Color image demosaicking is a key process in the digital imaging pipeline. In this paper, we present a rigorous
treatment of a classical demosaicking algorithm based on alternating projections (AP). Since its publication, the
AP algorithm has been wildly cited and served as a benchmark in a flurry of papers in the demosaicking literature.
Despite its impressive performances, a relative weakness of the AP algorithm is its high computational complexity.
In our work, we provide a rigorous analysis of the convergence of the AP algorithm based on the concept of
contraction mapping. Furthermore, we propose an efficient noniterative implementation of the AP algorithm in
the polyphase domain. Numerical experiments show that the proposed noniterative implementation achieves the
same results obtained by the original AP algorithm at convergence, but is about an order of magnitude faster
than the latter.