How to overcome scattering
As light propagates through the medium it interacts with it. The majority of photons will scatter a lot (diffused photons). Some will scatter just a little (snake photons), and a few photons don’t scatter at all, those are ballistic photons.
API uses all these photons simultaneously. The first step is estimating the physical process that explains the scattering (different materials will cause different scattering). The second step recovers the target based on the measurement and the estimated physical model. This makes our method calibration free as there is no need for extra measurements of the medium.
When we look at the time-resolved measurement, each frame in the movie contains a different distorted version of the target. Each frame shows information from photons that traveled a different path-length in the medium.
By comparing API to two other approaches the superiority of the method is established. The first is time-averaged, which doesn’t use any time-resolved information (it’s equivalent to a measurement with a regular camera), and the result is extremely blurry. The second uses just the ballistic photons. Since there are very few ballistic photons, this result is very noisy and somewhat blurry.
We quantitatively evaluate the results with two metrics: 1) PSNR (peak signal to noise ratio) measures how each pixel in the reconstruction is different from the actual target (higher PSNR is better). 2) SSIM (structural similarity) measures how similar the reconstruction and target are including spatial information (so it’s not just a point-by-point comparison). SSIM ranges between 0 and 1, higher is better.