# Deep Unfolded Recovery of Sub-Nyquist Sampled Ultrasound Image

arXiv: https://arxiv.org/abs/2103.01263 · HTML: https://mlsanity.com/paper/2103.01263/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 58 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 9 of 9)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Deep learning in ultrasound imaging](https://mlsanity.com/paper/1907.02994/) (2019)
- [Adaptive Ultrasound Beamforming using Deep Learning](https://mlsanity.com/paper/1909.10342/) (2019)
- [Learned SPARCOM: Unfolded Deep Super-Resolution Microscopy](https://mlsanity.com/paper/2004.09270/) (2020)
- [Deep-Learning Based Adaptive Ultrasound Imaging from Sub-Nyquist Channel Data](https://mlsanity.com/paper/2008.02628/) (2020)
- [Beamforming through regularized inverse problems in ultrasound medical imaging](https://mlsanity.com/paper/1507.08184/) (2015)
- [Sparse Array Design via Fractal Geometries](https://mlsanity.com/paper/2001.01217/) (2020)
- [Compressed Fourier-Domain Convolutional Beamforming for Wireless Ultrasound imaging](https://mlsanity.com/paper/2010.13171/) (2020)

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

- [Ultrasound Signal Processing: From Models to Deep Learning](https://mlsanity.com/paper/2204.04466/) (2022)
- [Deep Learning for Ultrasound Beamforming](https://mlsanity.com/paper/2109.11431/) (2021)
- [Unsupervised Unfolded rPCA (U2-rPCA): Deep Interpretable Clutter Filtering for Ultrasound Microvascular Imaging](https://mlsanity.com/paper/2510.00660/) (2025)
- [Deep Unrolled Networks in Representation Space Applied to MRI Reconstruction](https://mlsanity.com/paper/2606.21602/) (2026)

## Abstract (arXiv)

The most common technique for generating B-mode ultrasound (US) images is delay and sum (DAS) beamforming, where the signals received at the transducer array are sampled before an appropriate delay is applied. This necessitates sampling rates exceeding the Nyquist rate and the use of a large number of antenna elements to ensure sufficient image quality. Recently we proposed methods to reduce the sampling rate and the array size relying on image recovery using iterative algorithms, based on compressed sensing (CS) and the finite rate of innovation (FRI) frameworks. Iterative algorithms typically require a large number of iterations, making them difficult to use in real-time. Here, we propose a reconstruction method from sub-Nyquist samples in the time and spatial domain, that is based on unfolding the ISTA algorithm, resulting in an efficient and interpretable deep network. The inputs to our network are the subsampled beamformed signals after summation and delay in the frequency domain, requiring only a subset of the US signal to be stored for recovery. Our method allows reducing the number of array elements, sampling rate, and computational time while ensuring high quality imaging performance. Using in vivo data we demonstrate that the proposed method yields high-quality images while reducing the data volume traditionally used up to 36 times. In terms of image resolution and contrast, our technique outperforms previously suggested methods as well as DAS and minimum-variance (MV) beamforming, paving the way to real-time applicable recovery methods.