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The goal of color superresolution reconstruction and demosaicing is to get an enhanced resolution image from raw single-chip data of Bayer color filter array. Two parts of regularization method, fidelity and regularization terms, are discussed in detail to solve the problem. Elastic net is successfully applied to variable-selection method; we utilize it as a novel fidelity term to improve performance and make the reconstructed image more suitable for human visual system. Piecewise linear framelet operators are recently adopted to image denoising, which are utilized to detect multiorientation variation of the signal in color correlation space. K R as green (G) minus red and K B as G minus blue are a color correlation space of low-pass signal, and luminance component contains most of the information of a full-color image. Thus, K R/K B plus luminance component is considered as a color correlation space for regularization. Experimental results show that our algorithm is efficient in removing visual artifact, preserving the edges of image with high-peak signal-to-noise ratio, and satisfying visual effect.