Sparsity-Aware 3-D ToF Sensing

In this work, we propose several time-of-flight (ToF) sensing schemes which tackle the challenge of covering very-wide areas and long ranges in nearly real time, with relatively simple implementation and low associated computational load. We thoroughly describe two methodologies for the resolution of the inverse problem. First, we extend a greedy algorithm, such as orthogonal matching pursuit (OMP), by considering an initial refinement of the spatial domain in which the signal recovery is performed. Then, we propose various nonadaptive techniques for the construction of the sensing matrices, relying on the optimization of coherence and density. We further develop them by including an additional verification step which accounts for the noninstantaneous transitions from one element to another of the code and avoids any possible coincidence between rising and falling edges which may degrade the coherence. We also investigate the upper super-resolution limit, the over-sampling rate which yields unitary coherence, by considering the instrument response function (IRF) of the ToF sensor. Second, we expand an adaptive sensing scheme in which the rows of the sensing matrix are generated accounting for the information from previous measurements, such as adaptive progressive edge growth algorithm (APEG), by considering several groups of signals during the adaptation of the sensing matrices. The signals are then individually recovered for each pixel via OMP over the identified joint signal support. We validate the proposed methodologies by numerical simulations over datasets from stereo and ToF cameras.