Zero-delay Consistent Signal Reconstruction from Streamed Multivariate Time Series

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. This paper presents a method that consistently reconstructs streamed multivariate time series of quantization intervals under a zero-delay response requirement. On the other hand, previous work has shown that the temporal dependencies within univariate time series can be exploited to reduce the roughness of zero-delay signal reconstructions. This work shows that the spatiotemporal dependencies within multivariate time series can also be exploited to achieve improved results. Specifically, the spatiotemporal dependencies of the multivariate time series are learned, with the assistance of a recurrent neural network, to reduce the roughness of the signal reconstruction on average while ensuring consistency. 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.

Zero-delay Consistent and Smooth Trainable Interpolation

The question of how to produce a smooth interpolating curve from a stream of data points is addressed in this paper. To this end, we formalize the concept of real-time interpolator (RTI): a trainable unit that recovers smooth signals that are consistent with the received input samples in an online manner. Specifically, an RTI works under the requirement of producing a function section immediately after a sample is received (zero delay), without changing the reconstructed signal in past time sections. This work formulates the design of spline-based RTIs as a bi-level optimization problem. Their training consists in minimizing the average curvature of the interpolated signals over a set of example sequences. The latter are representative of the nature of the data sequence to be interpolated, allowing to tailor the RTI to a specific signal source. Our overall design allows for different possible schemes. In this work, we present two approaches, namely, the parametrized RTI and the recurrent neural network (RNN)-based RTI, including their architecture and properties. Experimental results show that the two proposed RTIs can be trained in a data-driven fashion to achieve improved performance (in terms of the curvature loss metric) with respect to a myopic-type RTI that only exploits the local information at each time sample, while maintaining smooth, zero-delay, and consistency requirements.