Sparse-View CT (SVCT) reconstruction improves temporal resolution and reduces radiation dose, yet its clinical use is hindered by artifacts due to view reduction and domain shifts from scanner, protocol, or anatomical variations, leading to performance degradation in out-of-distribution (OOD) scenarios. We propose a Cross-Distribution Diffusion Priors-Driven Iterative Reconstruction (CDPIR) framework to tackle the OOD problem in SVCT. CDPIR integrates cross-distribution diffusion priors, derived from a Scalable Interpolant Transformer (SiT), with model-based iterative reconstruction methods. Specifically, we train a SiT backbone, an extension of the Diffusion Transformer (DiT) architecture, to establish a unified stochastic interpolant framework, leveraging Classifier-Free Guidance (CFG) across multiple datasets. By randomly dropping the conditioning with a null embedding during training, the model learns a more transferable cross-distribution prior that encourages domain-invariant anatomical structures while allowing domain-specific appearance modulation. During sampling, the globally sensitive transformer-based diffusion model exploits the cross-distribution prior within the unified stochastic interpolant framework, enabling flexible and stable control over multi-distribution-to-noise interpolation paths and decoupled sampling strategies, thereby improving adaptation to OOD reconstruction. By alternating between data fidelity and sampling updates, our model achieves state-of-the-art performance with superior detail preservation in SVCT reconstructions. Extensive experimental results demonstrate that CDPIR significantly outperforms existing approaches, particularly under OOD conditions, highlighting its robustness and potential clinical value in challenging imaging scenarios. The code is available at https://github.com/Graeme-Lee/CDPIR.

Deep learning has been extensively applied in medical image reconstruction, where Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) represent the predominant paradigms, each possessing distinct advantages and inherent limitations: CNNs exhibit linear complexity with local sensitivity, whereas ViTs demonstrate quadratic complexity with global sensitivity. The emerging Mamba has shown superiority in learning visual representation, which combines the advantages of linear scalability and global sensitivity. In this study, we introduce MambaMIR, an Arbitrary-Masked Mamba-based model with wavelet decomposition for joint medical image reconstruction and uncertainty estimation. A novel Arbitrary Scan Masking (ASM) mechanism "masks out" redundant information to introduce randomness for further uncertainty estimation. Compared to the commonly used Monte Carlo (MC) dropout, our proposed MC-ASM provides an uncertainty map without the need for hyperparameter tuning and mitigates the performance drop typically observed when applying dropout to low-level tasks. For further texture preservation and better perceptual quality, we employ the wavelet transformation into MambaMIR and explore its variant based on the Generative Adversarial Network, namely MambaMIR-GAN. Comprehensive experiments have been conducted for multiple representative medical image reconstruction tasks, demonstrating that the proposed MambaMIR and MambaMIR-GAN outperform other baseline and state-of-the-art methods in different reconstruction tasks, where MambaMIR achieves the best reconstruction fidelity and MambaMIR-GAN has the best perceptual quality. In addition, our MC-ASM provides uncertainty maps as an additional tool for clinicians, while mitigating the typical performance drop caused by the commonly used dropout.

The reconstruction of limited data computed tomography (CT) aims to obtain high-quality images from a reduced set of projection views acquired from sparse views or limited angles. This approach is utilized to reduce radiation exposure or expedite the scanning process. Deep Learning (DL) techniques have been incorporated into limited data CT reconstruction tasks and achieve remarkable performance. However, these DL methods suffer from various limitations. Firstly, the distribution inconsistency between the simulation data and the real data hinders the generalization of these DL-based methods. Secondly, these DL-based methods could be unstable due to lack of kernel awareness. This paper addresses these issues by proposing an unrolling framework called Progressive Artifact Image Learning (PAIL) for limited data CT reconstruction. The proposed PAIL primarily consists of three key modules, i.e., a residual domain module (RDM), an image domain module (IDM), and a wavelet domain module (WDM). The RDM is designed to refine features from residual images and suppress the observable artifacts from the reconstructed images. This module could effectively alleviate the effects of distribution inconsistency among different data sets by transferring the optimization space from the original data domain to the residual data domain. The IDM is designed to suppress the unobservable artifacts in the image space. The RDM and IDM collaborate with each other during the iterative optimization process, progressively removing artifacts and reconstructing the underlying CT image. Furthermore, in order to void the potential hallucinations generated by the RDM and IDM, an additional WDM is incorporated into the network to enhance its stability. This is achieved by making the network become kernel-aware via integrating wavelet-based compressed sensing. The effectiveness of the proposed PAIL method has been consistently verified on two simulated CT data sets, a clinical cardiac data set and a sheep lung data set. Compared to other state-of-the-art methods, the proposed PAIL method achieves superior performance in various limited data CT reconstruction tasks, demonstrating its promising generalization and stability.

Low-dose digital radiography (DR) and computed tomography (CT) become increasingly popular due to reduced radiation dose. However, they often result in degraded images with lower signal-to-noise ratios, creating an urgent need for effective denoising techniques. The recent advancement of the single-image-based denoising approach provides a promising solution without requirement of pairwise training data, which are scarce in medical imaging. These methods typically rely on sampling image pairs from a noisy image for inter-supervised denoising. Although enjoying simplicity, the generated image pairs are at the same noise level and only include partial information about the input images. This study argues that generating image pairs at different noise levels while fully using the information of the input image is preferable since it could provide richer multi-perspective clues to guide the denoising process. To this end, we present a novel Multi-Level Noise Sampling (MNS) method for low-dose tomography denoising. Specifically, MNS method generates multi-level noisy sub-images by partitioning the high-dimensional input space into multiple low-dimensional sub-spaces with a simple yet effective strategy. The superiority of the MNS method in single-image-based denoising over the competing methods has been investigated and verified theoretically. Moreover, to bridge the gap between self-supervised and supervised denoising networks, we introduce an optimization function that leverages prior knowledge of multi-level noisy sub-images to guide the training process. Through extensive quantitative and qualitative experiments conducted on large-scale clinical low-dose CT and DR datasets, we validate the effectiveness and superiority of our MNS approach over other state-of-the-art supervised and self-supervised methods.

Construction and analysis of functional brain networks (FBNs) with resting-state functional magnetic resonance imaging (rs-fMRI) is a promising method to diagnose functional brain diseases. Nevertheless, the existing methods suffer from several limitations. First, the functional connectivities (FCs) of the FBN are usually measured by the temporal co-activation level between rs-fMRI time series from regions of interest (ROIs). While enjoying simplicity, the existing approach implicitly assumes simultaneous co-activation of all the ROIs, and models only their synchronous dependencies. However, the FCs are not necessarily always synchronous due to the time lag of information flow and cross-time interactions between ROIs. Therefore, it is desirable to model asynchronous FCs. Second, the traditional methods usually construct FBNs at individual level, leading to large variability and degraded diagnosis accuracy when modeling asynchronous FBN. Third, the FBN construction and analysis are conducted in two independent steps without joint alignment for the target diagnosis task. To address the first limitation, this paper proposes an effective sliding-window-based method to model spatiotemporal FCs in Transformer. Regarding the second limitation, we propose to learn common and individual FBNs adaptively with the common FBN as prior knowledge, thus alleviating the variability and enabling the network to focus on the individual disease-specific asynchronous FCs. To address the third limitation, the common and individual asynchronous FBNs are built and analyzed by an integrated network, enabling end-to-end training and improving the flexibility and discriminability. The effectiveness of the proposed method is consistently demonstrated on three data sets for mild cognitive impairment (MCI) diagnosis.

Coded aperture snapshot spectral imaging (CASSI) system is an effective manner for hyperspectral snapshot compressive imaging. The core issue of CASSI is to solve the inverse problem for the reconstruction of hyperspectral image (HSI). In recent years, Transformer-based methods achieve promising performance in HSI reconstruction. However, capturing both long-range dependencies and local information while ensuring reasonable computational costs remains a challenging problem. In this paper, we propose a Transformer-based HSI reconstruction method called dual-window multiscale Transformer (DWMT), which is a coarse-to-fine process, reconstructing the global properties of HSI with the long-range dependencies. In our method, we propose a novel U-Net architecture using a dual-branch encoder to refine pixel information and full-scale skip connections to fuse different features, enhancing the extraction of fine-grained features. Meanwhile, we design a novel self-attention mechanism called dual-window multiscale multi-head self-attention (DWM-MSA), which utilizes two different-sized windows to compute self-attention, which can capture the long-range dependencies in a local region at different scales to improve the reconstruction performance. We also propose a novel position embedding method for Transformer, named con-abs position embedding (CAPE), which effectively enhances positional information of the HSIs. Extensive experiments on both the simulated and the real data are conducted to demonstrate the superior performance, stability, and generalization ability of our DWMT. Code of this project is at https://github.com/chenx2000/DWMT.

Gradient boosting is an efficient and scalable supervised machine learning technique, and most scaling models based on gradient boosting perform well on point regression tasks, but they can only be run in batch settings and cannot be learned online on the data stream. To solve this problem, this paper proposes a tree regression method based on incremental gradient boosting (IGB). The proposed method uses gradient information as a splitting metric and applies the Hoeffding inequality incrementally to construct decision trees to achieve incremental gradient improvement. After a large number of experimental evaluations, the proposed method outperforms the existing online regression trees in point regression tasks, and in some cases, has comparable performance to the batch gradient boosting tree model.

Limited-angle tomographic reconstruction is one of the typical ill-posed inverse problems, leading to edge divergence with degraded image quality. Recently, deep learning has been introduced into image reconstruction and achieved great results. However, existing deep reconstruction methods have not fully explored data consistency, resulting in poor performance. In addition, deep reconstruction methods are still mathematically inexplicable and unstable. In this work, we propose an iterative residual optimization network (IRON) for limited-angle tomographic reconstruction. First, a new optimization objective function is established to overcome false negative and positive artifacts induced by limited-angle measurements. We integrate neural network priors as a regularizer to explore deep features within residual data. Furthermore, the block-coordinate descent is employed to achieve a novel iterative framework. Second, a convolution assisted transformer is carefully elaborated to capture both local and long-range pixel interactions simultaneously. Regarding the visual transformer, the multi-head attention is further redesigned to reduce computational costs and protect reconstructed image features. Third, based on the relative error convergence property of the convolution assisted transformer, a mathematical convergence analysis is also provided for our IRON. Both numerically simulated and clinically collected real cardiac datasets are employed to validate the effectiveness and advantages of the proposed IRON. The results show that IRON outperforms other state-of-the-art methods.

The multi-source stationary CT, where both the detector and X-ray source are fixed, represents a novel imaging system with high temporal resolution that has garnered significant interest. Limited space within the system restricts the number of X-ray sources, leading to sparse-view CT imaging challenges. Recent diffusion models for reconstructing sparse-view CT have generally focused separately on sinogram or image domains. Sinogram-centric models effectively estimate missing projections but may introduce artifacts, lacking mechanisms to ensure image correctness. Conversely, image-domain models, while capturing detailed image features, often struggle with complex data distribution, leading to inaccuracies in projections. Addressing these issues, the Dual-domain Collaborative Diffusion Sampling (DCDS) model integrates sinogram and image domain diffusion processes for enhanced sparse-view reconstruction. This model combines the strengths of both domains in an optimized mathematical framework. A collaborative diffusion mechanism underpins this model, improving sinogram recovery and image generative capabilities. This mechanism facilitates feedback-driven image generation from the sinogram domain and uses image domain results to complete missing projections. Optimization of the DCDS model is further achieved through the alternative direction iteration method, focusing on data consistency updates. Extensive testing, including numerical simulations, real phantoms, and clinical cardiac datasets, demonstrates the DCDS model's effectiveness. It consistently outperforms various state-of-the-art benchmarks, delivering exceptional reconstruction quality and precise sinogram.

The score-based generative model (SGM) has received significant attention in the field of medical imaging, particularly in the context of limited-angle computed tomography (LACT). Traditional SGM approaches achieved robust reconstruction performance by incorporating a substantial number of sampling steps during the inference phase. However, these established SGM-based methods require large computational cost to reconstruct one case. The main challenge lies in achieving high-quality images with rapid sampling while preserving sharp edges and small features. In this study, we propose an innovative rapid-sampling strategy for SGM, which we have aptly named the time-reversion fast-sampling (TIFA) score-based model for LACT reconstruction. The entire sampling procedure adheres steadfastly to the principles of robust optimization theory and is firmly grounded in a comprehensive mathematical model. TIFA's rapid-sampling mechanism comprises several essential components, including jump sampling, time-reversion with re-sampling, and compressed sampling. In the initial jump sampling stage, multiple sampling steps are bypassed to expedite the attainment of preliminary results. Subsequently, during the time-reversion process, the initial results undergo controlled corruption by introducing small-scale noise. The re-sampling process then diligently refines the initially corrupted results. Finally, compressed sampling fine-tunes the refinement outcomes by imposing regularization term. Quantitative and qualitative assessments conducted on numerical simulations, real physical phantom, and clinical cardiac datasets, unequivocally demonstrate that TIFA method (using 200 steps) outperforms other state-of-the-art methods (using 2000 steps) from available [0°, 90°] and [0°, 60°]. Furthermore, experimental results underscore that our TIFA method continues to reconstruct high-quality images even with 10 steps. Our code at https://github.com/tianzhijiaoziA/TIFADiffusion.

Score-based generative model (SGM) has risen to prominence in sparse-view CT reconstruction due to its impressive generation capability. The consistency of data is crucial in guiding the reconstruction process in SGM-based reconstruction methods. However, the existing data consistency policy exhibits certain limitations. Firstly, it employs partial data from the reconstructed image of the iteration process for image updates, which leads to secondary artifacts with compromising image quality. Moreover, the updates to the SGM and data consistency are considered as distinct stages, disregarding their interdependent relationship. Additionally, the reference image used to compute gradients in the reconstruction process is derived from the intermediate result rather than ground truth. Motivated by the fact that a typical SGM yields distinct outcomes with different random noise inputs, we propose a Multi-channel Optimization Generative Model (MOGM) for stable ultra-sparse-view CT reconstruction by integrating a novel data consistency term into the stochastic differential equation model. Notably, the unique aspect of this data consistency component is its exclusive reliance on original data for effectively confining generation outcomes. Furthermore, we pioneer an inference strategy that traces back from the current iteration result to ground truth, enhancing reconstruction stability through foundational theoretical support. We also establish a multi-channel optimization reconstruction framework, where conventional iterative techniques are employed to seek the reconstruction solution. Quantitative and qualitative assessments on 23 views datasets from numerical simulation, clinical cardiac and sheep's lung underscore the superiority of MOGM over alternative methods. Reconstructing from just 10 and 7 views, our method consistently demonstrates exceptional performance.

The score-based generative model (SGM) has demonstrated remarkable performance in addressing challenging under-determined inverse problems in medical imaging. However, acquiring high-quality training datasets for these models remains a formidable task, especially in medical image reconstructions. Prevalent noise perturbations or artifacts in low-dose Computed Tomography (CT) or under-sampled Magnetic Resonance Imaging (MRI) hinder the accurate estimation of data distribution gradients, thereby compromising the overall performance of SGMs when trained with these data. To alleviate this issue, we propose a wavelet-improved denoising technique to cooperate with the SGMs, ensuring effective and stable training. Specifically, the proposed method integrates a wavelet sub-network and the standard SGM sub-network into a unified framework, effectively alleviating inaccurate distribution of the data distribution gradient and enhancing the overall stability. The mutual feedback mechanism between the wavelet sub-network and the SGM sub-network empowers the neural network to learn accurate scores even when handling noisy samples. This combination results in a framework that exhibits superior stability during the learning process, leading to the generation of more precise and reliable reconstructed images. During the reconstruction process, we further enhance the robustness and quality of the reconstructed images by incorporating regularization constraint. Our experiments, which encompass various scenarios of low-dose and sparse-view CT, as well as MRI with varying under-sampling rates and masks, demonstrate the effectiveness of the proposed method by significantly enhanced the quality of the reconstructed images. Especially, our method with noisy training samples achieves comparable results to those obtained using clean data. Our code at https://zenodo.org/record/8266123.

Diffusion model has emerged as a potential tool to tackle the challenge of sparse-view CT reconstruction, displaying superior performance compared to conventional methods. Nevertheless, these prevailing diffusion models predominantly focus on the sinogram or image domains, which can lead to instability during model training, potentially culminating in convergence towards local minimal solutions. The wavelet transform serves to disentangle image contents and features into distinct frequency-component bands at varying scales, adeptly capturing diverse directional structures. Employing the wavelet transform as a guiding sparsity prior significantly enhances the robustness of diffusion models. In this study, we present an innovative approach named the Stage-by-stage Wavelet Optimization Refinement Diffusion (SWORD) model for sparse-view CT reconstruction. Specifically, we establish a unified mathematical model integrating low-frequency and high-frequency generative models, achieving the solution with an optimization procedure. Furthermore, we perform the low-frequency and high-frequency generative models on wavelet's decomposed components rather than the original sinogram, ensuring the stability of model training. Our method is rooted in established optimization theory, comprising three distinct stages, including low-frequency generation, high-frequency refinement and domain transform. The experimental results demonstrated that the proposed method outperformed existing state-of-the-art methods both quantitatively and qualitatively.

Metal artifact reduction (MAR) is important for clinical diagnosis with CT images. The existing state-of-the-art deep learning methods usually suppress metal artifacts in sinogram or image domains or both. However, their performance is limited by the inherent characteristics of the two domains, i.e., the errors introduced by local manipulations in the sinogram domain would propagate throughout the whole image during backprojection and lead to serious secondary artifacts, while it is difficult to distinguish artifacts from actual image features in the image domain. To alleviate these limitations, this study analyzes the desirable properties of wavelet transform in-depth and proposes to perform MAR in the wavelet domain. First, wavelet transform yields components that possess spatial correspondence with the image, thereby preventing the spread of local errors to avoid secondary artifacts. Second, using wavelet transform could facilitate identification of artifacts from image since metal artifacts are mainly high-frequency signals. Taking these advantages of the wavelet transform, this paper decomposes an image into multiple wavelet components and introduces multi-perspective regularizations into the proposed MAR model. To improve the transparency and validity of the model, all the modules in the proposed MAR model are designed to reflect their mathematical meanings. In addition, an adaptive wavelet module is also utilized to enhance the flexibility of the model. To optimize the model, an iterative algorithm is developed. The evaluation on both synthetic and real clinical datasets consistently confirms the superior performance of the proposed method over the competing methods.

Score-based generative model (SGM) has demonstrated great potential in the challenging limited-angle CT (LA-CT) reconstruction. SGM essentially models the probability density of the ground truth data and generates reconstruction results by sampling from it. Nevertheless, direct application of the existing SGM methods to LA-CT suffers multiple limitations. Firstly, the directional distribution of the artifacts attributing to the missing angles is ignored. Secondly, the different distribution properties of the artifacts in different frequency components have not been fully explored. These drawbacks would inevitably degrade the estimation of the probability density and the reconstruction results. After an in-depth analysis of these factors, this paper proposes a Wavelet-Inspired Score-based Model (WISM) for LA-CT reconstruction. Specifically, besides training a typical SGM with the original images, the proposed method additionally performs the wavelet transform and models the probability density in each wavelet component with an extra SGM. The wavelet components preserve the spatial correspondence with the original image while performing frequency decomposition, thereby keeping the directional property of the artifacts for further analysis. On the other hand, different wavelet components possess more specific contents of the original image in different frequency ranges, simplifying the probability density modeling by decomposing the overall density into component-wise ones. The resulting two SGMs in the image-domain and wavelet-domain are integrated into a unified sampling process under the guidance of the observation data, jointly generating high-quality and consistent LA-CT reconstructions. The experimental evaluation on various datasets consistently verifies the superior performance of the proposed method over the competing method.

Iodinated contrast medium (ICM) dose reduction is beneficial for decreasing potential health risk to renal-insufficiency patients in CT scanning. Due to the low-intensity vessel in ultra-low-dose-ICM CT angiography, it cannot provide clinical diagnosis of vascular diseases. Angiography reconstruction for ultra-low-dose-ICM CT can enhance vascular intensity for directly vascular diseases diagnosis. However, the angiography reconstruction is challenging since patient individual differences and vascular disease diversity. In this paper, we propose a Multiple Adversarial Learning based Angiography Reconstruction (i.e., MALAR) framework to enhance vascular intensity. Specifically, a bilateral learning mechanism is developed for mapping a relationship between source and target domains rather than the image-to-image mapping. Then, a dual correlation constraint is introduced to characterize both distribution uniformity from across-domain features and sample inconsistency within domain simultaneously. Finally, an adaptive fusion module by combining multi-scale information and long-range interactive dependency is explored to alleviate the interference of high-noise metal. Experiments are performed on CT sequences with different ICM doses. Quantitative results based on multiple metrics demonstrate the effectiveness of our MALAR on angiography reconstruction. Qualitative assessments by radiographers confirm the potential of our MALAR for the clinical diagnosis of vascular diseases.

Image denoising is a prerequisite for downstream tasks in many fields. Low-dose and photon-counting computed tomography (CT) denoising can optimize diagnostic performance at minimized radiation dose. Supervised deep denoising methods are popular but require paired clean or noisy samples that are often unavailable in practice. Limited by the independent noise assumption, current self-supervised denoising methods cannot process correlated noises as in CT images. Here we propose the first-of-its-kind similarity-based self-supervised deep denoising approach, referred to as Noise2Sim, that works in a nonlocal and nonlinear fashion to suppress not only independent but also correlated noises. Theoretically, Noise2Sim is asymptotically equivalent to supervised learning methods under mild conditions. Experimentally, Nosie2Sim recovers intrinsic features from noisy low-dose CT and photon-counting CT images as effectively as or even better than supervised learning methods on practical datasets visually, quantitatively and statistically. Noise2Sim is a general self-supervised denoising approach and has great potential in diverse applications.

Deep learning has attracted rapidly increasing attention in the field of tomographic image reconstruction, especially for CT, MRI, PET/SPECT, ultrasound and optical imaging. Among various topics, sparse-view CT remains a challenge which targets a decent image reconstruction from very few projections. To address this challenge, in this article we propose a Dual-domain Residual-based Optimization NEtwork (DRONE). DRONE consists of three modules respectively for embedding, refinement, and awareness. In the embedding module, a sparse sinogram is first extended. Then, sparse-view artifacts are effectively suppressed in the image domain. After that, the refinement module recovers image details in the residual data and image domains synergistically. Finally, the results from the embedding and refinement modules in the data and image domains are regularized for optimized image quality in the awareness module, which ensures the consistency between measurements and images with the kernel awareness of compressed sensing. The DRONE network is trained, validated, and tested on preclinical and clinical datasets, demonstrating its merits in edge preservation, feature recovery, and reconstruction accuracy.

Spectral computed tomography (CT) reconstructs material-dependent attenuation images from the projections of multiple narrow energy windows, which is meaningful for material identification and decomposition. Unfortunately, the multi-energy projection datasets usually have lower signal-noise ratios (SNR). Very recently, a spatial-spectral cube matching frame (SSCMF) was proposed to explore the non-local spatial-spectral similarities for spectral CT. This method constructs a group by clustering up a series of non-local spatial-spectral cubes. The small size of spatial patches for such a group makes the SSCMF fail to fully encode the sparsity and low-rank properties. The hard-thresholding and collaboration filtering in the SSCMF also cause difficulty in recovering the image features and spatial edges. While all the steps are operated on 4-D group, the huge computational cost and memory load might not be affordable in practice. To avoid the above limitations and further improve the image quality, we first formulate a non-local cube-based tensor instead of group to encode the sparsity and low-rank properties. Then, as a new regularizer, the Kronecker-basis-representation tensor factorization is employed into a basic spectral CT reconstruction model to enhance the capability of image feature extraction and spatial edge preservation, generating a non-local low-rank cube-based tensor factorization (NLCTF) method. Finally, the split-Bregman method is adopted to solve the NLCTF model. Both numerical simulations and preclinical mouse studies are performed to validate and evaluate the NLCTF algorithm. The results show that the NLCTF method outperforms the other state-of-the-art competing algorithms.