# Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound

arXiv: https://arxiv.org/abs/1811.08252 · HTML: https://mlsanity.com/paper/1811.08252/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2018.

## Built on by (most cited first, 30 of 44)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem](https://mlsanity.com/paper/2101.08286/) (2021)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detection](https://mlsanity.com/paper/2311.00917/) (2023)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Dehazing Ultrasound using Diffusion Models](https://mlsanity.com/paper/2307.11204/) (2023)
- [Stable and Interpretable Unrolled Dictionary Learning](https://mlsanity.com/paper/2106.00058/) (2021)
- [Towards Constituting Mathematical Structures for Learning to Optimize](https://mlsanity.com/paper/2305.18577/) (2023)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [DA-MUSIC: Data-Driven DoA Estimation via Deep Augmented MUSIC Algorithm](https://mlsanity.com/paper/2109.10581/) (2021)
- [Deep Unrolled Recovery in Sparse Biological Imaging](https://mlsanity.com/paper/2109.14025/) (2021)
- [Improving Generalizability in Limited-Angle CT Reconstruction with Sinogram Extrapolation](https://mlsanity.com/paper/2103.05255/) (2021)
- [Deep Unfolded Tensor Robust PCA with Self-supervised Learning](https://mlsanity.com/paper/2212.11346/) (2022)
- [SubspaceNet: Deep Learning-Aided Subspace Methods for DoA Estimation](https://mlsanity.com/paper/2306.02271/) (2023)
- [Deep Algorithm Unrolling for Biomedical Imaging](https://mlsanity.com/paper/2108.06637/) (2021)
- [Robust PCA Unrolling Network for Super-resolution Vessel Extraction in X-ray Coronary Angiography](https://mlsanity.com/paper/2204.08466/) (2022)
- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [DISTA-Net: Dynamic Closely-Spaced Infrared Small Target Unmixing](https://mlsanity.com/paper/2505.19148/) (2025)
- [Ultrasound Speckle Suppression and Denoising using MRI-derived Normalizing Flow Priors](https://mlsanity.com/paper/2112.13110/) (2021)
- [Optimization Guarantees of Unfolded ISTA and ADMM Networks With Smooth Soft-Thresholding](https://mlsanity.com/paper/2309.06195/) (2023)
- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)
- [Deep Unfolding of Iteratively Reweighted ADMM for Wireless RF Sensing](https://mlsanity.com/paper/2106.03686/) (2021)
- [Ultrasound Signal Processing: From Models to Deep Learning](https://mlsanity.com/paper/2204.04466/) (2022)
- [Deep Unrolling for Nonconvex Robust Principal Component Analysis](https://mlsanity.com/paper/2307.05893/) (2023)
- [Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCA](https://mlsanity.com/paper/2501.04565/) (2025)
- [Deep learned SVT: Unrolling singular value thresholding to obtain better MSE](https://mlsanity.com/paper/2105.06934/) (2021)
- [Working memory inspired hierarchical video decomposition with transformative representations](https://mlsanity.com/paper/2204.10105/) (2022)
- [Near Field Localization via AI-Aided Subspace Methods](https://mlsanity.com/paper/2504.00599/) (2025)
- [mSQUID: Model-Based Leanred Modulo Recovery at Low Sampling Rates](https://mlsanity.com/paper/2510.18729/) (2025)

## Abstract (arXiv)

Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented subwavelength spatial resolution by relying on super-resolution techniques. A typical preprocessing step in super-resolution ultrasound is to separate the microbubble signal from the cluttering tissue signal. This step has a crucial impact on the final image quality. Here, we propose a new approach to clutter removal based on robust principle component analysis (PCA) and deep learning. We begin by modeling the acquired contrast enhanced ultrasound signal as a combination of a low rank and sparse components. This model is used in robust PCA and was previously suggested in the context of ultrasound Doppler processing and dynamic magnetic resonance imaging. We then illustrate that an iterative algorithm based on this model exhibits improved separation of microbubble signal from the tissue signal over commonly practiced methods. Next, we apply the concept of deep unfolding to suggest a deep network architecture tailored to our clutter filtering problem which exhibits improved convergence speed and accuracy with respect to its iterative counterpart. We compare the performance of the suggested deep network on both simulations and in-vivo rat brain scans, with a commonly practiced deep-network architecture and the fast iterative shrinkage algorithm, and show that our architecture exhibits better image quality and contrast.