ABSTRACT Limited Angle Computed Tomography (LACT) often faces significant challenges due to missing angular information. Unlike previous methods that operate in the image domain, we propose a new method that focuses on sinogram inpaint-ing. We leverage MR-SDEs, a variant of diffusion models that characterize the diffusion process with mean-reverting stochastic differential equations, to fill in missing angular data at the projection level. Furthermore, by combining distillation with constraining the output of the model using the pseudo-inverse of the inpainting matrix, the diffusion process is accelerated and done in a step, enabling efficient and accurate sinogram completion. Quantitative experimental results demonstrate that the proposed method achieves state-of-the-art performance in both perceptual and fidelity quality, offering a promising solution for LACT reconstruction in scientific and clinical applications.

Abstract--Accurate PET imaging increasingly requires methods that support unconstrained detector layouts--from walk-through designs to long-axial rings--where gaps and open sides lead to severely undersampled sinograms. Instead of constraining the hardware to form complete cylinders, we propose treating the missing lines-of-responses as a learnable prior . Data-driven approaches, particularly generative models, offer a promising pathway to recover this missing information. In this work, we explore the use of conditional diffusion models to interpolate sparsely sampled sinograms, paving the way for novel, cost-efficient, and patient-friendly PET geometries in real clinical settings. Positron Emission Tomography (PET) relies on the coincidence detection of gamma photon pairs using scintillation crystals.

-- During raw - data acquisition in CT imaging, diverse factors can degrade the co llected sinograms, with un-dersampling and noise leading to severe artifacts and noise in reconstructed images and compromising diagnostic accuracy. Conventional correction methods rely on manually designed algorithms or fixed empirical parameters, but thes e approaches often lack generalizability across heterogeneous artifact types. To address these limitations, we propose UniSino, a foundation model for universal CT sino-gram standardization. Unlike existing foundational models that operate in image domain, UniSino directly standardizes dat a in the projection domain, which enables stronger generalization across diverse undersampling scenarios. Its training framework incorporates the physical characteristics of sinograms, enhancing generalization and enabling robust performance across mul tiple subtasks spanning four benchmark datasets. T he code is available at: https://github.com/yqx7150/UniSino . In CT imaging, the sinogram represents the raw pr ojection data before image reconstruction . However, in practical clinical data acquisition, raw sinogram data are frequently degraded by a multitude of factors -- including hardware limitations, environmental variability, and patient - induced factor s -- resulting in complex and heterogeneous data corruption [2]. Without effective preprocessing, such imperfections are readily amplified through the reconstruction process, which lead to severe image artifacts [3], including detector - induced ring patterns [4], beam ha rdening from metal implants [5], geometric distortions from miscalibration [6], and motion - induced inconsistencies [7, 8]. These artifacts not only degrade visual quality but critically compromise diagnostic reliability.

High-dimensional datasets often exhibit low-dimensional geometric structures, as suggested by the manifold hypothesis, which implies that data lie on a smooth manifold embedded in a higher-dimensional ambient space. While this insight underpins many advances in machine learning and inverse problems, fully leveraging it requires to deal with three key tasks: estimating the intrinsic dimension (ID) of the manifold, constructing appropriate local coordinates, and learning mappings between ambient and manifold spaces. In this work, we propose a framework that addresses all these challenges using a Mixture of Variational Autoencoders (VAEs) and tools from Riemannian geometry. We specifically focus on estimating the ID of datasets by analyzing the numerical rank of the VAE decoder pullback metric. The estimated ID guides the construction of an atlas of local charts using a mixture of invertible VAEs, enabling accurate manifold parameterization and efficient inference. We how this approach enhances solutions to ill-posed inverse problems, particularly in biomedical imaging, by enforcing that reconstructions lie on the learned manifold. Lastly, we explore the impact of network pruning on manifold geometry and reconstruction quality, showing that the intrinsic dimension serves as an effective proxy for monitoring model capacity.

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage of the computational speed and flexible boundary conditions offered by splines on a grid. We choose to regularize the Hessian of the spline via the nuclear norm to promote sparsity. As a result, the method is spatially adaptive and stable against the choice of the regularization parameter, which plays the role of the bandwidth. We test our computational pipeline on standard densities and provide software. We also present a new approach to PET rebinning as an application of our framework.

Reconstructing images using Computed Tomography (CT) in an industrial context leads to specific challenges that differ from those encountered in other areas, such as clinical CT. Indeed, non-destructive testing with industrial CT will often involve scanning multiple similar objects while maintaining high throughput, requiring short scanning times, which is not a relevant concern in clinical CT. Under-sampling the tomographic data (sinograms) is a natural way to reduce the scanning time at the cost of image quality since the latter depends on the number of measurements. In such a scenario, post-processing techniques are required to compensate for the image artifacts induced by the sinogram sparsity. We introduce the Self-supervised Denoiser Framework (SDF), a self-supervised training method that leverages pre-training on highly sampled sinogram data to enhance the quality of images reconstructed from undersampled sinogram data. The main contribution of SDF is that it proposes to train an image denoiser in the sinogram space by setting the learning task as the prediction of one sinogram subset from another. As such, it does not require ground-truth image data, leverages the abundant data modality in CT, the sinogram, and can drastically enhance the quality of images reconstructed from a fraction of the measurements. We demonstrate that SDF produces better image quality, in terms of peak signal-to-noise ratio, than other analytical and self-supervised frameworks in both 2D fan-beam or 3D cone-beam CT settings. Moreover, we show that the enhancement provided by SDF carries over when fine-tuning the image denoiser on a few examples, making it a suitable pre-training technique in a context where there is little high-quality image data. Our results are established on experimental datasets, making SDF a strong candidate for being the building block of foundational image-enhancement models in CT.

Recent advances in diffusion models have demonstrated exceptional performance in generative tasks across vari-ous fields. In positron emission tomography (PET), the reduction in tracer dose leads to information loss in sino-grams. Using diffusion models to reconstruct missing in-formation can improve imaging quality. Traditional diffu-sion models effectively use Gaussian noise for image re-constructions. However, in low-dose PET reconstruction, Gaussian noise can worsen the already sparse data by introducing artifacts and inconsistencies. To address this issue, we propose a diffusion model named residual esti-mation diffusion (RED). From the perspective of diffusion mechanism, RED uses the residual between sinograms to replace Gaussian noise in diffusion process, respectively sets the low-dose and full-dose sinograms as the starting point and endpoint of reconstruction. This mechanism helps preserve the original information in the low-dose sinogram, thereby enhancing reconstruction reliability. From the perspective of data consistency, RED introduces a drift correction strategy to reduce accumulated prediction errors during the reverse process. Calibrating the inter-mediate results of reverse iterations helps maintain the data consistency and enhances the stability of reconstruc-tion process. Experimental results show that RED effec-tively improves the quality of low-dose sinograms as well as the reconstruction results. The code is available at: https://github.com/yqx7150/RED.

Inverse problems arise in many applications, especially tomographic imaging. We develop a Learned Alternating Minimization Algorithm (LAMA) to solve such problems via two-block optimization by synergizing data-driven and classical techniques with proven convergence. LAMA is naturally induced by a variational model with learnable regularizers in both data and image domains, parameterized as composite functions of neural networks trained with domain-specific data. We allow these regularizers to be nonconvex and nonsmooth to extract features from data effectively. We minimize the overall objective function using Nesterov's smoothing technique and residual learning architecture. It is demonstrated that LAMA reduces network complexity, improves memory efficiency, and enhances reconstruction accuracy, stability, and interpretability. Extensive experiments show that LAMA significantly outperforms state-of-the-art methods on popular benchmark datasets for Computed Tomography.

Plug&Play (PnP) diffusion models are state-of-the-art methods in computed tomography (CT) reconstruction. Such methods usually consider applications where the sinogram contains a sufficient amount of information for the posterior distribution to be peaked, and consequently are evaluated using image-to-image metrics such as PSNR/SSIM. Instead, we are interested in reconstructing compressible flow images from sinograms having a small number of projections, which results in a posterior distribution no longer peaked or even multimodal. Thus, in this paper, we aim at evaluating the approximate posterior of PnP diffusion models and introduce two posterior evaluation criteria. We quantitatively evaluate three PnP diffusion methods on three different datasets for several numbers of projections. We surprisingly find that, for each method, the approximate posterior deviates from the true posterior when the number of projections decreases.

Inverse Synthetic Aperture Radar (ISAR) imaging presents a formidable challenge when it comes to small everyday objects due to their limited Radar Cross-Section (RCS) and the inherent resolution constraints of radar systems. Existing ISAR reconstruction methods including backprojection (BP) often require complex setups and controlled environments, rendering them impractical for many real-world noisy scenarios. In this paper, we propose a novel Analysis-through-Synthesis (ATS) framework enabled by Neural Radiance Fields (NeRF) for high-resolution coherent ISAR imaging of small objects using sparse and noisy Ultra-Wideband (UWB) radar data with an inexpensive and portable setup. Our end-to-end framework integrates ultra-wideband radar wave propagation, reflection characteristics, and scene priors, enabling efficient 2D scene reconstruction without the need for costly anechoic chambers or complex measurement test beds. With qualitative and quantitative comparisons, we demonstrate that the proposed method outperforms traditional techniques and generates ISAR images of complex scenes with multiple targets and complex structures in Non-Line-of-Sight (NLOS) and noisy scenarios, particularly with limited number of views and sparse UWB radar scans. This work represents a significant step towards practical, cost-effective ISAR imaging of small everyday objects, with broad implications for robotics and mobile sensing applications.