Bayesian methods for low-illumination sensing and imaging

Recent advances in fast and sensitive detectors have enabled the observation of physical phenomena from extremely sparse and noisy measurements. For instance, state-of-the-art single-photon detectors are able to quantify light at the particle level and find applications in several domains ranging from
biomedical imaging (fluorescence microscopy) to remote sensing (forest canopy monitoring) and defense. Analyzing such data, acquired under low-illumination conditions, using computational methods often consists of solving inverse problems that are ill-conditioned or ill-posed and thus difficult to solve. Moreover, the data quality induces significant intrinsic uncertainty about the solution obtained, which can limit significantly the value of algorithm outputs as evidence for scientific inquiry, sensor fusion and decision-making.

This talk illustrates how advanced Bayesian methods can be used to solve complex and high dimensional inverse problems by combining, in a formalised framework, observed data or images with additional information a-priori available. In particular, this talk will concentrate on stochastic simulation (Markov chain Monte Carlo, MCMC) methods to solve large-scale model selection problems while providing measures of uncertainty about parameters of interest. The proposed methodology is illustrated on a target detection problem from sparse single-photon Lidar waveforms, where an efficient adaptive reversible-jump MCMC method is proposed to compute posterior probabilities of target presence.