Monotonicity Prior for Cloud Tomography

We introduce a differentiable monotonicity prior, useful to express signals of monotonic tendency. An important natural signal of this tendency is the optical extinction coefficient, as a function of altitude in a cloud. Cloud droplets become larger as vapor condenses on them in an updraft. Reconstruction of the volumetric structure of clouds is important for climate research. Data for such reconstruction is multi-view images of each cloud taken simultaneously. This acquisition mode is expected by upcoming future spaceborne imagers. We achieve three-dimensional volumetric reconstruction through stochastic scattering tomography, which is based on optimization of a cost function. Part of the cost is the monotonicity prior, which helps to improve the reconstruction quality. The stochastic tomography is based on Monte-Carlo (MC) radiative transfer. It is formulated and implemented in a coarse-to-fine form, making it scalable to large fields.