# Optimization-Inspired Cross-Attention Transformer for Compressive Sensing

arXiv: https://arxiv.org/abs/2304.13986 · HTML: https://mlsanity.com/paper/2304.13986/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 68 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [End-to-End Video Instance Segmentation with Transformers](https://mlsanity.com/paper/2011.14503/) (2020)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Mask-guided Spectral-wise Transformer for Efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2111.07910/) (2021)
- [U-Net Transformer: Self and Cross Attention for Medical Image Segmentation](https://mlsanity.com/paper/2103.06104/) (2021)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Degradation-Aware Unfolding Half-Shuffle Transformer for Spectral Compressive Imaging](https://mlsanity.com/paper/2205.10102/) (2022)
- [Group-based Sparse Representation for Image Restoration](https://mlsanity.com/paper/1405.3351/) (2014)
- [Non-Local Color Image Denoising with Convolutional Neural Networks](https://mlsanity.com/paper/1611.06757/) (2016)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [Deep Image Demosaicking using a Cascade of Convolutional Residual Denoising Networks](https://mlsanity.com/paper/1803.05215/) (2018)
- [Dense Deep Unfolding Network with 3D-CNN Prior for Snapshot Compressive Imaging](https://mlsanity.com/paper/2109.06548/) (2021)
- [iPiano: Inertial Proximal Algorithm for Non-Convex Optimization](https://mlsanity.com/paper/1404.4805/) (2014)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization](https://mlsanity.com/paper/1404.7566/) (2014)

## Built on by (most cited first, 12 of 12)

- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging](https://mlsanity.com/paper/2505.23180/) (2025)
- [Dual-Scale Transformer for Large-Scale Single-Pixel Imaging](https://mlsanity.com/paper/2404.05001/) (2024)
- [RadioDUN: A Physics-Inspired Deep Unfolding Network for Radio Map Estimation](https://mlsanity.com/paper/2506.08418/) (2025)
- [Latent Space Imaging](https://mlsanity.com/paper/2407.07052/) (2024)
- [Inter and Intra Prior Learning-based Hyperspectral Image Reconstruction Using Snapshot SWIR Metasurface](https://mlsanity.com/paper/2407.07503/) (2024)
- [Using Powerful Prior Knowledge of Diffusion Model in Deep Unfolding Networks for Image Compressive Sensing](https://mlsanity.com/paper/2503.08429/) (2025)
- [Ultra-Low Complexity On-Orbit Compression for Remote Sensing Imagery via Block Modulated Imaging](https://mlsanity.com/paper/2412.18417/) (2024)
- [Physics-guided Deep Unfolding Network for Enhanced Kronecker Compressive sensing](https://mlsanity.com/paper/2508.09528/) (2025)
- [Dual-Path Hyperprior Informed Deep Unfolding Network for Image Compressive Sensing](https://mlsanity.com/paper/2605.09566/) (2026)
- [Beyond Single Solution: Multi-Hypothesis Collaborative Deep Unfolding Network for Image Compressive Sensing](https://mlsanity.com/paper/2606.03666/) (2026)
- [Newton Deep Unfolding for Compressed Sensing](https://mlsanity.com/paper/2609.14391/) (2026)

## Abstract (arXiv)

By integrating certain optimization solvers with deep neural networks, deep unfolding network (DUN) with good interpretability and high performance has attracted growing attention in compressive sensing (CS). However, existing DUNs often improve the visual quality at the price of a large number of parameters and have the problem of feature information loss during iteration. In this paper, we propose an Optimization-inspired Cross-attention Transformer (OCT) module as an iterative process, leading to a lightweight OCT-based Unfolding Framework (OCTUF) for image CS. Specifically, we design a novel Dual Cross Attention (Dual-CA) sub-module, which consists of an Inertia-Supplied Cross Attention (ISCA) block and a Projection-Guided Cross Attention (PGCA) block. ISCA block introduces multi-channel inertia forces and increases the memory effect by a cross attention mechanism between adjacent iterations. And, PGCA block achieves an enhanced information interaction, which introduces the inertia force into the gradient descent step through a cross attention block. Extensive CS experiments manifest that our OCTUF achieves superior performance compared to state-of-the-art methods while training lower complexity. Codes are available at https://github.com/songjiechong/OCTUF.