Optical eigenmode imaging (OEI) is an interesting nonlocal imaging method but has the drawback that the completeness of eigenmodes used in OEI is hard guarantee. This may lead to significant blurring of the reconstructed images. Here we show that in OEI with a sparse constraint, the correlation between the original target and the recovered image can be extremely close to 1 by retrieving lost information, and the compressibility is enhanced. In addition, high-quality images can be received for a wide range of both object and system parameters.