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This paper presents a new image-processing (IP) pipeline adopting an image-processing approach via nonlinear image-decomposition, for a digital color camera. This new IP pipeline is composed of four stages. At the first stage, with the multiplicative BV-G image-decomposition method, each primary color channel of observed raw color data mosaicked with the Bayer color filter array is decomposed as a product of two components. Its structural component corresponds to a cartoon signal-approximation and its texture component collects almost all oscillatory variations representing textures. At the second stage, each separated component is demosaicked with an interpolation method suitable to it. For demosaicing of the structural component, this paper employs our color-TV-regularization super-resolution deblurring-demosaicing method that can remove image blurs without producing ringing artifacts near edges. For interpolation of the texture component gathering most of observation noise, this paper employs a basic averaging-type demosaicing method that is robust against observation noise. At the third stage, white balancing, color enhancement and inverse gamma correction are applied to only the demosaicked structural component. At the final stage, the two processed components are combined. Our proposed IP pipeline succeeds in achieving color interpolation, denoising and deblurring, simultaneously.