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Color mosaic sampling schemes are widely used in digital cameras. Given the resolution of CCD sensor arrays, the image quality of digital cameras using mosaic sampling largely depends on the performance of the color demosaicking process. A common problem with existing color demosaicking algorithms is an inconsistency of sample interpolations in different primary color channels, which is the cause of the most objectionable color artifacts. To cure the problem, we propose a new primary-consistent soft-decision framework (PCSD) of color demosaicking. In the PCSD framework, we make multiple estimates of a missing color sample under different hypotheses on edge or texture directions. The estimates are made via a primary consistent interpolation, meaning that all three primary components of a color are interpolated in the same direction. The final estimate of a color sample is obtained by testing different interpolation hypotheses in the reconstructed full-resolution color image and selecting the best via an optimal statistical decision or inference process. A concrete color demosaicking method of the PCSD framework is presented. This new method eliminates certain types of color artifacts of existing color demosaicking methods. Extensive experimental results demonstrate that the PCSD approach can significantly improve the image quality of digital cameras in both subjective and objective measures. In some instances, our gain over the competing methods can be as much as 7dB.