Contextual Deep Learning Approaches for Time Series Reconstruction

The reconstruction of signals from partial data is a fundamental task in various applications, such as signal processing, computer vision, and time series analysis. Traditional interpolation techniques like polynomial fitting and frequency decomposition often struggle with complex or non-linear signals, particularly when the available data is limited or noisy. In this work, we explore the use of deep learning methods to address this signal reconstruction problem. Specifically, we present two neural network-based approaches: a simple autoencoder network and a convolutional neural network (CNN) autoencoder. The autoencoder is used to reconstruct 250-point time series from only 50 scattered data points, while the CNN autoencoder is applied to reconstruct 5000-point signals from 1000 downsampled points. Our results demonstrate that both neural network architectures significantly outperform classical polynomial interpolation, highlighting the potential of deep learning as a powerful alternative for signal reconstruction tasks. The CNN-based method, in particular, exhibits a strong ability to capture relevant local patterns, allowing effective generalization even from heavily subsampled inputs. This work contributes to the growing body of research on applying deep learning to solve challenging problems in signal processing and time series analysis.