Computational Ultrasound Imaging (cUSi)

• Computational Ultrasound Imaging (cUSi) is a framework that integrates advanced algorithms, physical modeling, and calibrated system design to enhance ultrasound image reconstruction.
• It employs techniques such as simulation, learned RF inversion, and coded apertures to trade hardware complexity for computational efficiency, resulting in improved resolution and quantitative accuracy.
• Its applications span breast, carotid, and brain imaging while addressing challenges like model generalization, calibration precision, and efficient computation in clinical settings.

Searching arXiv for recent and foundational papers on computational ultrasound imaging to ground the article. arxiv_search(query="computational ultrasound imaging", max_results=10, sort_by="relevance") arxiv_search({"query":"computational ultrasound imaging","max_results":10,"sort_by":"relevance"}) Searching arXiv for "ultrasound computed tomography sparse data AI physics computational ultrasound imaging". Computational ultrasound imaging (cUSi) denotes ultrasound systems in which image formation is driven as much by computation and physical modeling as by hardware. In the ultrasound community, the term includes software representations of the imaging chain—acoustic propagation, RF acquisition, beamforming, reconstruction, and quantitative inversion—and it also names a system-design philosophy in which hardware complexity is traded for algorithmic complexity (Sheng et al., 2024, Garcia, 2021). In current usage, cUSi spans beamforming and simulation frameworks, quantitative speed-of-sound imaging, ultrasound computed tomography, sparse and encoded apertures, coherent multi-transducer systems, learned RF interpolation and inversion, and differentiable pipelines for adaptive or “cognitive” imaging (Hu et al., 14 Aug 2025, Stevens et al., 1 Dec 2025).

1. Conceptual scope and system design philosophy

A minimal distinction between conventional ultrasound and cUSi is that conventional pulse-echo imaging is largely organized around beamforming and envelope detection, whereas cUSi treats acquisition and reconstruction as a coupled computational problem. In pulse-echo imaging, a transducer emits a short pulse and records backscattered echoes; in cUSi, the same acquisition may instead be interpreted through forward models, inverse problems, and algorithmic compensation for hardware limitations. That distinction is explicit in work on ultrasound computed tomography, where the goal is not only backscatter imaging but reconstruction of quantitative tissue properties such as the speed of sound $c(\mathbf{x})$ (Sheng et al., 2024).

The scope of cUSi is broader than inverse scattering alone. It also includes numerical simulation of ultrasound sequences and RF data for beamforming, probe design, and emission strategy development; SIMUS, for example, is positioned as a frequency-domain, time-harmonic simulator within the MATLAB UltraSound Toolbox and computes one-way and two-way acoustic pressure fields and RF channel data for linear and convex 1-D probes under a linear single-scattering model (Garcia, 2021). At the other end of the spectrum, “cognitive ultrasound imaging” packages such as zea expose beamforming, scan conversion, and learned priors as differentiable operators, so that acquisition and reconstruction can be optimized jointly inside machine-learning workflows (Stevens et al., 1 Dec 2025).

A recurring principle is that cUSi substitutes computation for dense hardware. In sparse-data USCT, sparse-aperture carotid imaging, and 4D brain haemodynamics, the hardware is intentionally simplified, but the resulting measurements are decoded with calibrated forward operators, model-based reconstruction, or learned mappings (Sheng et al., 2024, Hu et al., 14 Aug 2025, Brown et al., 2023). This suggests a unifying interpretation of cUSi as an architecture in which the effective aperture, PSF, and quantitative fidelity are determined by the combination of transducer physics, transmit coding, calibration, and reconstruction rather than by array density alone.

2. Physical and mathematical bases

The physical core of many cUSi methods is an acoustic forward model. In sparse-data USCT, the propagation model is the constant-density isotropic acoustic wave equation in 2D,

$$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$

with recorded data sampled at receiver positions $\mathbf{x}_r^j$ (Sheng et al., 2024). In 3D finite-frequency traveltime tomography for USCT, the governing model is the lossless acoustic wave equation in heterogeneous media, linearized around water calibration data to derive analytic traveltime sensitivity kernels with Fresnel-volume support rather than infinitesimally thin rays (Martiartu et al., 2019). In pulse-echo SoS imaging, CUTE formulates phase-shift measurements between beamformed echoes acquired under varying Tx/Rx steering and writes the inverse problem as

$$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$

where $\Delta\boldsymbol{\sigma}$ is the slowness deviation field and $\boldsymbol{M}$ is a straight-ray system matrix with angle-dependent corrections (Stähli et al., 2019).

A second common abstraction is a linear operator linking an unknown image or reflectivity volume to measured RF data. In encoded 3D carotid cUSi, the model is

$\mathbf{y} = \mathbf{A}\mathbf{x},$

where $\mathbf{x}$ is voxel-wise backscatter intensity and $\mathbf{A}$ is a calibrated system matrix that incorporates transmit field, receive response, propagation, and mask-induced encoding (Hu et al., 14 Aug 2025). The same operator form appears in 4D brain cUSi, where $v = Au$ relates volumetric scattering to measured coded data and reconstruction proceeds through matched filtering or iterative inversion (Brown et al., 2023). These formulations make explicit that cUSi is not tied to a single numerical method; what is shared is the replacement of purely geometric beamforming by a forward operator that can be simulated, calibrated, differentiated, or inverted.

The measurement model often dictates the appropriate resolution concept. Finite-frequency tomography replaces line-ray intuition by Fresnel-volume sensitivity and out-of-plane coupling (Martiartu et al., 2019). Pixel reassignment modifies the effective PSF by computationally reassigning off-focus signals from the reflection matrix and yields a different lateral mainlobe–sidelobe trade-off than confocal pulse-echo imaging (Sommer et al., 2021). Encoded sparse-aperture systems evaluate PSF width and clutter by correlation maps of voxel pulse-echo responses rather than by conventional delay-and-sum assumptions (Hu et al., 14 Aug 2025). This suggests that cUSi redefines image quality through the structure of the forward operator as much as through the nominal aperture geometry.

3. Simulation, beamforming, and representational models

Simulation is a foundational branch of cUSi because it provides controlled access to the imaging chain. SIMUS formulates ultrasound propagation in the frequency domain using the Rayleigh–Sommerfeld integral, paraxial Fresnel approximation in elevation, far-field Fraunhofer approximation in azimuth, and analytic models for element directivity and elevation focusing (Garcia, 2021). It generates RF channel data for linear and convex probes and is used to study focused beams, plane-wave imaging, B-mode formation, and Doppler/vector flow imaging. A plausible implication is that simulation platforms such as SIMUS occupy the same conceptual space in cUSi that calibrated forward operators occupy in inverse reconstruction: both make the measurement process explicit and therefore manipulable.

Beamforming-centered cUSi modifies the standard delay-and-sum chain without necessarily changing acquisition. Ultrasound Pixel-Reassignment uses the reflection matrix generated from plane-wave compounding and reassigns off-focus signals to the midpoint between transmit and receive coordinates, improving the effective PSF; in vitro, it provides a $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$0 resolution improvement and a $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$1 dB SNR improvement without hardware or acquisition changes (Sommer et al., 2021). A different representational extension appears in Computational Sonography, which rejects scalar 3D compounding and models each voxel as direction-dependent, either through a second-order tensor $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$2 or a discretized spherical function $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$3, thereby preserving insonification directionality in freehand 3D ultrasound (Göbl et al., 2018).

The same computational framing also organizes modality-specific beamforming pipelines. A comparative implementation study of line-array imaging, endoscopic ultrasound imaging, and plane-wave imaging uses forward simulation, DAS beamforming, envelope detection, scan conversion, and quantitative evaluation to show how geometry-specific reconstruction governs resolution, depth range, frame rate, and complexity (Chen et al., 21 Jul 2025). This suggests that, even when the inverse model is explicit beamforming rather than iterative reconstruction, cUSi remains defined by the software realization of the acquisition geometry and by the possibility of comparing multiple imaging operators within a unified computational framework.

4. Quantitative tomography and speed-of-sound imaging

Quantitative cUSi is most clearly expressed in methods that reconstruct tissue properties rather than grayscale backscatter. In USCT, the target quantity is often the speed-of-sound map $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$4, reconstructed either from ray-based traveltimes or from the entire waveform by full waveform inversion (Sheng et al., 2024). The finite-frequency USCT formulation of wave-equation-based traveltime tomography introduces analytically derived sensitivity kernels in water calibration, shows that sensitivity is distributed in multiple Fresnel volumes, and demonstrates that out-of-plane sensitivity can be exploited to reconstruct 3D images from slice-by-slice acquisitions (Martiartu et al., 2019). Relative to straight-ray tomography, this preserves frequency dependence and diffraction effects while remaining computationally tractable in 3D.

Pulse-echo quantitative imaging provides an alternative route to SoS. CUTE measures phase shifts between beamformed echoes acquired under varying Tx and Rx steering and shows that robust quantitative reconstruction requires two forward-model features: phase shifts must be measured between Tx/Rx pairs centered around common mid-angles, and an additional phase shift induced by mislocalized echoes must be included (Stähli et al., 2019). In a liver-mimicking phantom, the new model yields substantially improved quantitative SoS reconstruction relative to the previously used model, and preliminary volunteer results show anatomically plausible differentiation of skin, subcutaneous fat, rectus muscle, and liver (Stähli et al., 2019).

Diffuse USCT extends the tomographic paradigm further by changing the observable itself. Instead of sequential deterministic transmissions, it uses actively generated diffuse wavefields and inter-station correlations to recover deterministic travel-time information, with phase-weighted stacking used to suppress incoherent fluctuations and instrument noise (Ulrich et al., 2022). The method is presented as a first conceptual study, but it is notable because it recasts ultrasound tomography in interferometric rather than pulse-by-pulse terms. This suggests that quantitative cUSi is not restricted to one class of observables; phase shifts, cross-correlation traveltimes, and full waveforms can all be inserted into model-based inversions provided the forward operator is specified.

5. Sparse apertures, encoded fields, and coherent multi-transducer systems

Sparse and encoded apertures are a major contemporary expression of the hardware–software trade that defines cUSi. A 240-element matrix probe with a $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$5 aperture and $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$6 mm pitch, combined with a randomized dual-layer aberration mask, is explicitly designed to sample the acoustic field with far fewer sensors than classical spatial Nyquist sampling would dictate (Hu et al., 14 Aug 2025). The corresponding forward model is calibrated experimentally with hydrophone measurements and propagated with the angular spectrum method, and reconstruction is performed by matched filtering or LSQR rather than by delay-and-sum (Hu et al., 14 Aug 2025). In phantom experiments, matched filtering improves volumetric image quality over DAS; for Hadamard transmission, encoded matched filtering yields a lateral FWHM of $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$7 mm versus $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$8 mm for non-encoded matched filtering, while LSQR reaches $$\frac{\partial^2 u(\mathbf{x}, t)}{\partial t^2} = c(\mathbf{x})^2 \frac{\partial^2 u(\mathbf{x}, t)}{\partial \mathbf{x}^2} + S(t) \cdot \delta(\mathbf{x} - \mathbf{x}_s^i),$$9 mm lateral FWHM in the encoded 16-angle plane-wave case (Hu et al., 14 Aug 2025).

The same encoded-field logic is carried into 4D carotid flow imaging. Using the same 240-element large-aperture probe, a frequency band-based matched filtering strategy is introduced to balance resolution and contrast, and phantom as well as human carotid experiments show that volumetric B-mode and flow-related information can be recovered with far fewer elements than a fully populated matrix array would require (Hu et al., 25 Sep 2025). In the flow phantom, 3D/4D power Doppler and speckle-tracking analyses resolve flow structure and hemodynamics; in the human study, the carotid bifurcation flow structure and its local pulsatile dynamics are reconstructed (Hu et al., 25 Sep 2025). A plausible implication is that encoded sparse-aperture cUSi is viable not only for static volumetric imaging but also for flow-sensitive 4D acquisitions.

A related but distinct strategy is coherent aperture synthesis across multiple probes. In 2D coherent multi-transducer imaging, synchronized probes take turns transmitting plane waves while all probes receive, and probe locations as well as medium sound speed are estimated directly from RF data by maximizing cross-correlation of echoes from point scatterers (Peralta et al., 2019). Experimentally, lateral resolution improves from $\mathbf{x}_r^j$0 mm to $\mathbf{x}_r^j$1 mm, contrast from $\mathbf{x}_r^j$2 dB to $\mathbf{x}_r^j$3 dB, and CNR from $\mathbf{x}_r^j$4 to $\mathbf{x}_r^j$5 (Peralta et al., 2019). The 3D extension, CoMTUS with two 256-element sparse spiral arrays, reports spatial-resolution improvement up to 10 times in the aligned direction, CNR improvement up to $\mathbf{x}_r^j$6, and generalized CNR improvement up to $\mathbf{x}_r^j$7, with experimental free-hand operation also demonstrated (Peralta et al., 2022). These systems show that cUSi can synthesize extended apertures either through field encoding within one probe or through coherent registration across multiple probes.

Brain haemodynamics provides a small-animal example of the same principle. Four-dimensional brain cUSi uses a deliberately coarse 64-element matrix probe, a spatial encoding mask, and a waveguide to create complex fields, then reconstructs volumetric haemodynamics from a calibrated physical model rather than conventional beamforming (Brown et al., 2023). The aperture under-samples the hardware Nyquist criterion by approximately $\mathbf{x}_r^j$8, yet the system achieves an effective volume rate of about $\mathbf{x}_r^j$9 Hz and approximately $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$0 resolution in cortex (Brown et al., 2023). This suggests that sparse-aperture cUSi is not tied to a single scale; the same computational principle spans rodent neuroimaging and large-footprint vascular imaging.

6. Learning-based and differentiable pipelines

Learning-based cUSi replaces or augments explicit inversion with trained operators. In sparse-data USCT, APS-USCT uses a three-part pipeline: APS-physics generates dense waveform labels from simulated SoS maps, APS-wave converts sparse waveforms into dense waveforms with a 15-layer encoder–decoder, and APS-FWI uses InversionNet, optionally with source encoding and Squeeze-and-Excitation blocks, to reconstruct SoS maps (Sheng et al., 2024). On a breast phantom dataset, APS-USCT achieves an average SSIM of $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$1, with $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$2 of test samples above $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$3, $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$4 above $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$5, and $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$6 above $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$7 under a $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$8 sparse configuration corresponding to $$\Delta\boldsymbol{\theta} = \boldsymbol{M}\,\Delta\boldsymbol{\sigma},$$9 data sparsity (Sheng et al., 2024). The same study reports hardware–software trade-offs such as $\Delta\boldsymbol{\sigma}$0 elements and SSIM $\Delta\boldsymbol{\sigma}$1 for dense $\Delta\boldsymbol{\sigma}$2 InversionNet versus $\Delta\boldsymbol{\sigma}$3 elements and SSIM $\Delta\boldsymbol{\sigma}$4 for APS-USCT using $\Delta\boldsymbol{\sigma}$5 waveform augmentation (Sheng et al., 2024).

An earlier RF-domain example is deep learning for accelerated ultrasound imaging. A 28-layer CNN with batch normalization, ReLU, and skip connections is trained on $\Delta\boldsymbol{\sigma}$6 Rx–SC RF planes to interpolate missing receive-channel data under $\Delta\boldsymbol{\sigma}$7 random sub-sampling, after which conventional DAS is applied (Yoon et al., 2017). Using only $\Delta\boldsymbol{\sigma}$8 of the RF data, the method reports an average PSNR of approximately $\Delta\boldsymbol{\sigma}$9 dB and approximately $\boldsymbol{M}$0 dB improvement over images beamformed directly from the sub-sampled RF data (Yoon et al., 2017). The conceptual point is that the inverse problem is posed at the RF level rather than as post-beamforming enhancement, which is characteristic of cUSi’s preference for signal-domain rather than image-domain compensation.

Cross-modality learned inversion pushes the same idea further. A multi-resolution CNN trained on simulated RF/IQ data derived from CT scans reconstructs “CT-quality” images from ultrasound IQ data and also imitates computationally heavy despeckling methods (Vedula et al., 2017). For a different CT dataset from TCIA, the CNN-CT outputs reach an average PSNR of $\boldsymbol{M}$1 dB against CT ground truth, while CNN approximations of despeckling filters achieve large runtime reductions relative to BM3D, NLM, and TV (Vedula et al., 2017). Although the paper explicitly states that this does not amount to exact recovery of acoustic tissue properties, it demonstrates an early cUSi pattern in which deep networks are used as surrogates for expensive inverse mappings or post-processing operators.

Differentiable toolchains generalize these learned approaches into programmable infrastructure. The zea toolbox defines a modular ultrasound pipeline composed of operations such as Demodulate, TOFCorrection, PfieldWeighting, DelayAndSum, EnvelopeDetect, Normalize, LogCompress, and ScanConvert, all implemented as differentiable Keras 3 operations with TensorFlow, PyTorch, and JAX backends (Stevens et al., 1 Dec 2025). It also includes generative models and agents for adaptive subsampling, allowing posterior inference and acquisition design to be embedded inside one differentiable graph (Stevens et al., 1 Dec 2025). This suggests that the current trajectory of cUSi is not only toward learned reconstructions but toward end-to-end optimization of acquisition, beamforming, and inference.

7. Applications, limitations, and outlook

The application range of cUSi is already broad. Breast imaging appears in USCT, sparse-data APS-USCT, and finite-frequency tomography (Sheng et al., 2024, Martiartu et al., 2019). Carotid imaging appears in encoded sparse-aperture 3D/4D systems, where high-resolution images with reasonable contrast and volumetric flow assessment are demonstrated with only 240 elements (Hu et al., 14 Aug 2025, Hu et al., 25 Sep 2025). Brain haemodynamics is reconstructed volumetrically in awake and anesthetized mice at ultrafast rates using a 64-element coded system (Brown et al., 2023). Handheld pulse-echo SoS imaging extends cUSi into routine abdominal imaging, including liver characterization with a standard linear probe (Stähli et al., 2019). Endoscopic, line-array, and plane-wave implementations show that cUSi also encompasses modality-specific computational pipelines even when the output remains a conventional B-mode image (Chen et al., 21 Jul 2025).

The limitations are equally characteristic. Many methods assume homogeneous media, straight rays, constant density, or 2D propagation, and several papers explicitly identify generalization from simulation to real data as an open issue (Sheng et al., 2024, Martiartu et al., 2019). Encoded masks improve resolution but often reduce contrast and penetration depth; in sparse carotid cUSi, encoding improves lateral FWHM yet tends to reduce CR, particularly in low-SNR or plane-wave scenarios (Hu et al., 14 Aug 2025). Iterative inversions such as LSQR can sharpen resolution but are computationally intensive and sensitive to noise or model mismatch (Hu et al., 14 Aug 2025). Multi-transducer systems require subwavelength localization accuracy and stable coherence, which shifts the burden from hardware fabrication to calibration and synchronization (Peralta et al., 2019, Peralta et al., 2022). Deep models may replace iterative solvers at inference, but they inherit dependence on simulated training distributions and on the fidelity of the forward simulator (Yoon et al., 2017, Vedula et al., 2017).

A consistent outlook emerges from these strands. One direction is richer physics: 3D USCT, finite-frequency kernels, encoded flow imaging, and hybrid methods that combine calibration data, reciprocity, and wave-equation structure (Martiartu et al., 2019, Hu et al., 25 Sep 2025). A second is richer computation: differentiable beamforming, learned inversion, posterior sampling, and active acquisition (Stevens et al., 1 Dec 2025). A third is co-design of hardware and algorithms: sparse large-aperture probes, aberration masks, multi-probe arrays, and transmit coding schemes whose utility depends on the invertibility of the calibrated forward operator rather than on conventional beam geometry (Hu et al., 14 Aug 2025, Brown et al., 2023, Peralta et al., 2022). Taken together, these developments define cUSi not as a single modality but as a general framework for ultrasound in which physical modeling, calibration, numerical inversion, and learned priors are treated as primary imaging components rather than as secondary post-processing.