# Resampling and super-resolution of hexagonally sampled images using deep learning

arXiv: https://arxiv.org/abs/2111.02520 · HTML: https://mlsanity.com/paper/2111.02520/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 55 references that are in the map.
- First posted on arXiv 3 Nov 2021.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [AID: A Benchmark Dataset for Performance Evaluation of Aerial Scene Classification](https://mlsanity.com/paper/1608.05167/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [MemNet: A Persistent Memory Network for Image Restoration](https://mlsanity.com/paper/1708.02209/) (2017)
- [EnhanceNet: Single Image Super-Resolution Through Automated Texture Synthesis](https://mlsanity.com/paper/1612.07919/) (2016)
- [Fast and Accurate Image Super-Resolution with Deep Laplacian Pyramid Networks](https://mlsanity.com/paper/1710.01992/) (2017)
- [Learned Image Downscaling for Upscaling using Content Adaptive Resampler](https://mlsanity.com/paper/1907.12904/) (2019)
- [Orientation-aware Semantic Segmentation on Icosahedron Spheres](https://mlsanity.com/paper/1907.12849/) (2019)
- [HexaConv](https://mlsanity.com/paper/1803.02108/) (2018)
- [Face Recognition in Low Quality Images: A Survey](https://mlsanity.com/paper/1805.11519/) (2018)
- [HexagDLy - Processing hexagonally sampled data with CNNs in PyTorch](https://mlsanity.com/paper/1903.01814/) (2019)
- [Gated Fusion Network for Degraded Image Super Resolution](https://mlsanity.com/paper/2003.00893/) (2020)

## Abstract (arXiv)

Super-resolution (SR) aims to increase the resolution of imagery. Applications include security, medical imaging, and object recognition. We propose a deep learning-based SR system that takes a hexagonally sampled low-resolution image as an input and generates a rectangularly sampled SR image as an output. For training and testing, we use a realistic observation model that includes optical degradation from diffraction and sensor degradation from detector integration. Our SR approach first uses non-uniform interpolation to partially upsample the observed hexagonal imagery and convert it to a rectangular grid. We then leverage a state-of-the-art convolutional neural network (CNN) architecture designed for SR known as Residual Channel Attention Network (RCAN). In particular, we use RCAN to further upsample and restore the imagery to produce the final SR image estimate. We demonstrate that this system is superior to applying RCAN directly to rectangularly sampled LR imagery with equivalent sample density. The theoretical advantages of hexagonal sampling are well known. However, to the best of our knowledge, the practical benefit of hexagonal sampling in light of modern processing techniques such as RCAN SR is heretofore untested. Our SR system demonstrates a notable advantage of hexagonally sampled imagery when employing a modified RCAN for hexagonal SR.