  The task of reconstructing smooth signals from streamed data in the form of
signal samples arises in various applications. This work addresses such a task
subject to a zero-delay response; that is, the smooth signal must be
reconstructed sequentially as soon as a data sample is available and without
having access to subsequent data. State-of-the-art approaches solve this
problem by interpolating consecutive data samples using splines. Here, each
interpolation step yields a piece that ensures a smooth signal reconstruction
while minimizing a cost metric, typically a weighted sum between the squared
residual and a derivative-based measure of smoothness. As a result, a
zero-delay interpolation is achieved in exchange for an almost certainly higher
cumulative cost as compared to interpolating all data samples together. This
paper presents a novel approach to further reduce this cumulative cost on
average. First, we formulate a zero-delay smoothing spline interpolation
problem from a sequential decision-making perspective, allowing us to model the
future impact of each interpolated piece on the average cumulative cost. Then,
an interpolation method is proposed to exploit the temporal dependencies
between the streamed data samples. Our method is assisted by a recurrent neural
network and accordingly trained to reduce the accumulated cost on average over
a set of example data samples collected from the same signal source generating
the signal to be reconstructed. Finally, we present extensive experimental
results for synthetic and real data showing how our approach outperforms the
abovementioned state-of-the-art.
