To address the key image interpolation issue in microgrid polarimeters, we propose a machine learning model based on sparse representation. The sparsity and non-local self-similarity priors are used as regularization terms to enhance the stability of an interpolation model. Moreover, to make the best of the correlation among different polarization orientations, patches of different polarization channels are joined to learn adaptive sub-dictionary. Synthetic and real images are used to evaluate the interpolated performance. The experimental results demonstrate that our proposed method achieves state-of-the-art results in terms of quantitative measures and visual quality.