Optimized Color Filter Arrays for Sparse Representation-Based Demosaicking

Demosaicking is the problem of reconstructing a color image from the raw image captured by a digital color camera that covers its only imaging sensor with a color filter array (CFA). Sparse representation-based demosaicking has been shown to produce superior reconstruction quality. However, almost all existing algorithms in this category use the CFAs, which are not specifically optimized for the algorithms. In this paper, we consider optimally designing CFAs for sparse representation-based demosaicking, where the dictionary is well-chosen. The fact that CFAs correspond to the projection matrices used in compressed sensing inspires us to optimize CFAs via minimizing the mutual coherence. This is more challenging than that for traditional projection matrices because CFAs have physical realizability constraints. However, most of the existing methods for minimizing the mutual coherence require that the projection matrices should be unconstrained, making them inapplicable for designing CFAs. We consider directly minimizing the mutual coherence with the CFA's physical realizability constraints as a generalized fractional programming problem, which needs to find sufficiently accurate solutions to a sequence of nonconvex nonsmooth minimization problems. We adapt the redistributed proximal bundle method to address this issue. Experiments on benchmark images testify to the superiority of the proposed method. In particular, we show that a simple sparse representation-based demosaicking algorithm with our specifically optimized CFA can outperform LSSC [1]. To the best of our knowledge, it is the first sparse representation-based demosaicking algorithm that beats LSSC in terms of CPSNR.