# RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation

arXiv: https://arxiv.org/abs/2508.04190 · HTML: https://mlsanity.com/paper/2508.04190/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 157 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 30 of 64)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [U2-Net: Going Deeper with Nested U-Structure for Salient Object Detection](https://mlsanity.com/paper/2005.09007/) (2020)
- [Faster Segment Anything: Towards Lightweight SAM for Mobile Applications](https://mlsanity.com/paper/2306.14289/) (2023)
- [ResUNet-a: a deep learning framework for semantic segmentation of remotely sensed data](https://mlsanity.com/paper/1904.00592/) (2019)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [The Secrets of Salient Object Segmentation](https://mlsanity.com/paper/1406.2807/) (2014)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Searching Central Difference Convolutional Networks for Face Anti-Spoofing](https://mlsanity.com/paper/2003.04092/) (2020)
- [Salient Object Detection in the Deep Learning Era: An In-Depth Survey](https://mlsanity.com/paper/1904.09146/) (2019)
- [Asymmetric Contextual Modulation for Infrared Small Target Detection](https://mlsanity.com/paper/2009.14530/) (2020)
- [Dense Nested Attention Network for Infrared Small Target Detection](https://mlsanity.com/paper/2106.00487/) (2021)
- [UIU-Net: U-Net in U-Net for Infrared Small Object Detection](https://mlsanity.com/paper/2212.00968/) (2022)
- [Attentional Local Contrast Networks for Infrared Small Target Detection](https://mlsanity.com/paper/2012.08573/) (2020)
- [Salient Object Detection: A Survey](https://mlsanity.com/paper/1411.5878/) (2014)
- [Large Selective Kernel Network for Remote Sensing Object Detection](https://mlsanity.com/paper/2303.09030/) (2023)
- [Salient Object Detection: A Discriminative Regional Feature Integration Approach](https://mlsanity.com/paper/1410.5926/) (2014)
- [White-Box Transformers via Sparse Rate Reduction](https://mlsanity.com/paper/2306.01129/) (2023)
- [Reweighted Infrared Patch-Tensor Model With Both Non-Local and Local Priors for Single-Frame Small Target Detection](https://mlsanity.com/paper/1703.09157/) (2017)
- [Infrared Small Target Detection with Scale and Location Sensitivity](https://mlsanity.com/paper/2403.19366/) (2024)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)

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

- [Lightweight Deep Unfolding Networks with Enhanced Robustness for Infrared Small Target Detection](https://mlsanity.com/paper/2509.08205/) (2025)
- [Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detection](https://mlsanity.com/paper/2509.07654/) (2025)
- [CPCANet: Deep Unfolding Common Principal Component Analysis for Domain Generalization](https://mlsanity.com/paper/2605.05136/) (2026)
- [STGBD-Net: Spatio-temporal Gradient Basis Decomposition Network for Infrared Small Target Detection](https://mlsanity.com/paper/2512.03470/) (2025)
- [Robust Principal Component Completion](https://mlsanity.com/paper/2603.25132/) (2026)
- [Off-the-shelf Vision Models Benefit Image Manipulation Localization](https://mlsanity.com/paper/2604.09096/) (2026)
- [LCPNet: Latent Consistent Proximal Unfolding Network for Infrared Small Target Detection](https://mlsanity.com/paper/2607.04603/) (2026)
- [Effective Receptive Field Ordering Matters for Infrared Small Target Detection](https://mlsanity.com/paper/2607.23994/) (2026)
- [SPARK-SAM: Learning How to Prompt and Respond for Infrared Small Target Segmentation](https://mlsanity.com/paper/2608.20754/) (2026)
- [RDANet: Relative Degradation Aware Network for Infrared Small Target Detection](https://mlsanity.com/paper/2608.20870/) (2026)
- [PICANet: Physics-Informed Cascaded Asymmetric Network for Infrared Small Target Detection](https://mlsanity.com/paper/2609.07515/) (2026)
- [Learning to Select Features with Manifold Deep Unfolding PCA](https://mlsanity.com/paper/2610.19436/) (2026)

## Abstract (arXiv)

Robust principal component analysis (RPCA) decomposes an observation matrix into low-rank background and sparse object components. This capability has enabled its application in tasks ranging from image restoration to segmentation. However, traditional RPCA models suffer from computational burdens caused by matrix operations, reliance on finely tuned hyperparameters, and rigid priors that limit adaptability in dynamic scenarios. To solve these limitations, we propose RPCANet++, a sparse object segmentation framework that fuses the interpretability of RPCA with efficient deep architectures. Our approach unfolds a relaxed RPCA model into a structured network comprising a Background Approximation Module (BAM), an Object Extraction Module (OEM), and an Image Restoration Module (IRM). To mitigate inter-stage transmission loss in the BAM, we introduce a Memory-Augmented Module (MAM) to enhance background feature preservation, while a Deep Contrast Prior Module (DCPM) leverages saliency cues to expedite object extraction. Extensive experiments on diverse datasets demonstrate that RPCANet++ achieves state-of-the-art performance under various imaging scenarios. We further improve interpretability via visual and numerical low-rankness and sparsity measurements. By combining the theoretical strengths of RPCA with the efficiency of deep networks, our approach sets a new baseline for reliable and interpretable sparse object segmentation. Codes are available at our Project Webpage https://fengyiwu98.github.io/rpcanetx.