Coherence, Distance and Error: Understanding Coded Demodulation in PB-ToF Imaging

One of the main objectives in coded Time-of-Flight is to precisely determine the position of the recovered target(s) with very few measurements or, in other words, to increase the resolution of the sensing system at high frame rates. In this scenario, we may cope with highly-coherent sensing matrices, i. e., there exist several columns very similar to each other. This may yield severe errors during the depth’s retrieval. In this paper, we show that the foreseen potential (probable) mismatches in the support estimation are related to the distance between the most cross-correlated columns over the sensing matrix, and propose a, to our knowledge, new metric which allows for estimating the average (absolute) recovery error. The metric is given by the mean absolute distance between each column and the most cross-correlated columns over the sensing matrix. We numerically evaluate various state-of-the-art demodulation schemes, and demonstrate that our metric reliably provides an estimation of their recovery performance, and complements other metrics traditionally used in Computational Sensing.