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Color Filter Arrays: A Design Methodology

In the companion report [14], we have shown that a full color image sampled with a rectangular color filter array (CFA) is equivalent to the frequency domain multiplexing of multiplex components: a luminance component (luma) at the baseband and several chrominance components (chromas) at high frequency bands. A matrix, called the frequency structure of a CFA, is defined to represent this modulation, with which we can easily analyze the characteristics of CFAs. The frequency structure can be computed by applying the symbolic discrete Fourier transform (DFT) to the CFA pattern. In this paper, we present a CFA design methodology in the frequency domain. In this methodology, a good frequency structure of the CFA is first selected, mainly according to the following criteria: (i). the number of nonzero chromas should be as small as possible; (ii). the distance between nonzero multiplex components should be as large as possible; and (iii). dependent (e.g., identical, negative, or conjugate) chromas should be as many as possible; and then the optimal primary CFA patterns are computed by minimizing the norm of the demosaicking matrix under constraints that: (i). the primary CFA patterns are all real and nonnegative; and (ii). their sum is an all-one matrix. The constraints can be determined by applying the inverse symbolic DFT to the specified frequency structure. Finally, the desired CFA pattern is the symbolic sum of the optimal primary CFA patterns. Using our methodology, a series of new CFA patterns are found which outperform the currently commercialized and published ones. Experiments demonstrate the effectiveness of our CFA design methodology and the superiority of our new CFA patterns.