Numerical simulation of ultrasound images can facilitate the training of sonographers. A realistic appearance of simulated ultrasonic speckle is essential for a plausible ultrasound simulation. An efficient and realistic model for ultrasonic speckle is the convolution of the ultrasound point-spread function with a parametrized distribution of point scatterers. Nevertheless, for a given arbitrary tissue, such scatterer distributions that would generate a realistic image are not known a priori, and currently there is no principled method to extract such scatterer patterns for given target tissues to be simulated. In this paper we propose to solve the inverse problem, in which an underlying scatterer map for a given sample ultrasound image is estimated. From such scatterer maps, it is also shown that a parametrization distribution model can be built, using which other instances of the same tissue can be simulated by feeding into a standard speckle generation method. This enables us to synthesize images of different tissue types from actual ultrasound images to be used in simulations with arbitrary view angles and transducer settings. We show in numerical phantoms and actual physical tissue that the appearance of the synthesized images closely match the real images.