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We propose a novel approach to imaging that is not based on traditional optical imaging architecture. With the new approach, the image is reconstructed and visualized from random projections of the input object. The random projections are implemented within a single exposure by using a random phase mask which can be placed on a lens. For objects that have sparse representation in some known domain (e.g., Fourier or wavelet), the novel imaging systems have larger effective space - bandwidth product than conventional imaging systems. This implies, for example, that more object pixels may be reconstructed and visualized than the number of pixels of the image sensor. We present simulation results on the utility of the new approach. The proposed approach can have broad applications in efficient imaging capture, visualization, and display given ever increasing demands for larger and higher resolution images, faster image communications, and multidimensional image communications such as 3-D TV and display.