To overcome shortcomings of digital images or to reproduce traditional film grains, some photographers add noise to digital image. In an effort to find a factor of preferable noise, the authors analyzed how a professional photographer introduces noise into black-and-white images and found two characteristics: (1) There is more noise in midtones than in highlights and shadows and (2) histograms in highlights are skewed toward shadows, and vice versa, while almost symmetrical in midtones. The authors also found that by approximating the symmetrical histograms by a Gaussian distribution and skewed ones by a chi-squared distribution, the noise could be reproduced to an extent that well satisfies the professional. Comparison of professional's noise to film grain showed that they have the following in common: (1) more noise in midtones but almost none in brightest and darkest region and (2) asymmetrical histograms in highlights and shadows. The authors think that these characteristics might be candidates for "good" noise" that allows simulation of traditional film photography.
Takehito Kurihara, Yoshitsugu Manabe, Naokazu Aoki, Hiroyuki Kobayashi, "Digital Image Improvement by Adding Noise: An Example by a Professional Photographer" in Journal of Imaging Science and Technology, 2011, pp 30503-1 - 30503-9, https://doi.org/10.2352/J.ImagingSci.Technol.2011.55.3.030503