Current and upcoming wide-field, ground-based, broad-band imaging surveys promise to address a wide range of outstanding problems in galaxy formation and cosmology. Several such uses of ground-based data, especially weak gravitational lensing, require highly precise measurements of galaxy image statistics with careful correction for the effects of the point-spread function (PSF). The SHERA (SHEar Reconvolution Analysis) software simulates ground-based imaging data with realistic galaxy morphologies and observing conditions, starting from space-based data (from COSMOS, the Cosmological Evolution Survey) and accounting for the effects of the space-based PSF. This code simulates ground-based data, optionally with a weak lensing shear applied, in a model-independent way using a general Fourier space formalism. The utility of this pipeline is that it allows for a precise, realistic assessment of systematic errors due to the method of data processing, for example in extracting weak lensing galaxy shape measurements or galaxy radial profiles, given user-supplied observational conditions and real galaxy morphologies. Moreover, the simulations allow for the empirical test of error estimates and determination of parameter degeneracies, via generation of many noise maps. The public release of this software, along with a large sample of cleaned COSMOS galaxy images (corrected for charge transfer inefficiency), should enable upcoming ground-based imaging surveys to achieve their potential in the areas of precision weak lensing analysis, galaxy profile measurement, and other applications involving detailed image analysis.