We consider the blind separation of source layers from superimposed mixtures thereof, involving unknown motions and unknown mixing coefficients of layers in each mixture. Previous blind separation approaches for such problems assume motions to be uniform translations, and hence are limited for real world applications. In this paper, we develop a sparse blind separation algorithm to estimate both parameterized motions and mixing coefficients. Then, a novel reconstruction approach is presented to recover all layers, by utilizing not only the mixing model but also the statistical properties of natural images. The whole method can handle more general motions than translations, including scalings, rotations and other transformations. In addition, the number of layers is automatically identified, and all layers can be recovered even in the under-determined case where mixtures are fewer than layers. The effectiveness of this technology is shown in the experiments on two simulated mixtures of four layers, real photos containing transparency and reflections, and real crossfade images from videos.