Efficient Separation of Convolutive Image Mixtures

Convolutive mixtures of images are common in photography of semi-reflections. They also occur in microscopy and tomography. Their formation process involves focusing on an object layer, over which defocused layers are superimposed. Blind source separation (BSS) of convolutive image mixtures by direct optimization of mutual information is very complex and suffers from local minima. Thus, we devise an efficient approach to solve these problems. Our method is fast, while achieving high quality image separation. The convolutive BSS problem is converted into a set of instantaneous (pointwise) problems, using a short time Fourier transform (STFT). Standard BSS solutions for instantaneous problems suffer, however, from scale and permutation ambiguities. We overcome these ambiguities by exploiting a parametric model of the defocus point spread function. Moreover, we enhance the efficiency of the approach by exploiting the sparsity of the STFT representation as a prior.