Multi-Resolution Aitchison Geometry Image Denoising for Low-Light Photography

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.