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A complex diffusion process based on Schro??dinger wave equation is proposed and implemented as a nonlinear filter to perform homomorphic filtering for reducing speckle noise from digital images. Due to the multiplicative and complex nature of speckle noise it becomes practically difficult to restore a degraded image, hence a homomorphic filtering approach is used for the reduction of the same. The homomorphic filtering refers to applying logarithm transformation on input image to convert the multiplicative noise to additive one, applying complex diffusion based inverse filter and finally taking the exponential of filter output to produce the restored image. For digital implementations, the proposed PDE is discretized using finite difference scheme. For software implementation MATLAB 7.0 was used and performance of the proposed scheme was evaluated for different speckle noise variance of the gray test images both qualitatively and quantitatively and the results obtained justify the applicability of proposed scheme.