Statistical detection and imaging of objects hidden in turbid media using ballistic photons

Abstract

We exploit recent advances in active high-resolution imaging through scattering media with ballistic photons. We derive the fundamental limits on the accuracy of the estimated parameters of a mathematical model that describes such an imaging scenario and compare the performance of ballistic and conventional imaging systems. This model is later used to derive optimal single-pixel statistical tests for detecting objects hidden in turbid media. To improve the detection rate of the aforementioned single-pixel detectors, we develop a multiscale algorithm based on the generalized likelihood ratio test framework. Moreover, considering the effect of diffraction, we derive a lower bound on the achievable spatial resolution of the proposed imaging systems. Furthermore, we present the first experimental ballistic scanner that directly takes advantage of novel adaptive sampling and reconstruction techniques.

Imaging Through Obscuring, Discrete-Scatterer Media With Chirped Trains of Wide-Band Pulses

“…The "chirped train" signal consisting of pulses is then given by (7) where are the starting times of individual pulses (8) and the pulse-pulse intervals are given by (9) Here the parameter determines the chirp bandwidth [(10) below], is the average pulse spacing, and is the "chirp center frequency." According to (9), the instantaneous frequency with which the pulses are emitted varies from to , the chirp bandwidth is given by (10) and the total duration of the train is . The Fourier transform of the signal (7) is then (11) where the quantity (12) the Fourier transform of a sequence of delta-functions-will be referred to as the "train chirp profile".…”

“…Hence, the range resolution would drastically deteriorate to , a value much larger than the resolution or of a single pulse. The presence of the chirp in (7), however, suggests that the bandwidth of the train chirp profile should be given by (10) and, hence, the time and range resolutions obtained with the chirped train of pulses should be closely related to those obtained with a conventional chirp signal. We will devote Section V and Appendix A to the discussion of this issue.…”

Sparsity based denoising of spectral domain optical coherence tomography images

“…The first hardware implemented experiment demonstrating the superiority of adaptive sampling in improving the scanning speed and SNR of ballistic photon based imagers was reported in [23]. More recently, application of compressive sensing theory for speeding up the SDOCT scanning time has attracted sizable attention [24–27].…”

3D imaging in volumetric scattering media using phase-space measurements

“…The scattered images still contain significant information about the object, however, so one has a chance to undo scattering either optically or computationally. Some approaches aim to filter out the scattered light [1][2][3][4][5], leaving a very weak signal. Instead, we wish to use the scattered light in reconstructing the signal [6].…”