In the low-photon imaging regime, noise in the image sensors is dominated by shot noise, best modeled statistically as Poisson distribution. In this work, we show that the Poisson likelihood function is very well matched with the Bayesian estimation of the "difference of log of contrast of pixel intensities." More specifically, our work is rooted in statistical compositional data analysis, whereby we reinterpret the Aitchison geometry as a multi-resolution analysis in the log-pixel domain. We demonstrate that the difference-log-contrast has wavelet-like properties that correspond well with the human visual system, while being robust to illumination variations. We derive a denoising technique based on an approximate conjugate prior for the latent Aitchison variable that gives rise to an explicit minimum mean squared error estimation. The resulting denoising technique preserves image contrast details that are arguably more meaningful to human vision than the pixel intensity values themselves.

We propose corrupted reference image quality assessment (CRIQA), a novel foundation for reasoning about image quality and image denoising problems jointly. In order to assess the visual quality of a processed image relative to an ideal reference image (not provided), we predict the full-reference image quality assessment (FRIQA) scores of denoised images without having the direct access to the ideal reference image, but with the help of the observed corrupted image, instead. Our simulation studies verify that the CRIQA scores of denoised images indeed agree with the corresponding FRIQA scores, and human subject studies confirm that CRIQA scores are more consistent with the perceived image denoising quality than the NRIQA scores. We demonstrated the usefulness of CRIQA with an application in denoising parameter tuning.

The distribution of real camera sensor is well approximated by Poisson, and the estimation of the light intensity signal from the Poisson count data plays a prominent role in digital imaging. It is highly desirable for imaging devices to carry the ability to assess the performance of Poisson image restoration. Drawing on a new category of image quality assessment called corrupted reference image quality assessment (CR-QA), we develop a computational technique for predicting the quality score of the popular structural similarity index (SSIM) without having the direct access to the ideal reference image. We verified via simulation that the CR-SSIM scores indeed agrees with the full reference scores; and the visually optimal denoising experiments performed on real camera sensor data give credibility to the impact CR-QA has on real imaging systems.