In this work we formulate ultrasound multistatic recovery from arbitrary transmit sequences as a Bayesian inference problem. To that end, we train a deep generative prior on multistatic data sets to tackle the rank-deficient regime in which classical linear REFoCUS decoders fail. This appproach, which we term Deep Bayesian REFoCUS, outperforms the linear baselines for all regimes of rank-deficiency and noise levels, and regresses to linear decoding when inversion is exact. The model also expresses uncertainty in the null space of the acquisitions, whereas the linear REFoCUS decoders only provide point estimates. Finally, we analyze the impact of distribution shift between simulation and in-vivo acquisitions, showing remarkable generalization ability without any fine-tuning or adaptation.
Figures & tables
Fig. 1: Schematic of the Deep Bayesian REFoCUS sampling process. A multistatic data set is initialized with random Gaussian noise. The diffusion process is guided by the residual of the measurements, which we obtain through transmit beamforming. The neural network steps introduce the multistatic prior statistics, and the adjoint guidance steps transport the generation process towards the measurements.
Fig. 2: Multistatic data generation example for an EchoNet-LVH frame. Point scatterers are sampled based on pixel intensities, full-rank STA firings are simulated with zea. For reference, the multistatic data set is beamformed.
Stage
Output (tx × ax × rx)
Channels
Blocks
Attn.
Stem
80×512×20
96
—
—
Encoder stage 1
80×512×20
96
4
—
Encoder stage 2
40×256×10
192
3
✓
Encoder stage 3
20×128×5
384
3
✓
Bottleneck
10×64×5
384
3
✓
Decoder stage 3
20×128×5
384
3
✓
TABLE I: U-Net and training configuration.
Fig. 3: Comparison of reconstruction quality of linear REFoCUS decoders and Deep Bayesian REFoCUS. For the simulation a single plane wave is fired and the target is the simulation multistatic ground truth. For the in vivo 40 harmonic wide beams are fired, and the target shows 80 harmonic wide beams.
Fig. 4: Complex correlation of DB-REFoCUS recovered multistatic data sets against the ground truth. Panels show different transmit schemes, the lines show different numbers of transmit events. We sweep guidance strength to find the global operating point ζ=0.35 .
Fig. 5: Complex correlation of DB-REFoCUS compared with the linear baselines for a range of Nbeams at 10dB measurement SNR. The noiseless Tikhonov method shows that linear recovery is limited by rank deficiency of the inversion.
Fig. 6: Heatmap showing NMSE, PSNR and SSIM of DB-REFoCUS relative to the best performing linear decoder, oracle Tikhonov.
Figure 8
Fig. 10: In vivo complex correlation for different Nbeams for all transmit types. The complex correlation is calculated on a held-out set of the remaining 80−Nbeams transmits that belong to the same frame. The recovered multistatic data set is transmit beamformed to these acquisitions to compare.
Fig. 11: In vivo NMSE, PSNR and SSIM of DB-REFoCUS relative to the oracle Tikhonov linear decoder. NMSE is calculated through transmit beamforming to the held-out set, the image-domain metrics are calculated with respect to the Nbeams=80 image.
Ultrasound imaging uses sound waves to visualize anatomy and function, with AI improving image reconstruction, diagnosis, measurement, and scan guidance.
Ultrasound imaging increasingly targets portable, point-of-care, and wearable settings where constraints on power, bandwidth, and hardware complexity often necessitate sparse data acquisition in spatiotemporal scanning. However, image reconstruction using the sparse data can introduce insufficient phase information in coherent beamforming process, resulting in grating-lobe artifacts that degrade imaging contrast resolution. We present a physics-guided, data-driven framework for sparse-to-dense radio-frequency (RF) reconstruction that aligns training with downstream image formation. Our approach trains an end-to-end interpolation network using a hybrid supervision scheme that combines an RF-domain and a beamforming-domain loss with exponential moving average (EMA) to stabilize the multi-objective training. To improve generalization under variable acquisition layouts, we also introduce a random-skip masking strategy that varies sparsity patterns during training so a single model can handle diverse decimation factors and irregular channel configurations. We evaluate the framework on a held-out test set using the mean structural similarity index measure (SSIM) between reconstructed and ground-truth beamformed images. Across decimation factors ×2 to ×13, the best-performing configuration maintains mean SSIM around 0.95. Overall, the results show consistent gains in RF reconstruction and post-beamforming image quality across diverse acquisition conditions. This approach enables robust, high-quality ultrasound imaging at resource-constrained settings by allowing more sparse scanning in spatiotemporal domain.
Luoyuan Zhang, Yiyang You, Ananya Tandri +4
University of North Carolina at Chapel Hill, Chapel Hill, NC, USA · Johns Hopkins University, Baltimore, MD, USA
Medical imaging aims to recover underlying tissue properties, using inexact (simplified/linearized) imaging models and often from inaccurate and incomplete measurements. Analytical reconstruction methods rely on hand-crafted regularization, sensitive to noise assumptions and parameter tuning. Among deep learning alternatives, plug-and-play (PnP) approaches learn regularization while incorporating imaging physics during inference, outperforming purely data-driven methods. The performance of all these approaches, however, still strongly depends on measurement quality and imaging model accuracy. In this work, we propose DenOiS, a framework that denoises both input observations and resulting solution in their respective domains. It consists of an observation refinement strategy that corrects degraded measurements while compensating for imaging model simplifications, and a diffusion-based PnP reconstruction approach that remains robust under missing measurements. DenOiS enables generalization to real data from training only in simulations, resulting in high-fidelity image reconstruction with noisy observations and inexact imaging models. We demonstrate this for speed-of-sound imaging as a challenging setting of quantitative ultrasound image reconstruction.
Can Deniz Bezek, Orcun Goksel
Department of Information Technology, Uppsala University, Sweden
Physically-based differentiable rendering enables gradient-based optimization of scene parameters by matching rendered images to measurements, but has so far mainly focused on light transport. We extend this paradigm to medical ultrasound, where image formation resembles transient rendering: echoes are binned by time-of-flight rather than projected onto an image plane. We present UltraDiff, a modular framework for differentiable ultrasound ray tracing. UltraDiff formulates ultrasound image formation as a path-space integral, gated by travel time between the transducer and tissue interfaces, and derives a Monte Carlo estimator of both the forward model and its gradients with respect to scene parameters. We demonstrate this on an inverse geometry estimation: starting from a sphere, an SDF is optimized until simulated echoes match measured ones, recovering vertebral surfaces from simulated B-mode sweeps and from a real robotic acquisition of a spine phantom. Unlike state-of-the-art ultrasound shape reconstruction methods, which rely on pre-segmented images, our approach operates unsupervised on B-mode images through analysis-by-synthesis, while achieving competitive geometric accuracy. Implemented on top of Mitsuba 3, UltraDiff brings differentiable path tracing to a new sensing modality and provides a foundation for inverse problems in acoustic imaging.
Felix Duelmer, Magdalena Wysocki, Nassir Navab +1
Technical University of Munich & Munich Center for Machine Learning