Simulation-Based Imaging: Learning Acoustic Inverse Problems from Simulated Data

Learning phase diversity for solving ill-posed inverse problems in imaging

Inverse problems in imaging are typically ill-posed and are solved using regularized optimization techniques or - in recent times, by employing deep neural networks. While the deep network method enables fast end-to-end reconstruction from raw measurements, it does not necessarily alter the fundamentally ill-posed nature of the underlying inverse problem. It is well known that diverse, non-redundant measurements can improve the robustness of reconstruction algorithms. However, acquiring multiple measurements typically - involves additional hardware and more complex system setups, that may not always be desirable for field deployment. In this work, we note that in both incoherent and coherent (phase retrieval) optical imaging, the irradiance patterns corresponding to two phase diverse measurements associated with the same test object have implicit local correlations, which may be learned by a suitable deep network. A physics informed data augmentation scheme is then described where a trained network is used for generating a phase diverse pseudo-data based on a ground truth data frame, typically acquired using a standard imaging system. We validate this data augmentation approach for both incoherent and coherent optical imaging - configurations, with vortex phase as a - diversity mechanism. Specifically, we observe that the generated pseudo-data closely match the corresponding ground-truth data, with comparable noise characteristics. We further demonstrate that the true data along with the augmented pseudo-data provide- high quality inverse solutions with simpler robust reconstruction algorithms. Our results may open new avenues for leaner, high-fidelity computational imaging systems across a broad range of applications.

Matrix-Free Photoacoustic Image Reconstruction via Sensor-Token Self-Attention

Photoacoustic tomography (PAT) combines the optical absorption contrast of biological tissue with the spatial resolution of ultrasound, yet recovering the initial pressure distribution from sparse-view sensor measurements remains an ill-posed inverse problem. Iterative compressive-sensing solvers and unrolled deep networks both retain a dependence on the system matrix at inference, which leaves real-time clinical reconstruction computationally expensive. This paper proposes the Sensor Attention Network (SAN), a Transformer-based architecture that treats the full time series of each sensor as a token and maps raw measurements directly to the reconstructed image without invoking the system matrix at inference. For training and benchmarking, an analytical k-space H-matrix is constructed and validated against the k-Wave pseudo-spectral solver under matched geometry, achieving a mean per-sensor Pearson correlation of 0.919 +/- 0.049, with k-space apodization and Gaussian temporal damping acting synergistically to reduce the energy-normalized mismatch by 49%. Trained with a vessel-weighted loss on 488 augmented samples and evaluated on 46 held-out samples against ISTA, split-Bregman total variation (SBTV), and learned ISTA (LISTA), SAN attains the highest mean SSIM (0.522) and PSNR (22.09 dB) and the lowest NMSE (0.233). Paired t-tests and Wilcoxon signed-rank tests confirm the superiority of SAN over LISTA on PSNR, NMSE, and Pearson correlation at p<1e-8, and over ISTA and SBTV on all fidelity metrics. By bypassing the H-matrix at inference, SAN reduces reconstruction time by at least an order of magnitude, supporting real-time PAT reconstruction.

Amortised neural acoustic tomography: domain-specific encoder design and topology-dependent Eikonal analysis

We present an amortised neural framework for three-dimensional acoustic diffraction tomography that reconstructs scene geometry as signed distance functions from boundary element method (BEM) pressure observations. Our central finding is that domain-specific encoder design, rather than physics-informed loss terms, drives reconstruction accuracy. Building on a transfer function decomposition that separates scattering from free-space propagation, we introduce an encoder that maps complex pressure measurements to latent geometry codes through magnitude–phase input representation and frequency-selective attention pooling. Across 100 synthetic scenes spanning 12 shape categories (3 random seeds), this encoder attains 0.644±0.015 mean intersection over union, a 51.0% improvement over a domain-agnostic baseline ( p=0.0015), while the physics losses evaluated in this amortised setting provide zero or negative benefit. Inference is a single forward pass ( ∼127 ms, a ∼950× speedup over per-scene optimisation). A systematic Eikonal regularisation ablation reveals a topology- and architecture-dependent asymmetry: any benefit is confined to specific convex shapes with reconstruction headroom in the per-scene auto-decoder and vanishes under encoder amortisation, whereas the harm—a flattening of topological features—is universal across architectures. Combined with Helmholtz partial differential equation failure and Laplacian supervision dead-ends, these findings challenge the assumption that physics losses universally benefit neural acoustic surrogates and suggest that architectural physics integration is more effective than loss-based approaches. We will release a 100-scene 3D BEM benchmark dataset, deterministically regenerable from the accompanying code, for reproducibility.

Data-Driven Deep Learning for Imaging Through Scattering Media: Architectures, Learning Paradigms, and Methodological Frontiers

Imaging through scattering media continues to be a persistent challenge in optical imaging due to the fact that scattering disrupts the direct relationship between the object and the measured signal. Once this relationship is degraded, reconstructing the original scene turns into a challenging inverse problem, for which standard imaging models are frequently insufficient. Recently, deep learning has emerged as an effective framework for reconstruction, since it allows the mapping from scattered measurements to object estimates to be learned directly from data. This review focuses particularly on purely data-driven methods, in which the neural network acts as the primary reconstruction engine instead of functioning as a supplementary element. The reviewed studies are examined in three dimensions: reconstruction frameworks, learning regimes, and system-level integration. Within this framework, we examine how various approaches trade off reconstruction accuracy, robustness, portability, and computational expense. We also consider training data requirements, adaptation strategies, generalization behavior, and evaluation practice. The literature shows clear progress toward more adaptive and robust reconstruction systems. However, several limitations continue to hinder broader applicability, including dependence on paired training data, fragmented out-of-distribution evaluation, the absence of standardized robustness and benchmarking protocols, and limited reporting on practical deployment. On the basis of this analysis, we identify several priorities for future research, encompassing the development of weakly supervised learning methodologies, the establishment of standardized multi-dimensional robustness assessment protocols, the advancement of modular physics-informed design strategies, and the exploration of more tightly integrated reconstruction frameworks.

Toward a Foundation Plug-and-Play Prior for Computed Tomography Reconstruction via a Multimodal Diffusion Model

Computed tomography (CT) throughput is limited by scan time, which grows with both the number of projections acquired and the detector integration time for each. Reconstructing high-quality volumes from sparse-view or low-dose measurements therefore depends on an informative prior, typically a neural network trained for one specific scan setting and retrained whenever the modality, geometry, or material changes. We investigate whether a single diffusion model trained across several imaging domains can instead serve as a prior for many CT problems simultaneously. We evaluate the proposed method using the same frozen model on three datasets that differ in modality, beam geometry, material, and degradation type, spanning flaw analysis in additively manufactured metal parts imaged with cone-beam X-ray CT and concrete microstructure imaged with parallel-beam neutron CT. Our proposed method out-performs analytic reconstructions in all three cases, providing a step toward a reusable foundation prior for heterogeneous CT reconstruction problems.

Fast and Robust IVIM Parameter Estimation in Breast MRI Using Physics-Informed Deep Learning