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Digital cameras sample scenes using a color filter array of mosaic pattern (e.g., the Bayer pattern). The demosaicking of the color samples is critical to the image quality. This paper presents a new color demosaicking technique of optimal directional filtering of the green-red and green-blue difference signals. Under the assumption that the primary difference signals (PDS) between the green and red/blue channels are low pass, the missing green samples are adaptively estimated in both horizontal and vertical directions by the linear minimum mean square-error estimation (LMMSE) technique. These directional estimates are then optimally fused to further improve the green estimates. Finally, guided by the demosaicked full-resolution green channel, the other two color channels are reconstructed from the LMMSE filtered and fused PDS. The experimental results show that the presented color demosaicking technique outperforms the existing methods both in PSNR measure and visual perception.