eess.IVSep 23, 2026

Physics-Guided Multi-Objective Deep Learning for Ultrasound RF Data Interpolation in Resource-Constrained Imaging

Authors: Luoyuan Zhang, Yiyang You, Ananya Tandri, Yinan Feng, Hyunwoo Song, Jeeun Kang, Youzuo Lin

Organizations: University of North Carolina at Chapel Hill, Chapel Hill, NC, USA · Johns Hopkins University, Baltimore, MD, USA

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Abstract

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\times 2 to ×13\times 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.

Figures & tables

Figure 1 : Overview of our physics-guided pipeline for training and inference. A random-skip mask produces the sparse RF input, which a neural network maps to a dense RF estimate. Training is supervised by an RF ℓ1\ell_{1} loss and an image-domain MSE computed from the beamformed images; the beamforming loss is weighted by λt\lambda_{t} , updated via an Exponential Moving Average (EMA). Red dashed arrows indicate backpropagation paths. Bottom: inference path from sparse RF →\rightarrow neural network →\rightarrow dense RF →\rightarrow B(⋅)B(\cdot) →\rightarrow final image.
Figure 2 : Illustration of the random-skip masking strategy (maximum skip length RR = 7). Blue stems mark retained channels (value 1); gaps down to 0 indicate consecutively skipped channels. A new mask is sampled for each training instance and epoch, producing diverse, spatially varying sparsity patterns while keeping the input size SS unchanged.
Figure 3 : Architecture and block design. (a) U - Net style encoder–decoder with four encoder stages (E1–E4), a bottleneck, and four decoder stages (D1–D4). (b) HGNet-V2 encoder block: three parallel 3×33{\times}3 Conv–BN–ReLU branches, concatenation, and a 1×11{\times}1 projection with a residual connection. (c) CAFormer encoder block: LayerNorm →\rightarrow token mixer →\rightarrow LayerNorm →\rightarrow MLP (GELU, dropout) with residual additions. (d) Decoder block: upsampling, concatenation with the encoder skip, followed by two 3×33{\times}3 Conv–ReLU layers. Red dashed curves indicate skip connections, including U - Net long skips and the residual paths within blocks.
Array parametersDetails
Transducer typeLinear
Number of elements128
Speed of sound1540 m/s
Array pitch0.43 mm
Element width0.42 mm
Element height7 mm
Table 1 : Array and imaging parameters.
Figure 4 : Simulation setup. (a) Scatterer layout with point targets and speckle regions. (b) Steered plane-wave transmissions for radial scanning.
Figure 5 : Example simulated RF channel data (channel–time matrix) from one transmit, shown before beamforming.
ParameterSetting
Training loaderBatch size =16=16
Validation loaderBatch size =16=16
Test loaderBatch size =16=16
OptimizerAdam
Learning rate1×10−41\times 10^{-4}
Epochs100
Table 2 : Training and evaluation configuration.
Figure 6 : Representative training example in the RF domain. (a) Sparse RF input generated using random-skip masking with a maximum skip length of R=7R=7 . (b) Dense ground-truth RF data VfullV_{\text{full}} . (c) Network prediction V^\hat{V} .
Figure 7 : Representative held-out test example at a fixed decimation factor of ×6\times 6 . (a) Regularly decimated RF input. (b) Dense ground-truth RF data VfullV_{\text{full}} . (c) Network prediction V^\hat{V} .
Figure 8 : SSIM across decimation levels. In-distribution (ID) covers ×2\times 2 – ×8\times 8 , and out-of-distribution (OOD) covers ×9\times 9 – ×13\times 13 . We compare six settings: (a) sparse input, (b) spline interpolation, (c) no BF loss, (d) HGNet-V2 (no EMA), (e) HGNet-V2 + EMA, and (f) CAFormer + EMA. Higher SSIM values indicate better reconstruction quality with respect to the densely sampled ground truth image.
Figure 9 : Qualitative comparison at ×6\times 6 decimation (in-distribution). (a) Full RF (ground truth); (b) sparse input + DAS; (c) spline interpolation; (d) RF-only loss; (e) RF + BF loss; (f) RF + BF loss + EMA; (g) RF + BF loss + EMA (CAFormer). Red boxes highlight regions where physics-guided supervision reduces grating-lobe artifacts and better preserves structures.
Figure 10 : Qualitative comparison at ×13\times 13 decimation (out-of-distribution). (a) Full RF (ground truth); (b) sparse input + DAS; (c) spline interpolation; (d) RF-only loss; (e) RF + BF loss; (f) RF + BF loss + EMA; (g) RF + BF loss + EMA (CAFormer). Red boxes highlight regions where physics-guided supervision mitigates grating-lobe artifacts under severe undersampling.
Figure 11 : Angular-response analysis at ×6\times 6 decimation. (a) The five analyzed regions, centered at depths of 13.30, 26.33, 39.36, 52.39, and 65.13 mm. (b)–(d) Normalized angular responses for the fully sampled ground truth, sparse input, and reconstructed prediction, respectively.
Decimation factorDecimated MGR (dB)Reconstructed MGR (dB)
×2\times 214.03±2.6914.03\pm 2.6916.98±1.4516.98\pm 1.45
×4\times 47.85±4.817.85\pm 4.8116.58±1.3616.58\pm 1.36
×6\times 63.58±3.003.58\pm 3.0015.96±1.0415.96\pm 1.04
×8\times 82.25±1.652.25\pm 1.6515.75±0.9515.75\pm 0.95
×10\times 101.53±1.151.53\pm 1.1515.05±0.7215.05\pm 0.72
×12\times 121.10±1.031.10\pm 1.0314.39±1.2014.39\pm 1.20
Table 3 : MGR across decimation factors. Values are the mean ±\pm standard deviation across the five analyzed depth regions ( n=5n=5 ). The fully sampled reference has an MGR of 16.44±1.2616.44\pm 1.26 dB for all decimation factors.
Table 4 : SSIM for models trained with fixed or randomized decimation, evaluated across ×2\times 2 , ×4\times 4 , and ×8\times 8 test decimation levels. The best result in each row is shown in bold.
BF-domain loss×2\times 2×4\times 4×6\times 6×8\times 8×10\times 10
MS_SSIM0.9484090.9503410.9472180.9392330.921916
MSE0.9626860.9623720.9624670.9615010.958763
Perceptual0.9496290.9532740.9527390.9458690.938023
Table 5 : Ablation of the beamforming-domain loss based on mean SSIM on the validation set. Rows indicate the loss used in LBF\mathcal{L}_{\mathrm{BF}} , and columns indicate the validation decimation factor. The best result in each column is shown in bold .
Training skip×2\times 2×4\times 4×6\times 6×8\times 8×10\times 10
Skip 1–30.9644780.9628600.9461920.9120690.881246
Skip 1–70.9626860.9623720.9624670.9615010.958763
Skip 1–90.9500260.9546310.9557410.9580990.959251
Table 6 : Ablation of the maximum skip length RR in random-skip masking based on mean SSIM on the validation set. Rows indicate the training setting (Skip 1– RR ), and columns indicate the validation decimation factor. The best result in each column is shown in bold .
Figure 12 : Mean SSIM under additive white Gaussian noise injected at test time. Curves correspond to fixed decimation factors; the x-axis shows the approximate input SNR (dB).
Figure 13 : Generalization test on a resolution phantom-like dataset under domain shift. (a) Ground-truth beamformed image from fully sampled RF. (b) Direct beamforming of the ×6\times 6 decimated sparse input (baseline). (c) Zero-shot prediction of our method (no fine-tuning). (d) Our method after fine-tuning on 34 paired examples from the phantom-like dataset.

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