# Depth-Aware Super-Resolution via Distance-Adaptive Variational Formulation

arXiv: https://arxiv.org/abs/2509.05746 · HTML: https://mlsanity.com/paper/2509.05746/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 58 references that are in the map.
- First posted on arXiv 6 Sep 2025.

## Builds on (most cited first, 30 of 30)

- [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)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [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)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Sketch-based Manga Retrieval using Manga109 Dataset](https://mlsanity.com/paper/1510.04389/) (2015)
- [Single Image Super-Resolution via a Holistic Attention Network](https://mlsanity.com/paper/2008.08767/) (2020)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [FutureSightDrive: Thinking Visually with Spatio-Temporal CoT for Autonomous Driving](https://mlsanity.com/paper/2505.17685/) (2025)
- [Transformer for Single Image Super-Resolution](https://mlsanity.com/paper/2108.11084/) (2021)
- [Cross-Scale Internal Graph Neural Network for Image Super-Resolution](https://mlsanity.com/paper/2006.16673/) (2020)
- [LAPAR: Linearly-Assembled Pixel-Adaptive Regression Network for Single Image Super-Resolution and Beyond](https://mlsanity.com/paper/2105.10422/) (2021)
- [SwinFIR: Revisiting the SwinIR with Fast Fourier Convolution and Improved Training for Image Super-Resolution](https://mlsanity.com/paper/2208.11247/) (2022)
- [On Efficient Transformer-Based Image Pre-training for Low-Level Vision](https://mlsanity.com/paper/2112.10175/) (2021)
- [ResDiff: Combining CNN and Diffusion Model for Image Super-Resolution](https://mlsanity.com/paper/2303.08714/) (2023)
- [DRCT: Saving Image Super-resolution away from Information Bottleneck](https://mlsanity.com/paper/2404.00722/) (2024)
- [Hierarchical Neural Architecture Search for Single Image Super-Resolution](https://mlsanity.com/paper/2003.04619/) (2020)
- [Single Image Super Resolution based on a Modified U-net with Mixed Gradient Loss](https://mlsanity.com/paper/1911.09428/) (2019)
- [Conjugated Semantic Pool Improves OOD Detection with Pre-trained Vision-Language Models](https://mlsanity.com/paper/2410.08611/) (2024)
- [CausalSR: Structural Causal Model-Driven Super-Resolution with Counterfactual Inference](https://mlsanity.com/paper/2501.15852/) (2025)
- [Joint Self-supervised Depth and Optical Flow Estimation towards Dynamic Objects](https://mlsanity.com/paper/2310.00011/) (2023)
- [Self-supervised Monocular Depth Estimation on Water Scenes via Specular Reflection Prior](https://mlsanity.com/paper/2404.07176/) (2024)
- [Pyramid Frequency Network with Spatial Attention Residual Refinement Module for Monocular Depth Estimation](https://mlsanity.com/paper/2204.02386/) (2022)
- [Single-image reflection removal via self-supervised diffusion models](https://mlsanity.com/paper/2412.20466/) (2024)
- [City Scene Super-Resolution via Geometric Error Minimization](https://mlsanity.com/paper/2401.07272/) (2024)
- [Semi-supervised Chinese Poem-to-Painting Generation via Cycle-consistent Adversarial Networks](https://mlsanity.com/paper/2410.19307/) (2024)
- [CLIP-aware Domain-Adaptive Super-Resolution](https://mlsanity.com/paper/2505.12391/) (2025)

## Built on by (most cited first, 4 of 4)

- [SwiftVLA: Unlocking Spatiotemporal Dynamics for Lightweight VLA Models at Minimal Overhead](https://mlsanity.com/paper/2512.00903/) (2025)
- [Does Tone Change the Answer? Evaluating Prompt Politeness Effects on Modern LLMs: GPT, Gemini, and LLaMA](https://mlsanity.com/paper/2512.12812/) (2025)
- [BlackMirror: Black-Box Backdoor Detection for Text-to-Image Models via Instruction-Response Deviation](https://mlsanity.com/paper/2603.05921/) (2026)
- [Audio-Visual Segmentation via Depth-Guided Collaborative Modeling](https://mlsanity.com/paper/2608.16285/) (2026)

## Abstract (arXiv)

Single image super-resolution traditionally assumes spatially-invariant degradation models, yet real-world imaging systems exhibit complex distance-dependent effects including atmospheric scattering, depth-of-field variations, and perspective distortions. This fundamental limitation necessitates spatially-adaptive reconstruction strategies that explicitly incorporate geometric scene understanding for optimal performance. We propose a rigorous variational framework that characterizes super-resolution as a spatially-varying inverse problem, formulating the degradation operator as a pseudodifferential operator with distance-dependent spectral characteristics that enable theoretical analysis of reconstruction limits across depth ranges. Our neural architecture implements discrete gradient flow dynamics through cascaded residual blocks with depth-conditional convolution kernels, ensuring convergence to stationary points of the theoretical energy functional while incorporating learned distance-adaptive regularization terms that dynamically adjust smoothness constraints based on local geometric structure. Spectral constraints derived from atmospheric scattering theory prevent bandwidth violations and noise amplification in far-field regions, while adaptive kernel generation networks learn continuous mappings from depth to reconstruction filters. Comprehensive evaluation across five benchmark datasets demonstrates state-of-the-art performance, achieving 36.89/0.9516 and 30.54/0.8721 PSNR/SSIM at 2 and 4 scales on KITTI outdoor scenes, outperforming existing methods by 0.44dB and 0.36dB respectively. This work establishes the first theoretically-grounded distance-adaptive super-resolution framework and demonstrates significant improvements on depth-variant scenarios while maintaining competitive performance across traditional benchmarks.