CapsBeam Ultrasound Beamformer

• CapsBeam is a capsule-network–based ultrasound beamformer that directly predicts complex envelope outputs from time-of-flight–corrected RF data.
• It leverages localized convolutional capsules with pixel-wise dynamic routing to emulate adaptive MVDR beamforming, improving contrast and resolution over DAS.
• It achieves significant computational savings through structured pruning and 16-bit fixed-point quantization, reducing load from 28.79 to about 6 GOPs per frame for FPGA deployment.

Searching arXiv for the specified paper and closely related context. CapsBeam is a capsule-network–based ultrasound beamformer for non-steered plane-wave imaging that operates directly on time-of-flight–corrected RF channel data from a single $0^\circ$ transmission and predicts the beamformed complex envelope, i.e., per-pixel $I$ and $Q$ components, rather than starting from a DAS image. It is designed for single-angle plane-wave ultrasound in which DAS is hardware-efficient but limited by low contrast, strong sidelobes, clutter, and poor lateral resolution, while CPWC and MVDR improve image quality at substantially higher acquisition or computational cost. The method targets an intermediate regime: image quality approaching adaptive beamforming, but with a model small and regular enough to be pruned, quantized, and fully accelerated on a resource-constrained FPGA (Rahoof et al., 3 Sep 2025).

1. Problem formulation and design objective

CapsBeam is situated in the receive-beamforming problem for high-frame-rate ultrasound under non-steered plane-wave insonification. In this setting, all transducer elements transmit a broad plane wave simultaneously and all echoes are received on all channels, enabling hundreds to thousands of FPS, but reconstruction quality becomes highly sensitive to the receive beamformer (Rahoof et al., 3 Sep 2025).

The baseline addressed explicitly is DAS. DAS applies precomputed delays, optionally apodization, and sums channel data, making it simple, fast, and well-suited to hardware. For single-angle plane waves, however, it yields low contrast, strong sidelobes, poor lateral resolution, clutter, and artifacts. CPWC improves contrast and resolution by coherently combining multiple steering angles, but requires multiple transmissions and increases computational load linearly with the number of angles. MVDR, or Capon beamforming, uses data-adaptive apodization weights derived from covariance matrices and yields a narrower mainlobe with reduced sidelobes, but its complexity is dominated by matrix inversions, approximately $O(n^3)$ per aperture; for a frame size $368 \times 128$, the reported cost is about $98.78$ GOPs per frame, making real-time edge deployment difficult (Rahoof et al., 3 Sep 2025).

Deep-learning beamformers are introduced in the same context as a means of emulating or surpassing adaptive beamforming while suppressing clutter and improving contrast and resolution from single-angle input. The specific difficulty is that FCNN, CNN, U-Net, and GoogLeNet-based beamformers typically require large 2D or 3D models, often exceeding $90$ GOPs per frame for $368 \times 128$ frames, with hundreds of thousands to millions of parameters and an implicit assumption of GPU-class memory and compute. CapsBeam is therefore posed as a compact RF-domain alternative intended to achieve MVDR/CPWC-like quality at substantially lower computational cost and without CPU or GPU assistance in the deployment loop (Rahoof et al., 3 Sep 2025).

2. Network structure and signal representation

CapsBeam takes as input a 3D tensor of delayed RF data of shape $(368, 128, 128)$, corresponding to depth, lateral position, and receive channels, for a single non-steered plane-wave transmission. Delay compensation is performed outside the network. The output is a tensor of shape $(368, 128, 2)$, where the last dimension contains the predicted $I$0 and $I$1 values for each pixel. Envelope magnitude is then formed as

$I$2

followed by standard log compression for B-mode display (Rahoof et al., 3 Sep 2025).

Architecturally, CapsBeam consists of two standard convolution layers, two convolutional capsule layers, and four point-wise fully connected layers applied independently at each pixel. The first two convolution layers extract local spatio-channel features. The capsule layers then perform 2D convolutions followed by pixel-wise dynamic routing. Finally, four small dense layers map capsule features to the two scalar outputs $I$3 and $I$4. The model is explicitly organized around a per-pixel $I$5 RF-domain receptive field, which is intended to mimic the MVDR covariance window (Rahoof et al., 3 Sep 2025).

The reported unpruned model has $I$6 parameters and a compute complexity of $I$7 GOPs per frame for frame size $I$8. The first convolution uses a $I$9 kernel with $Q$0 input channels and $Q$1 output channels before pruning; after pruning, the output channels are reduced to $Q$2. The second convolution is also $Q$3, and the two capsule-stage convolutions extend the receptive field from $Q$4 to $Q$5 (Rahoof et al., 3 Sep 2025).

A central distinction from image-domain beamformers is that CapsBeam works at the RF level rather than from a DAS image. Another is that it predicts complex envelope components directly. A plausible implication is that the learned mapping is closer to adaptive receive processing than to post-beamforming image enhancement, because the network consumes channel-domain delayed data and replaces the adaptive beamformer itself rather than refining an already formed B-mode image.

3. Capsule routing, supervision, and optimization objective

CapsBeam uses standard Sabour-style capsule routing, adapted to a convolutional, pixel-wise dataflow. For capsules in layer $Q$6 with output vectors $Q$7, and capsules in layer $Q$8 with vectors $Q$9, the paper gives the routing relations as

$O(n^3)$0

$O(n^3)$1

$O(n^3)$2

and

$O(n^3)$3

Routing is performed independently for each pixel using its local feature tensor rather than over broader spatial neighborhoods, and the capsule layers use 2D convolution combined with pixel-wise dynamic routing (Rahoof et al., 3 Sep 2025).

The training target is the complex MVDR beamformed envelope obtained from the same delayed RF input. The MVDR target is computed with subarray length $O(n^3)$4 and temporal averaging over $O(n^3)$5 samples. Training minimizes MSE on the predicted and target $O(n^3)$6 and $O(n^3)$7 components before log compression. Fine-tuning then uses CPWC outputs generated from five transmit angles, $O(n^3)$8, $O(n^3)$9, $368 \times 128$0, $368 \times 128$1, and $368 \times 128$2, so that inference still uses a single $368 \times 128$3 transmission while the learned target quality reflects compounded imaging (Rahoof et al., 3 Sep 2025).

The training setup reported is Adam with batch size $368 \times 128$4, initial learning rate $368 \times 128$5, and fine-tuning at $368 \times 128$6, implemented in TensorFlow 2.4 on a 12th-gen Intel Core i9-12900K with an NVIDIA RTX A4500 GPU. No explicit regularization term beyond the regression objective is highlighted; instead, model compactness, the shallow architecture, and later pruning function as the main constraints on capacity (Rahoof et al., 3 Sep 2025).

A common misconception would be to equate CapsBeam with a generic CapsNet ported into ultrasound. The formulation is narrower: the routing is pixel-wise, the receptive field is fixed at $368 \times 128$7, the network is trained against MVDR and then CPWC targets, and the dataflow is explicitly organized for FPGA realization.

4. Compression strategy and FPGA-oriented modifications

The paper identifies parameter storage and external-memory traffic as the principal deployment bottlenecks. Even though the original CapsBeam is already smaller than large CNN beamformers and much cheaper than MVDR, naïve FPGA implementation would still incur substantial DRAM traffic because the first convolution alone uses filters of size $368 \times 128$8 over input tensors of shape $368 \times 128$9. CapsBeam therefore combines structured pruning, fixed-point quantization, simplified nonlinear operators, and parallelized compute kernels (Rahoof et al., 3 Sep 2025).

The pruning method is multi-layer LookAhead Kernel Pruning, LAKP-ML. For a kernel $98.78$0 in layer $98.78$1, the multi-layer pruning score is defined as

$98.78$2

where $98.78$3 is typically the $98.78$4 norm, and the neighboring kernel subsets are those connected to $98.78$5 through the preceding and succeeding layers. Kernels are ranked by this score, iteratively pruned, fine-tuned, and evaluated not only with MSE but also with axial and lateral resolution and contrast metrics, specifically CR, CNR, and gCNR. The selected operating point retains image quality while reducing parameters by $98.78$6, leaving only $98.78$7 of original weights and lowering computation from $98.78$8 GOPs to about $98.78$9 GOPs per frame (Rahoof et al., 3 Sep 2025).

Quantization uses 16-bit fixed-point for all weights and activations. The softmax exponential is approximated by a 5-term Taylor expansion,

$90$0

and the squash norm uses built-in hls::sqrt with fixed-point inputs. Convolution loops are tiled and unrolled onto a $90$1 PE array, while routing loops are reorganized for vectorized execution. The reported effect is to increase dynamic-routing throughput from $90$2 GOPS in the naïve design to $90$3 GOPS, while convolution reaches $90$4 GOPS (Rahoof et al., 3 Sep 2025).

The hardware platform is a Xilinx ZU7EV FPGA on ZCU104 at $90$5 MHz. The accelerator contains two DMAs, one for weights and biases and one for inputs and intermediate feature maps, on-chip BRAM for weights, line buffers, row buffers, and routing intermediates, separate convolution and dynamic-routing modules, a nonlinear unit for approximate exponential and squash, and a controller coordinating address generation and scheduling. The optimized implementation uses $90$6 slice LUTs ($90$7), $90$8 LUTRAM ($90$9), $368 \times 128$0 BRAM ($368 \times 128$1), and $368 \times 128$2 DSP48E ($368 \times 128$3), with power reported as $368 \times 128$4 W (Rahoof et al., 3 Sep 2025).

5. Empirical performance and comparative results

The experimental pipeline includes in-house Verasonics Vantage 128 acquisitions with an L11-5v linear array, CUBDL data for fine-tuning, and PICMUS datasets for evaluation. The frame size throughout is $368 \times 128$5. Evaluation spans in-silico phantoms, in-vitro phantoms, and in-vivo carotid and breast data (Rahoof et al., 3 Sep 2025).

For in-silico cyst contrast, DAS yields CR $368 \times 128$6 dB, CNR $368 \times 128$7, and gCNR $368 \times 128$8, whereas CapsBeam yields CR $368 \times 128$9 dB, CNR $(368, 128, 128)$0, and gCNR $(368, 128, 128)$1. This corresponds to an approximately $(368, 128, 128)$2 CR increase relative to DAS and an increase in gCNR from $(368, 128, 128)$3 to $(368, 128, 128)$4. For simulated point-scatterer resolution, DAS gives axial $(368, 128, 128)$5 mm and lateral $(368, 128, 128)$6 mm, while CapsBeam gives axial $(368, 128, 128)$7 mm and lateral $(368, 128, 128)$8 mm, corresponding to about $(368, 128, 128)$9 and $(368, 128, 2)$0 improvements, respectively (Rahoof et al., 3 Sep 2025).

For in-vitro contrast, DAS reports CR $(368, 128, 2)$1 dB, CNR $(368, 128, 2)$2, and gCNR $(368, 128, 2)$3, while CapsBeam reports CR $(368, 128, 2)$4 dB, CNR $(368, 128, 2)$5, and gCNR $(368, 128, 2)$6. The corresponding improvements are $(368, 128, 2)$7 in CR, $(368, 128, 2)$8 in CNR, and approximately $(368, 128, 2)$9 in gCNR relative to DAS. For in-vitro point resolution, DAS gives axial $I$00 mm and lateral $I$01 mm, while CapsBeam gives axial $I$02 mm and lateral $I$03 mm, amounting to gains of $I$04 and $I$05 (Rahoof et al., 3 Sep 2025).

Qualitative in-vivo results are reported for carotid artery and breast-mass imaging. In the carotid case, CapsBeam produces higher contrast between lumen and vessel walls than DAS, Tiny-CNN, and Tiny-VBF, with substantial reduction of clutter described as “white shades” in the lumen and surrounding tissues. In the breast-mass case from CUBDL JHU, it better delineates lesion boundaries and suppresses speckle and clutter more effectively than DAS, Tiny-CNN, and Tiny-VBF. The paper characterizes these appearances as closer to a 5-angle CPWC reference, even though inference uses only a single $I$06 transmission (Rahoof et al., 3 Sep 2025).

Hardware and software comparisons reinforce that the method is neither the fastest overall beamformer nor merely a quality-oriented academic model. On an RTX A4500, DAS reaches $I$07 FPS, MVDR $I$08 FPS, a GoogLeNet-based beamformer $I$09 FPS, Tiny-CNN $I$10 FPS, Tiny-VBF $I$11 FPS, and non-optimized CapsBeam $I$12 FPS. On FPGA, the custom GoogLeNet-based accelerator reaches $I$13 FPS, Tiny-CNN $I$14 FPS, Tiny-VBF about $I$15 FPS, non-optimized CapsBeam $I$16 FPS, and optimized CapsBeam $I$17 FPS with latency $I$18 s per frame. The comparison made in the paper is therefore primarily a trade-off argument: optimized CapsBeam achieves the strongest reported FPGA throughput among the tinyML beamformers while preserving a higher image-quality level than DAS and the tiny baselines (Rahoof et al., 3 Sep 2025).

6. Scope, limitations, and technical significance

CapsBeam is restricted in scope. It is designed for non-steered $I$19 plane-wave imaging, and generalization to multiple steered angles or diverging-wave imaging is not addressed. Training and evaluation are centered on linear-array data from the L11-5v probe and PICMUS-style configurations; behavior on phased-array or curvilinear probes, other frequency bands, or substantially different acoustic regimes is not studied. The ZCU104 implementation already uses $I$20 of LUTs and $I$21 of DSPs, so scaling to larger frames or 3D imaging would likely require further pruning, more aggressive quantization such as 8-bit, or more capable hardware. The achieved FPGA frame rate is approximately $I$22 FPS, which is below the $I$23–$I$24 FPS often associated with real-time B-mode operation (Rahoof et al., 3 Sep 2025).

These constraints clarify two frequent misunderstandings. First, CapsBeam is not a general replacement for CPWC acquisition; it is a single-angle inference model trained so that its output approximates MVDR and CPWC-like image quality. Second, it is not a real-time FPGA beamformer in the conventional clinical frame-rate sense on the reported platform, despite clear throughput gains over other compact learned beamformers. Its contribution is instead the demonstration that capsule-style dynamic routing, when localized to a per-pixel receptive field and combined with structured pruning, fixed-point arithmetic, and bespoke dataflow, can be reconciled with embedded FPGA constraints (Rahoof et al., 3 Sep 2025).

The broader significance lies in the particular synthesis of algorithmic and architectural choices. CapsBeam couples RF-domain learning, complex-envelope regression, pixel-wise convolutional capsules, LAKP-ML pruning, and a specialized FPGA accelerator into a single beamforming system. This suggests that capsule networks, usually considered computationally difficult because of routing, can be made practical for ultrasound beamforming when the routing domain is spatially localized, the nonlinearities are hardware-approximated, and pruning is guided by inter-layer connectivity rather than layer-local weight magnitude alone.