A Compressed Sensing Framework for Accurate and Robust Waveform Reconstruction and Phase Retrieval Using the Photonic Mixer Device


A common approach of performing section-shift-based time-of-flight imaging combines the emission of never-ending-wave (CW) illumination signal with correlation with some reference signals at the detector array. This is the case for the well-known photonic mixer device (PMD), which correlates against displaced versions of the illumination control signal, at known section shifts, and needs only four correlation values to estimate the phase shift. The most disadvantage of such approaches is that they require the belief of nonrealistic hypothesis regarding the sensing process, leading to simple sensing models that, despite allowing quick depth estimation from few acquisitions, typically ignore relevant concerns for real operation, leaving the door open for systematic errors that affect the ultimate depth accuracy. Typical examples are ignoring the result of the illumination devices on the final shape of the illumination signal, supposing a sinusoidal reference signal at pixel level, or not accounting for multipath effects. In this work, we have a tendency to gift a completely unique framework for PMD-based mostly signal acquisition and recovery that exploits the sparsity of CW illumination signals in the frequency domain to supply correct reconstruction of the illumination waveforms as received by the PMD pixels. Our technique is very robust to signal distortion and noise, since no assumption is created on the illumination signal, alternative than being a periodic signal. Our approach ensures that no valuable information is lost during the sensing process and permits, so, correct section shift estimation in a very wider vary of operation conditions, getting rid of unrealistic assumptions.

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