Color demosaicking with an image formation model and adaptive PCA

Color demosaicking is an ill-posed inverse problem of image restoration. The performance of a color demosaicking algorithm depends on how thoroughly it can exploit domain knowledge to confine the solution space for the underlying true color image. We propose an ℓ ₁ minimization technique for color demosaicking that exploits spectral and spatial sparse representations of natural images jointly. The spectral sparse representation is derived from a physical image formation model; the spatial sparse representation is based on a windowed adaptive principal component analysis. In some of most challenging cases of color demosaicking, the new technique outperforms many existing techniques by a large margin in PSNR and achieves higher visual quality.