maximum stable region of the processing point, besides, local statistical characteristics of the image are considered. Experimental results show that the statistical analysis of the noise and proposed mathematical model can rather accurately describe the characteristics of speckle pattern and the proposed filtering method can effectively remove various noises and remain useful information.