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Introduction: In this paper, we deal with the demosaicing problem when the Bayer pattern is used. We propose a fast heuristic algorithm, consisting of three parts. Methods: In the first one, we initialize the green channel by means of an edge-directed and weighted average technique. In the second part, the red and blue channels are updated, thanks to an equality constraint on the second derivatives. The third part consists of a constant-hue-based interpolation. Results: We show experimentally how the proposed algorithm gives in mean better reconstructions than more computationally expensive algorithms.

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In order to precondition Toeplitz systems, we present a new class of simultaneously diagonalizable real matrices, the γ-matrices, which include both symmetric circulant matrices and a subclass of the set of all reverse circulant matrices. We define some algorithms for fast computation of the product between a γ-matrix and a real vector and between two γ-matrices. Moreover, we illustrate a technique of approximating a real symmetric Toeplitz matrix by a γ-matrix, and we show that the eigenvalues of the preconditioned matrix are clustered around zero with the exception of at most a finite number of terms.