Computational and Optical techniques for single photon sensors

• Optimal flux and attenuation for single photon sensors (Under Review, manuscript available on request):
  Single photon avalanche diodes (SPAD) are depth sensors that are highly photon-efficient and have high timing resolution. However they suffer from non-linear distortions under high flux conditions, due to their peculiar image formation model. We model the problem of depth recovery as statistical parameter estimation, and derive an optimal flux criterion using a notion of statistical efficiency. This leads to an attenuation-based solution that dramatically improves performance.
• Asynchronous shifting for single photon sensors (In progress):
  LiDAR (light based depth ranging) systems typically use a synchronous acquisition scheme, where the laser and sensor operate in phase at the same frequency. While this is inconsequential for standard sensors, we show that for single photon sensors, asynchronization eliminates non-linear distortions and reduces depth error. Using a first-order analysis of the random measurement sequence of a SPAD, we derive the optimal shift in frequency that achieves the lowest error.

Statistical learning theory

Best arm identification with cascading bandits:
I worked on a variant of the problem of best arm identification in multi-arm bandits, called cascading bandits, where a stochastic number of arms receive a reward in each round. This problem was motivated by another computer vision problem that I was working on. Since each round potentially provides information about more than one arm, the sample complexity is much lower than in the standard formulation. I introduced a subroutine to perform uniform sampling, that allowed me to adapt an optimal algorithm for the standard version to this variant. I provided an upper bound on sample complexity using this algorithm, and a nearly matching lower bound. Furthermore, it turns out that cascading bandits are interesting in other contexts too such as search rankings, where regret minimization is used. I am working on extending the study of multi-arm bandits to a new framework where the goal is to estimate the mean reward of each arm to ε-accuracy, again motivated by practical applications.