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We describe two methods by which foveated (variable resolution) images can be created using the techniques of compressive sensing (CS). Foveated sampling (FS) combines a linear shift-variant foveation filter with the CS measurement operator. Foveated sampling and reconstruction (FSR) combines the foveation filter with the CS measurement operator and also with the sparse signal estimation algorithm used to reconstruct images. Both methods are shown to provide accurate reconstruction of foveated images at much higher compression levels than uniform resolution CS.