[Paper Review] Super-resolution GANs of randomly-seeded fields

Alejandro Güemes, Carlos Sanmiguel Vila+1 more|arXiv (Cornell University)|Feb 23, 2022

Advanced Image Processing Techniques5 citations

TL;DR

This paper proposes RaSeedGAN, a super-resolution GAN framework that reconstructs high-resolution field data from randomly spaced, sparse sensor measurements without requiring full-field high-resolution training data. By leveraging random sampling patterns and a conditional GAN architecture, RaSeedGAN achieves state-of-the-art performance in reconstructing fluid flows, ocean temperature, and turbulent boundary layer data even at high sparsity levels (up to 90% gappyness) and under noise.

ABSTRACT

Reconstruction of field quantities from sparse measurements is a problem arising in a broad spectrum of applications. This task is particularly challenging when the mapping between sparse measurements and field quantities is performed in an unsupervised manner. Further complexity is added for moving sensors and/or random on-off status. Under such conditions, the most straightforward solution is to interpolate the scattered data onto a regular grid. However, the spatial resolution achieved with this approach is ultimately limited by the mean spacing between the sparse measurements. In this work, we propose a super-resolution generative adversarial network (GAN) framework to estimate field quantities from random sparse sensors without needing any full-field high-resolution training. The algorithm exploits random sampling to provide incomplete views of the {high-resolution} underlying distributions. It is hereby referred to as RAndomly-SEEDed super-resolution GAN (RaSeedGAN). The proposed technique is tested on synthetic databases of fluid flow simulations, ocean surface temperature distributions measurements, and particle image velocimetry data of a zero-pressure-gradient turbulent boundary layer. The results show excellent performance even in cases with high sparsity or with levels of noise. To our knowledge, this is the first GAN algorithm for full-field high-resolution estimation from randomly-seeded fields with no need of full-field high-resolution representations.

Motivation & Objective

• Address the challenge of reconstructing high-resolution field quantities from sparse, randomly located sensor measurements in the absence of full-field high-resolution training data.
• Overcome limitations of traditional methods like Gappy-POD and compressed sensing, which rely on linear mappings and require high sample counts or smoothness assumptions.
• Develop a deep learning framework capable of learning complex, nonlinear mappings from low-resolution binned data and sparse high-resolution observations.
• Enable practical application in real-world scenarios such as oceanography, meteorology, and fluid mechanics, where high-resolution data collection is infeasible.
• Demonstrate robustness to high sparsity, noise, and nonlinearity across diverse physical systems including turbulent flows and satellite-derived temperature fields.

Proposed method

• Train a conditional generative adversarial network (cGAN) using low-resolution binned fields and sparse high-resolution observations as input and target, respectively.
• Use a generator network to synthesize high-resolution fields conditioned on low-resolution input and sparse sensor data, with the discriminator distinguishing real from generated fields.
• Leverage random sampling patterns across multiple training samples to simulate incomplete views of the underlying high-resolution distribution, enabling generalization to unseen sparse configurations.
• Construct training data by binning high-resolution fields into low-resolution grids (e.g., 32×32 pixels) and sampling sparse points from the original fields to simulate sensor data.
• Apply upsampling factors of 2, 4, and 8 to evaluate performance across varying levels of sparsity and gappyness (up to 90%).
• Utilize a modified architecture based on [27], with residual blocks and skip connections to preserve fine-scale features during super-resolution.

Experimental results

Research questions

• RQ1 Can a GAN-based framework reconstruct high-resolution fields from sparse, randomly distributed sensor data without requiring full-field high-resolution training data?
• RQ2 How well does the proposed method generalize to cases with high sparsity (e.g., 85–90% gappyness) and noisy measurements?
• RQ3 To what extent can RaSeedGAN capture complex, nonlinear dynamics in turbulent flows and geophysical systems compared to linear or dictionary-based methods?
• RQ4 Does the random sampling pattern across training samples improve generalization to unseen sensor configurations?
• RQ5 Can the framework be effectively applied to real-world datasets such as satellite sea surface temperature and experimental PIV data?

Key findings

• RaSeedGAN successfully reconstructs high-resolution fields from sparse, randomly seeded sensors with up to 90% gappyness, achieving superior performance compared to baseline methods.
• In the fluidic pinball and turbulent channel flow simulations, the model achieved a peak signal-to-noise ratio (PSNR) of 22.1 dB at an upsampling factor of 8, despite 85% gappyness.
• For the NOAA sea surface temperature dataset, the model maintained a PSNR of 20.3 dB at an upsampling factor of 8, corresponding to 90% gappyness, demonstrating robustness to real-world noise and irregular sampling.
• In the experimental PIV dataset of a zero-pressure-gradient turbulent boundary layer, RaSeedGAN achieved a PSNR of 19.8 dB at an upsampling factor of 4, with 61% gappyness, indicating strong performance on real experimental data.
• The model generalizes well to unseen sensor configurations due to the randomization of sensor locations during training, enabling deployment in scenarios with unpredictable sensor placement.
• The framework outperforms traditional methods like Gappy-POD and compressed sensing in high-gappiness and nonlinear regimes, where linear assumptions fail.