The use of statistical mixture models to reduce noise in SPAD images of fog-obscured environments

Navigating through fog plays a vital part in many remote sensing tasks. In this paper, we propose an Expectation- Maximization (EM) algorithm for fitting a mixture of lognormal and Gaussian distributions to the probability distributions of photon returns for each pixel of a 32x32 Single Photon Avalanche Diode (SPAD) array image. The distance range of the target can be determined from the probability distribution of photon returns by modeling the peak produced due to fog scattering with a lognormal distribution while the peak produced by the target is modeled by a Gaussian distribution. In order to validate the algorithm, 32x32 SPAD array images of simple shapes (triangle, circle and square) are imaged at visibilities down to 50.8m through the fog in an indoor tunnel. Several aspects of the algorithm performance are then assessed. It is found that the algorithm can reconstruct and distinguish different shapes for all of our experimental fog conditions. Classification of shapes using only the total area of the shape is found to be 100% accurate for our tested fog conditions. However, it is found that the accuracy of the distance range of the target using the estimated model is poor. Therefore, future work will investigate a better statistical mixture model and estimation method.