Comparison of PDE based and other techniques for speckle reduction from digitally reconstructed holographic images

Abstract

In this paper, the partial differential equation (PDE) based homomorphic filtering technique is proposed for speckle reduction from digitally reconstructed holographic images based on the concepts of complex diffusion processes. For digital implementations, the proposed scheme was discretized using finite differences scheme. Further, the performance of the proposed PDE-based technique is compared with other speckle reduction techniques such as homomorphic anisotropic diffusion filter based on extended concept of Perona and Malik (1990) [2], homomorphic Weiner filter, Lee filter, Frost filter, Kuan filter, speckle reducing anisotropic diffusion (SRAD) filter and hybrid filter in the context of digital holography. For the comparison of various speckle reduction techniques, the performance is evaluated quantitatively in terms of all possible parameters that justify the applicability of a scheme for a specific application. The chosen parameters are mean-square-error (MSE), normalized mean-square-error (NMSE), peak signal-to-noise ratio (PSNR), speckle index, average signal-to-noise ratio (SNR), effective number of looks (ENL), correlation parameter (CP), mean structure similarity index map (MSSIM) and execution time in seconds. For experimentation and computer simulation MATLAB 7.0 has been used and the performance is evaluated and tested for various sample holographic images for varying amount of speckle variance. The results obtained justify the applicability of proposed schemes.