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This paper addresses extracting two layers from an image where one layer is smoother than the other. This problem arises most notably in intrinsic image decomposition and reflection interference removal. Layer decomposition from a single-image is inherently ill-posed and solutions require additional constraints to be enforced. We introduce a novel strategy that regularizes the gradients of the two layers such that one has a long tail distribution and the other a short tail distribution. While imposing the long tail distribution is a common practice, our introduction of the short tail distribution on the second layer is unique. We formulate our problem in a probabilistic framework and describe an optimization scheme to solve this regularization with only a few iterations. We apply our approach to the intrinsic image and reflection removal problems and demonstrate high quality layer separation on par with other techniques but being significantly faster than prevailing methods.

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