End-to-end learning of energy-based representations for irregularly-sampled signals and images

Abstract: For numerous domains, including for instance earth observation, medical imaging, astrophysics,..., available image and signal datasets often involve irregular space-time sampling patterns and large missing data rates. These sampling properties may be critical to apply state-of-the-art learning-based (e.g., auto-encoders, CNNs,...), fully benefit from the available large-scale observations and reach breakthroughs in the reconstruction and identification of processes of interest. In this paper, we address the end-to-end learning of representations of signals, images and image sequences from irregularly-sampled data, i.e. when the training data involved missing data. From an analogy to Bayesian formulation, we consider energy-based representations. Two energy forms are investigated: one derived from auto-encoders and one relating to Gibbs priors. The learning stage of these energy-based representations (or priors) involve a joint interpolation issue, which amounts to solving an energy minimization problem under observation constraints. Using a neural-network-based implementation of the considered energy forms, we can state an end-to-end learning scheme from irregularly-sampled data. We demonstrate the relevance of the proposed representations for different case-studies: namely, multivariate time series, 2D images and image sequences.

• The paper introduces a unified energy-based learning framework that integrates neural networks with interpolation to handle gaps in irregularly-sampled data.
• It employs a NN-based Gibbs energy representation to capture local data interactions, outperforming traditional methods by up to 30% in interpolation accuracy.
• Experimental validation on datasets like MNIST and Lorenz-63 demonstrates the framework's versatility across multivariate time series, static images, and temporal sequences.

Energy-Based Representations for Irregularly-Sampled Data

The paper "End-to-End Learning of Energy-Based Representations for Irregularly-Sampled Signals and Images" presents a sophisticated approach to addressing challenges in domains where observation datasets suffer from irregular sampling patterns and significant data gaps. Key sectors affected by these issues include earth observation, medical imaging, and astrophysics. The work is pioneering in its attempt to extend state-of-the-art learning frameworks to efficiently manage and learn from such incomplete datasets by employing an energy-based representation strategy.

Core Contributions

The authors introduce an end-to-end framework that integrates energy-based models for signal and image representation, directly incorporating irregular sampling into the learning process. The approach is three-fold:

1. End-to-End Learning with Energy-Based Models: The methodology leverages neural networks to integrate both an energy model and an interpolation scheme in a single framework. This integration facilitates learning from data that include significant gaps.
2. NN-Based Gibbs-Energy Representation: Apart from conventional auto-encoders, the paper introduces representations derived from Gibbs energy models, which capture the local interactions within the data, akin to Markovian priors embedded within CNN architectures.
3. Demonstration on Diverse Data Types: The efficacy of the proposed method is validated across multivariate time series, static images, and temporal image sequences with high missing data rates.

Methodological Advancements

The mathematical formulation is grounded in a classic Bayesian approach, where interpolation is cast as an energy minimization problem under specific constraints. The authors detail the neural network-based parameterization of the energy function and subsequent learning of the associated interpolation operator. By leveraging fixed-point iterative methods and gradient-based descent within a neural network framework, the proposed approach efficiently estimates the hidden states from irregularly-sampled data.

Experimental Validation

Comprehensive experiments are conducted on datasets like MNIST for images and Lorenz-63 for time series, alongside satellite-derived sea surface temperatures for image sequences. The results demonstrate notable improvements over traditional methods such as DINEOF and ensemble Kalman smoothers. Notably, the approach achieves significant gains in interpolation scores (up to 30% improvement), which underscore the model's ability to reconstruct missing data and enhance reconstruction accuracy.

Implications and Future Work

The implications of this work are far-reaching in fields requiring accurate data reconstruction and representation from incomplete datasets. The proposed framework could extend to various other applications including environmental monitoring and medical diagnostics.

Future research directions may explore enhancements in computational efficiency, particularly in deeper architectures for the gradient-based methods. Moreover, the integration of alternative energy-based representations could unveil new perspectives in unsupervised learning with irregular datasets. As the field progresses, adapting these techniques for real-time processing and multi-resolution data will be an essential area of focus.

In conclusion, this study systematically advances our understanding of energy-based modeling for irregularly-sampled data. It redefines conventional boundaries in data reconstruction, offering robust frameworks that pave the way for breakthroughs across multiple scientific and engineering domains.