Recently, several red-green-blue-white (RGBW) color filter arrays (CFAs), which include highly sensitive W pixels, have been proposed. However, RGBW CFA patterns suffer from spatial resolution degradation owing to the sensor composition having more color components than the Bayer CFA pattern. RGBW CFA demosaicing methods reconstruct resolution using the correlation between white (W) pixels and pixels of other colors, which does not improve the red-green-blue (RGB) channel sensitivity to the W channel level. In this paper, we thus propose a demosaiced image post-processing method to improve the RGBW CFA sensitivity and resolution. The proposed method decomposes texture components containing image noise and resolution information. The RGB channel sensitivity and resolution are improved through updating the W channel texture component with those of RGB channels. For this process, a cross multilateral filter (CMF) is proposed. It decomposes the smoothness component from the texture component using color difference information and distinguishes color components through that information. Moreover, it decomposes texture components, luminance noise, color noise, and color aliasing artifacts from the demosaiced images. Finally, by updating the texture of the RGB channels with the W channel texture components, the proposed algorithm improves the sensitivity and resolution. Results show that the proposed method is effective, while maintaining W pixel resolution characteristics and improving sensitivity from the signal-to-noise ratio value by approximately 4.5 dB.