Dictionary methods have proved very useful in compressive sensing. Herein we show that, for dictionaries to represent the point spread functions (PSFs) of image formation in atmospheric turbulence, it is possible to construct dictionaries computationally. Computationally created dictionaries make unnecessary the exhaustive collection of PSF data, for arbitrarily large numbers of conditions of turbulence and optical image formation systems, while also reducing the overall number of dictionaries that need to be created and stored.