  Digitalizing real-world analog signals typically involves sampling in time
and discretizing in amplitude. Subsequent signal reconstructions inevitably
incur an error that depends on the amplitude resolution and the temporal
density of the acquired samples. From an implementation viewpoint, consistent
signal reconstruction methods have proven a profitable error-rate decay as the
sampling rate increases. Despite that, these results are obtained under offline
settings. Therefore, a research gap exists regarding methods for consistent
signal reconstruction from data streams. Solving this problem is of great
importance because such methods could run at a lower computational cost than
the existing offline ones or be used under real-time requirements without
losing the benefits of ensuring consistency. In this paper, we formalize for
the first time the concept of consistent signal reconstruction from streaming
time-series data. Then, we present a signal reconstruction method able to
enforce consistency and also exploit the spatiotemporal dependencies of
streaming multivariate time-series data to further reduce the signal
reconstruction error. Our experiments show that our proposed method achieves a
favorable error-rate decay with the sampling rate compared to a similar but
non-consistent reconstruction.
