# Unsupervised Unfolded rPCA (U2-rPCA): Deep Interpretable Clutter Filtering for Ultrasound Microvascular Imaging

arXiv: https://arxiv.org/abs/2510.00660 · HTML: https://mlsanity.com/paper/2510.00660/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 51 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound](https://mlsanity.com/paper/1811.08252/) (2018)
- [Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery](https://mlsanity.com/paper/1711.09492/) (2017)
- [Multimodal Deep Unfolding for Guided Image Super-Resolution](https://mlsanity.com/paper/2001.07575/) (2020)
- [Exponential Signal Reconstruction with Deep Hankel Matrix Factorization](https://mlsanity.com/paper/2007.06246/) (2020)
- [Self-supervised Deep Unrolled Reconstruction Using Regularization by Denoising](https://mlsanity.com/paper/2205.03519/) (2022)
- [Deep Unfolded Recovery of Sub-Nyquist Sampled Ultrasound Image](https://mlsanity.com/paper/2103.01263/) (2021)
- [Super-Resolved Microbubble Localization in Single-Channel Ultrasound RF Signals Using Deep Learning](https://mlsanity.com/paper/2204.04537/) (2022)
- [BUbble Flow Field: a Simulation Framework for Evaluating Ultrasound Localization Microscopy Algorithms](https://mlsanity.com/paper/2211.00754/) (2022)
- [High-resolution Power Doppler Using Null Subtraction Imaging](https://mlsanity.com/paper/2301.03719/) (2023)

## Abstract (arXiv)

High-sensitivity clutter filtering is a fundamental step in ultrasound microvascular imaging. Singular value decomposition (SVD) and robust principal component analysis (rPCA) are the main clutter filtering strategies. However, both strategies are limited in feature modeling and separation of tissue and blood flow for high-quality microvascular imaging. Recently, deep learning-based clutter filtering has shown potential in more thoroughly separating tissue and blood flow signals. However, the existing supervised filters face the lack of interpretability and the training ground truth. While the interpretability issue can be addressed by algorithm deep unfolding, the training ground truth remains unsolved. This paper proposes an unsupervised unfolded rPCA (U2-rPCA) method that preserves mathematical interpretability and is insusceptible to learning labels. Specifically, U2-rPCA is unfolded from an iteratively reweighted least squares (IRLS) rPCA baseline with intrinsic low-rank and sparse regularization. In addition, a sparse-enhancement unit is plugged into the network to strengthen its capability to capture the sparse micro-flow signals. U2-rPCA is like an adaptive filter that is trained with part of the image sequence and then used for the following frames. Experimental validations on a in-silico dataset and public in-vivo datasets demonstrated the outperformance of U2-rPCA when compared with the SVD filter, the rPCA baseline, and another deep learning-based filter. Particularly, the proposed method improved the contrast-to-noise ratio (CNR) of the power Doppler image by 1.91 dB to 8.48 dB compared to other methods. Furthermore, the effectiveness of the building modules of U2-rPCA was validated through ablation studies.