Resolving multipath interference in time-of-flight imaging via modulation frequency diversity and sparse regularization

Abstract

Time-of-flight (ToF) cameras calculate depth maps by reconstructing phase shifts of amplitudemodulated signals. For broad illumination or transparent objects, reflections from multiple scene points can illuminate a given pixel, giving rise to an erroneous depth map. We report here a sparsity regularized solution that separates K interfering components using multiple modulation frequency measurements. The method maps ToF imaging to the general framework of spectral estimation theory and has applications in improving depth profiles and exploiting multiple scattering.

Computational single-photon depth imaging without transverse regularization

“…For multi-depth imaging, we studied the performance for K = 2, which is used in applications such as second-order multipath interference mitigation [22] and looking through a scattering layer [23] via ToF imaging. We compared two algorithms: the mixture-ofGaussian (MoG) estimator using greedy histogram fitting, and our proposed imager that uses convex optimization.…”

Imaging in scattering media using correlation image sensors and sparse convolutional coding

“…One can see that, although these pixels are dominated by direct reflections, the signals are not sparse at all, and time-domain sparse backscatter models as used by Freedman et al's SRA [10], or Bhandari et al [15] are not capable of close reconstructions. Our method, on the other hand, produces solutions that follow the ground-truth distributions more closely than any of the competing models.…”

“…Several recent works [10,14,15] attempt to resolve multi-path interference by assuming sparsity of i in the Dirac basis. The vastly popular idea of compressed sensing [11] is applied in a straightforward manner, by trying to solve…”

Application of lidar techniques to time-of-flight range imaging

“…Dorrington et al [19] used two modulation frequencies, one double the other, to resolve two propagation paths. Bhandari et al [20] used sparse deconvolution and multiple complex measurements to resolve K propagation paths. Fourier analysis on the multifrequency measurements for transient imaging was done by Lin et al [21].…”