The Bayer and RGBW color filter array (CFA) raw images, denoted by <inline-formula> <tex-math notation="LaTeX">$I^{Bayer}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$I^{RGB}$ </tex-math></inline-formula>, respectively, have been widely used in consumer markets. In the demosaicking-first compression scheme, chroma subsampling is necessary prior to compressing <inline-formula> <tex-math notation="LaTeX">$I^{RGB}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$I^{RGBW}$ </tex-math></inline-formula>. Several linear interpolation-based chroma subsampling methods have been developed for <inline-formula> <tex-math notation="LaTeX">$I^{Bayer}$ </tex-math></inline-formula>, but no nonlinear interpolation-based chroma subsampling methods have targeted the above two CFA image types simultaneously. In this paper, we first propose a nonlinear interpolation-based, namely the cubic convolution interpolation-based (CCI-based), <inline-formula> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> block-distortion function for each <inline-formula> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> CFA block <inline-formula> <tex-math notation="LaTeX">$B^{CbCr}$ </tex-math></inline-formula>. Next, using the Cauchy-Schwarz inequality, we prove that the proposed block-distortion function is a convex function in the real domain, which further serves as the base of the initial subsampled chroma solution. Then, a CCI-based iterative method is proposed to improve the initial subsampled chroma solution. The results of comprehensive experimental tests using Bayer and RGBW CFA images created from the three RGB full-color datasets, namely IMAX, SCI (screen content images), and CI (classical images), demonstrate that on the Versatile Video Coding (VVC) platform VTM-11.0, the proposed method achieves substantial quality enhancement and quality-bitrate tradeoff merits of the reconstructed Bayer and RGBW CFA images compared with existing chroma subsampling methods.
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