Abhinav V. Sambasivan

Abhinav V. Sambasivan, Liam J. Coulter, Richard G. Paxman et al.

This work focuses on assessing the information-theoretic limits of scene parameter estimation in plenoptic imaging systems. A general framework to compute lower bounds on the parameter estimation error from noisy plenoptic observations is presented, with a particular focus on passive indirect imaging problems, where the observations do not contain line-of-sight information about the parameter(s) of interest. Using computer graphics rendering software to synthesize the often-complicated dependence among parameter(s) of interest and observations, i.e. the forward model, the proposed framework evaluates the Hammersley-Chapman-Robbins bound to establish lower bounds on the variance of any unbiased estimator of the unknown parameters. The effects of inexact rendering of the true forward model on the computed lower bounds are also analyzed, both theoretically and via simulations. Experimental evaluations compare the computed lower bounds with the performance of the Maximum Likelihood Estimator on a canonical object localization problem, showing that the lower bounds computed via the framework proposed here are indicative of the true underlying fundamental limits in several nominally representative scenarios.

Mohammadreza Soltani, Swayambhoo Jain, Abhinav Sambasivan

Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the target distribution are easily available. However, in many applications, this assumption is violated. In this paper, we consider the observation setting when the samples from target distribution are given by the superposition of two structured components and leverage GANs for learning the structure of the components. We propose two novel frameworks: denoising-GAN and demixing-GAN. The denoising-GAN assumes access to clean samples from the second component and try to learn the other distribution, whereas demixing-GAN learns the distribution of the components at the same time. Through extensive numerical experiments, we demonstrate that proposed frameworks can generate clean samples from unknown distributions, and provide competitive performance in tasks such as denoising, demixing, and compressive sensing.

Abhinav V. Sambasivan, Jarvis D. Haupt

This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our main contributions come in the form of minimax lower bounds for the expected per-element squared error for this problem under under several common noise models. Specifically, we analyze scenarios where the corruptions are characterized by additive Gaussian noise or additive heavier-tailed (Laplace) noise, Poisson-distributed observations, and highly-quantized (e.g., one-bit) observations, as instances of our general result. Our results establish that the error bounds derived in (Soni et al., 2016) for complexity-regularized maximum likelihood estimators achieve, up to multiplicative constants and logarithmic factors, the minimax error rates in each of these noise scenarios, provided that the nominal number of observations is large enough, and the sparse factor has (on an average) at least one non-zero per column.