Benefits from a speckle noise family on a coherent imaging transmission

We analyze image transmission in a coherent imaging system, in the presence of speckle noise modeled with the family of Gamma probability density functions of varying order. It is demonstrated that speckle noise can improve the transmission of a coherent image. Exact analytical expressions are obtained for both the best achievable performance and the optimal amount of speckle noise maximizing the transmission efficacy. These expressions allow us to analyze and control the conditions under which the coherent imaging system can take advantage of the speckle noise. The influence of the contrast in the coherent image, and of the order of the Gamma probability density describing the statistical fluctuations of the speckle, are given special attention. These results make a contribution to the understanding of the mechanisms of improvement by noise in nonlinear information processing.