Inverse problems in time-of-flight imaging : theory, algorithms and applications

Abstract

Time-of-Fight (ToF) cameras utilize a combination of phase and amplitude information to return real-time, three dimensional information of a scene in form of depth images. Such cameras have a number of scientific and consumer oriented applications. In this work, we formalize a mathematical framework that leads to unifying perspective on tackling inverse problems that arise in the ToF imaging context. Starting from first principles, we discuss the implications of time and frequency domain sensing of a scene. From a linear systems perspective, this amounts to an operator sampling problem where the operator depends on the physical parameters of a scene or the bio-sample being investigated. Having presented some examples of inverse problems, we discuss detailed solutions that benefit from scene based priors such sparsity and rank constraints. Our theory is corroborated by experiments performed using ToF/Kinect cameras. Applications of this work include multi-bounce light decomposition, ultrafast imaging and fluorophore lifetime estimation.