Anant Gupta

Shashank Rajput, Anant Gupta, Dimitris Papailiopoulos

Stochastic gradient descent without replacement sampling is widely used in practice for model training. However, the vast majority of SGD analyses assumes data is sampled with replacement, and when the function minimized is strongly convex, an $\mathcal{O}\left(\frac{1}{T}\right)$ rate can be established when SGD is run for $T$ iterations. A recent line of breakthrough works on SGD without replacement (SGDo) established an $\mathcal{O}\left(\frac{n}{T^2}\right)$ convergence rate when the function minimized is strongly convex and is a sum of $n$ smooth functions, and an $\mathcal{O}\left(\frac{1}{T^2}+\frac{n^3}{T^3}\right)$ rate for sums of quadratics. On the other hand, the tightest known lower bound postulates an $Ω\left(\frac{1}{T^2}+\frac{n^2}{T^3}\right)$ rate, leaving open the possibility of better SGDo convergence rates in the general case. In this paper, we close this gap and show that SGD without replacement achieves a rate of $\mathcal{O}\left(\frac{1}{T^2}+\frac{n^2}{T^3}\right)$ when the sum of the functions is a quadratic, and offer a new lower bound of $Ω\left(\frac{n}{T^2}\right)$ for strongly convex functions that are sums of smooth functions.

Anant Gupta, Atul Ingle, Mohit Gupta

Single-photon avalanche diodes (SPADs) are becoming popular in time-of-flight depth-ranging due to their unique ability to capture individual photons with picosecond timing resolution. However, ambient light (e.g., sunlight) incident on a SPAD-based 3D camera leads to severe non-linear distortions (pileup) in the measured waveform, resulting in large depth errors. We propose asynchronous single-photon 3D imaging, a family of acquisition schemes to mitigate pileup during data acquisition itself. Asynchronous acquisition temporally misaligns SPAD measurement windows and the laser cycles through deterministically predefined or randomized offsets. Our key insight is that pileup distortions can be "averaged out" by choosing a sequence of offsets that span the entire depth range. We develop a generalized image formation model and perform theoretical analysis to explore the space of asynchronous acquisition schemes and design high-performance schemes. Our simulations and experiments demonstrate an improvement in depth accuracy of up to an order of magnitude as compared to the state-of-the-art, across a wide range of imaging scenarios, including those with high ambient flux.

Anant Gupta, Atul Ingle, Andreas Velten et al.

Single photon avalanche diodes (SPADs) are starting to play a pivotal role in the development of photon-efficient, long-range LiDAR systems. However, due to non-linearities in their image formation model, a high photon flux (e.g., due to strong sunlight) leads to distortion of the incident temporal waveform, and potentially, large depth errors. Operating SPADs in low flux regimes can mitigate these distortions, but, often requires attenuating the signal and thus, results in low signal-to-noise ratio. In this paper, we address the following basic question: what is the optimal photon flux that a SPAD-based LiDAR should be operated in? We derive a closed form expression for the optimal flux, which is quasi-depth-invariant, and depends on the ambient light strength. The optimal flux is lower than what a SPAD typically measures in real world scenarios, but surprisingly, considerably higher than what is conventionally suggested for avoiding distortions. We propose a simple, adaptive approach for achieving the optimal flux by attenuating incident flux based on an estimate of ambient light strength. Using extensive simulations and a hardware prototype, we show that the optimal flux criterion holds for several depth estimators, under a wide range of illumination conditions.