Model-based Reconstruction Method Research Articles

QRAGE-Simultaneous multiparametric quantitative MRI of water content, T1, T2*, and magnetic susceptibility at ultrahigh field strength.

To introduce quantitative rapid gradient-echo (QRAGE), a novel approach for the simultaneous mapping of multiple quantitative MRI parameters, including water content, T1, T2*, and magnetic susceptibility at ultrahigh field strength. QRAGE leverages a newly developed multi-echo MPnRAGE sequence, facilitating the acquisition of 171 distinct contrast images across a range of inversion and TE points. To maintain a short acquisition time, we introduce MIRAGE2, a novel model-based reconstruction method that exploits prior knowledge of temporal signal evolution, represented as damped complex exponentials. MIRAGE2 minimizes local Block-Hankel and Casorati matrices. Parameter maps are derived from the reconstructed contrast images through postprocessing steps. We validate QRAGE through extensive simulations, phantom studies, and in vivo experiments, demonstrating its capability for high-precision imaging. In vivo brain measurements show the promising performance of QRAGE, with test-retest SDs and deviations from reference methods of < 0.8% for water content, < 17 ms for T1, and < 0.7 ms for T2*. QRAGE achieves whole-brain coverage at a 1-mm isotropic resolution in just 7 min and 15 s, comparable to the acquisition time of an MP2RAGE scan. In addition, QRAGE generates a contrast image akin to the UNI image produced by MP2RAGE. QRAGE is a new, successful approach for simultaneously mapping multiple MR parameters at ultrahigh field.

Reconstruction method suitable for fast CT imaging

Reconstructing computed tomography (CT) images from an extremely limited set of projections is crucial in practical applications. As the available projections significantly decrease, traditional reconstruction and model-based iterative reconstruction methods become constrained. This work aims to seek a reconstruction method applicable to fast CT imaging when available projections are highly sparse. To minimize the time and cost associated with projections acquisition, we propose a deep learning model, X-CTReNet, which parameterizes a nonlinear mapping function from orthogonal projections to CT volumes for 3D reconstruction. The proposed model demonstrates effective capability in inferring CT volumes from two-view projections compared to baseline methods, highlighting the significant potential for drastically reducing projection acquisition in fast CT imaging.

Model-based reconstruction for looping-star MRI.

The aim of this study was to develop a reconstruction method that more fully models the signals and reconstructs gradient echo (GRE) images without sacrificing the signal to noise ratio and spatial resolution, compared to conventional gridding and model-based image reconstruction method. By modeling the trajectories for every spoke and simplifying the scenario to only echo-in and echo-out mixture, the approach explicitly models the overlapping echoes. After modeling the overlapping echoes with two system matrices, we use the conjugate gradient algorithm (CG-SENSE) with the nonuniform FFT (NUFFT) to optimize the image reconstruction cost function. The proposed method is demonstrated in phantoms and in-vivo volunteer experiments for three-dimensional, high-resolution T2*-weighted imaging and functional MRI tasks. Compared to the gridding method, the high resolution protocol exhibits improved spatial resolution and reduced signal loss as a result of less intra-voxel dephasing. The fMRI task shows that the proposed model-based method produced images with reduced artifacts and blurring as well as more stable and prominent time courses. The proposed model-based reconstruction results shows improved spatial resolution and reduced artifacts. The fMRI task shows improved time series and activation map due to the reduced overlapping echoes and under-sampling artifacts.

Model-based super-resolution reconstruction for pseudo-continuous Arterial Spin Labeling

Arterial spin labeling (ASL) is a promising, non-invasive perfusion magnetic resonance imaging technique for quantifying cerebral blood flow (CBF). Unfortunately, ASL suffers from an inherently low signal-to-noise ratio (SNR) and spatial resolution, undermining its potential. Increasing spatial resolution without significantly sacrificing SNR or scan time represents a critical challenge towards routine clinical use. In this work, we propose a model-based super-resolution reconstruction (SRR) method with joint motion estimation that breaks the traditional SNR/resolution/scan-time trade-off. From a set of differently oriented 2D multi-slice pseudo-continuous ASL images with a low through-plane resolution, 3D-isotropic, high resolution, quantitative CBF maps are estimated using a Bayesian approach. Experiments on both synthetic whole brain phantom data, and on in vivo brain data, show that the proposed SRR Bayesian estimation framework outperforms state-of-the-art ASL quantification.

SOUL-Net: A Sparse and Low-Rank Unrolling Network for Spectral CT Image Reconstruction.

Spectral computed tomography (CT) is an emerging technology, that generates a multienergy attenuation map for the interior of an object and extends the traditional image volume into a 4-D form. Compared with traditional CT based on energy-integrating detectors, spectral CT can make full use of spectral information, resulting in high resolution and providing accurate material quantification. Numerous model-based iterative reconstruction methods have been proposed for spectral CT reconstruction. However, these methods usually suffer from difficulties such as laborious parameter selection and expensive computational costs. In addition, due to the image similarity of different energy bins, spectral CT usually implies a strong low-rank prior, which has been widely adopted in current iterative reconstruction models. Singular value thresholding (SVT) is an effective algorithm to solve the low-rank constrained model. However, the SVT method requires a manual selection of thresholds, which may lead to suboptimal results. To relieve these problems, in this article, we propose a sparse and low-rank unrolling network (SOUL-Net) for spectral CT image reconstruction, that learns the parameters and thresholds in a data-driven manner. Furthermore, a Taylor expansion-based neural network backpropagation method is introduced to improve the numerical stability. The qualitative and quantitative results demonstrate that the proposed method outperforms several representative state-of-the-art algorithms in terms of detail preservation and artifact reduction.

Model-based deep CNN-regularized reconstruction for digital breast tomosynthesis with a task-based CNN image assessment approach

Objective. Digital breast tomosynthesis (DBT) is a quasi-three-dimensional breast imaging modality that improves breast cancer screening and diagnosis because it reduces fibroglandular tissue overlap compared with 2D mammography. However, DBT suffers from noise and blur problems that can lower the detectability of subtle signs of cancers such as microcalcifications (MCs). Our goal is to improve the image quality of DBT in terms of image noise and MC conspicuity. Approach. We proposed a model-based deep convolutional neural network (deep CNN or DCNN) regularized reconstruction (MDR) for DBT. It combined a model-based iterative reconstruction (MBIR) method that models the detector blur and correlated noise of the DBT system and the learning-based DCNN denoiser using the regularization-by-denoising framework. To facilitate the task-based image quality assessment, we also proposed two DCNN tools for image evaluation: a noise estimator (CNN-NE) trained to estimate the root-mean-square (RMS) noise of the images, and an MC classifier (CNN-MC) as a DCNN model observer to evaluate the detectability of clustered MCs in human subject DBTs. Main results. We demonstrated the efficacies of CNN-NE and CNN-MC on a set of physical phantom DBTs. The MDR method achieved low RMS noise and the highest detection area under the receiver operating characteristic curve (AUC) rankings evaluated by CNN-NE and CNN-MC among the reconstruction methods studied on an independent test set of human subject DBTs. Significance. The CNN-NE and CNN-MC may serve as a cost-effective surrogate for human observers to provide task-specific metrics for image quality comparisons. The proposed reconstruction method shows the promise of combining physics-based MBIR and learning-based DCNNs for DBT image reconstruction, which may potentially lead to lower dose and higher sensitivity and specificity for MC detection in breast cancer screening and diagnosis.

MMV-Net: A Multiple Measurement Vector Network for Multifrequency Electrical Impedance Tomography.

Multifrequency electrical impedance tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods suffer from low spatial resolution, unconstrained frequency correlation, and high computational cost. Deep learning has been extensively applied in solving the EIT inverse problem in biomedical and industrial process imaging. However, most existing learning-based approaches deal with the single-frequency setup, which is inefficient and ineffective when extended to the multifrequency setup. This article presents a multiple measurement vector (MMV) model-based learning algorithm named MMV-Net to solve the mfEIT image reconstruction problem. MMV-Net considers the correlations between mfEIT images and unfolds the update steps of the Alternating Direction Method of Multipliers for the MMV problem (MMV-ADMM). The nonlinear shrinkage operator associated with the weighted l2,1 regularization term of MMV-ADMM is generalized in MMV-Net with a cascade of a Spatial Self-Attention module and a Convolutional Long Short-Term Memory (ConvLSTM) module to better capture intrafrequency and interfrequency dependencies. The proposed MMV-Net was validated on our Edinburgh mfEIT Dataset and a series of comprehensive experiments. The results show superior image quality, convergence performance, noise robustness, and computational efficiency against the conventional MMV-ADMM and the state-of-the-art deep learning methods.

A frequency-domain model-based reconstruction method for transcranial photoacoustic imaging: A 2D numerical investigation

Phase aberration caused by the skull is a major barrier to achieving high quality photoacoustic images of human and non-human primates’ brains. To address this issue, time-reversal methods have been used but they are computationally demanding and slow due to relying on solving the full-wave equation. The proposed approach is based on model-based image reconstruction in the frequency-domain to achieve near real-time image reconstruction. The relationship between an imaging region and transducer array elements can be mathematically described as a model matrix and the image reconstruction can be performed by pseudo-inverse of the model matrix. The model matrix is numerically calculated due to the lack of analytical solutions for transcranial ultrasound. However, this calculation only needs to be performed once for a given experimental setup and the same acoustic medium, and is an offline process not affecting the actual image reconstruction time. This non-iterative mode-based method demonstrates a substantial improvement in image reconstruction time, being approximately 18 times faster than the time-reversal method, all while maintaining comparable image quality.

Sparse-view reconstruction for photoacoustic tomography combining diffusion model with model-based iteration

As a non-invasive hybrid biomedical imaging technology, photoacoustic tomography combines high contrast of optical imaging and high penetration of acoustic imaging. However, the conventional standard reconstruction under sparse view could result in low-quality image in photoacoustic tomography. Here, a novel model-based sparse reconstruction method for photoacoustic tomography via diffusion model was proposed. A score-based diffusion model is designed for learning the prior information of the data distribution. The learned prior information is utilized as a constraint for the data consistency term of an optimization problem based on the least-square method in the model-based iterative reconstruction, aiming to achieve the optimal solution. Blood vessels simulation data and the animal in vivo experimental data were used to evaluate the performance of the proposed method. The results demonstrate that the proposed method achieves higher-quality sparse reconstruction compared with conventional reconstruction methods and U-Net. In particular, under the extreme sparse projection (e.g., 32 projections), the proposed method achieves an improvement of ∼ 260 % in structural similarity and ∼ 30 % in peak signal-to-noise ratio for in vivo data, compared with the conventional delay-and-sum method. This method has the potential to reduce the acquisition time and cost of photoacoustic tomography, which will further expand the application range.

State-of-health estimation for lithium-ion battery using model-based feature optimization and deep extreme learning machine

Accurate and reliable estimation of state of health (SOH) is essential for the safe and efficient operation of battery energy storages. However, random charging/discharging behaviors and ambient conditions complicate the online SOH estimation. Aiming at an accurate and robust online SOH estimation for lithium-ion batteries, this paper proposes a SOH estimation method using model-based feature optimization and improved machine learning. First, an empirical model-based voltage reconstruction method is proposed to reconstruct the voltage curve for solving disturbance-free different time (DT) curves under measurement noises and high C-rates and extract model-associated health features (HFs). Then, an optimal charging voltage window (CVW) determination method is proposed, which extracts the CVW-associated HFs by determining the optimal CVW from partial charging voltage ranges. Finally, a set of informative and multi-attribute HFs are extracted to train an improved deep extreme learning machine (DELM) mode for online SOH estimation. The proposed method is validated based on three datasets of batteries with different materials. The results demonstrate high accuracy and strong robustness to partial voltage range, noise corruption, and ambient temperature fluctuation.

Low-count PET image reconstruction based on truncated inverse radon layer and U-shaped network

Objective. Positron emission tomography (PET) is a functional imaging widely used in various applications such as tumour detection. PET image reconstruction is an ill-posed inverse problem, and the model-based iterative reconstruction methods commonly used in clinical practice have disadvantages such as long time consumption and low signal-to-noise ratio, especially at low doses. Approach. In this study, we propose a deep learning-based reconstruction method that is capable of reconstructing images directly from low-count sinograms. Our network consists of two parts, a truncated inverse radon layer for implementing domain transform and a U-shaped network for image enhancement. Main result. We validated our method on both simulation data and real data. Compared to ordered subset expectation maximization with a post-Guassian filter, the structural similarity can be improved from 0.9357 to 0.9613 and the peak signal-to-noise ratio can be improved by 5 dB. Significance. The proposed method can directly convert low-count sinograms into PET images, while obtaining improved image quality and having less time consumption than iterative reconstruction algorithms and the state-of-the-art convolutional neural network.

Model-Based Simultaneous Multi-Slice (SMS) Reconstruction with Hankel Subspace Learning for Accelerated MR T1 Mapping

Herein, we propose a novel model-based simultaneous multi-slice (SMS) reconstruction method by exploiting data-driven parameter modeling for highly accelerated T1 parameter quantification. We assume that the predefined slice-specific null space operator remains invariant along the parameter dimension. We incorporate the parameter dimension into SMS-HSL to exploit Hankel-structured and Casorati matrices. Given this consideration, the SMS signal is reformulated in k-p space as a constrained optimization problem that exploits rank deficiency for the Hankel-structured matrix and a finite-dimensional basis for a subspace containing slowly evolving signals in the parameter direction. The proposed model-based SMS reconstruction method is validated on in vivo data and compared with state-of-the-art methods with slice acceleration factors of 3 and 5, including an in-plane acceleration factor of 2. The experimental results demonstrate that the proposed method performs effective slice unfolding and signal recovery in reconstructed images and T1 maps with high precision as compared to the state-of-the-art methods.

A novel protocol for abdominal low-dose CT scans adapted with a model-based iterative reconstruction method.

This study aims to introduce a novel low-dose abdominal computed tomography (CT) protocol adapted with model-based iterative reconstruction (MBIR), To validate the adaptability of this protocol, objective image quality and subjective clinical scores of low-dose MBIR images are compared with the normal-dose images. Normal-dose abdominal CT images of 58 patients and low-dose abdominal CT images of 52 patients are reconstructed using both conventional filtered back projection (FBP) and MBIR methods with and without smooth applying. Signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) are used to compare image quality between the normal-dose and low-dose CT scans. CT dose indices (CTDI) of normal-dose and low-dose abdominal CT images on post-contrast venous phase are also compared. The SNR, CNR and clinical score of low-dose MBIR images all show significant higher values (Bonferroni p < 0.05) than those of normal-dose images with conventional FBP method. A total of around 40% radiation dose reduction (CTDI: 5.3 vs 8.7 mGy) could be achieved via our novel abdominal CT protocol. With the higher SNR/CNR and clinical scores, the low-dose CT abdominal imaging protocol with MBIR could effectively reduce the radiation for patients and provide equal or even higher image quality and also its adaptability in clinical abdominal CT image diagnosis.

Stochastic optimization of three-dimensional non-Cartesian sampling trajectory.

Optimizing three-dimensional (3D) k-space sampling trajectories is important for efficient MRI yet presents a challenging computational problem. This work proposes a generalized framework for optimizing 3D non-Cartesian sampling patterns via data-driven optimization. We built a differentiable simulation model to enable gradient-based methods for sampling trajectory optimization. The algorithm can simultaneously optimize multiple properties of sampling patterns, including image quality, hardware constraints (maximum slew rate and gradient strength), reduced peripheral nerve stimulation (PNS), and parameter-weighted contrast. The proposed method can either optimize the gradient waveform (spline-based freeform optimization) or optimize properties of given sampling trajectories (such as the rotation angle of radial trajectories). Notably, the method can optimize sampling trajectories synergistically with either model-based or learning-based reconstruction methods. We proposed several strategies to alleviate the severe nonconvexity and huge computation demand posed by the large scale. The corresponding code is available as an open-source toolbox. We applied the optimized trajectory to multiple applications including structural and functional imaging. In the simulation studies, the image quality of a 3D kooshball trajectory was improved from 0.29 to 0.22 (NRMSE) with Stochastic optimization framework for 3D NOn-Cartesian samPling trajectorY (SNOPY) optimization. In the prospective studies, by optimizing the rotation angles of a stack-of-stars (SOS) trajectory, SNOPY reduced the NRMSE of reconstructed images from 1.19 to 0.97 compared to the best empirical method (RSOS-GR). Optimizing the gradient waveform of a rotational EPI trajectory improved participants' rating of the PNS from "strong" to "mild." SNOPY provides an efficient data-driven and optimization-based method to tailor non-Cartesian sampling trajectories.

Method of sparse-view coded-aperture x-ray diffraction tomography

Objective. X-ray diffraction (XRD) has been considered as a valuable diagnostic technology providing material specific ‘finger-print’ information i.e. XRD pattern to distinguish different biological tissues. XRD tomography (XRDT) further obtains spatial-resolved XRD pattern distribution, which has become a frontier biological sample inspection method. Currently, XRD computed tomography (XRD-CT) featured by the conventional CT scan mode with rotation has the best spatial resolution among various XRDT methods, but its scan process takes hours. Meanwhile, snapshot XRDT methods such as coded-aperture XRDT (CA-XRDT) aim at direct imaging without scan movements. With compressed-sensing acquisition applied, CA-XRDT significantly shortens data acquisition time. However, the snapshot acquisition results in a significant drop in spatial resolution. Hence, we need an advanced XRDT method that significantly accelerates XRD-CT acquisition and still maintains an acceptable imaging accuracy for biological sample inspection. Approach. Inspired by the high spatial resolution of XRD-CT from rotational scan and the fast compressed-sensing acquisition in snapshot CA-XRDT (SnapshotCA-XRDT), we proposed a new XRDT imaging method: sparse-view rotational CA-XRDT (RotationCA-XRDT). It takes SnapshotCA-XRDT as a preliminary depth-resolved XRDT method, and combines rotational scan to significantly improve the spatial resolution. A model-based iterative reconstruction (MBIR) method is adopted for RotationCA-XRDT. Moreover, we suggest a refined system model calculation for the RotationCA-XRDT MBIR which is a key factor to improve reconstruction image quality. Main results. We conducted our experimental validation based on Monte-Carlo simulation for a breast sample. The results show that the proposed RotationCA-XRDT method succeeded in producing good images for detecting 2 mm square carcinoma with a 15-view scan. The spatial resolution is significantly improved from current SnapshotCA-XRDT methods. With our refined system model, MBIR can obtain high quality images with little artifacts. Significance. In this work, we proposed a new high spatial resolution XRDT method combining coded-aperture compressed-sensing acquisition and sparse-view scan. The proposed RotationCA-XRDT method obtained significantly better image resolution than current SnapshotCA-XRDT methods in the field. It is of great potential for biological sample XRDT inspection. The proposed RotationCA-XRDT is the fastest millimetre-resolution XRDT method in the field which reduces the scan time from hours to minutes.

Linearized Analysis of Noise and Resolution for DL-Based Image Generation.

Deep-learning (DL) based CT image generation methods are often evaluated using RMSE and SSIM. By contrast, conventional model-based image reconstruction (MBIR) methods are often evaluated using image properties such as resolution, noise, bias. Calculating such image properties requires time consuming Monte Carlo (MC) simulations. For MBIR, linearized analysis using first order Taylor expansion has been developed to characterize noise and resolution without MC simulations. This inspired us to investigate if linearization can be applied to DL networks to enable efficient characterization of resolution and noise. We used FBPConvNet as an example DL network and performed extensive numerical evaluations, including both computer simulations and real CT data. Our results showed that network linearization works well under normal exposure settings. For such applications, linearization can characterize image noise and resolutions without running MC simulations. We provide with this work the computational tools to implement network linearization. The efficiency and ease of implementation of network linearization can hopefully popularize the physics-related image quality measures for DL applications. Our methodology is general; it allows flexible compositions of DL nonlinear modules and linear operators such as filtered-backprojection (FBP). For the latter, we develop a generic method for computing the covariance images that is needed for network linearization.

Hybrid reconstruction of the physical model with the deep learning that improves structured illumination microscopy

Structured illumination microscopy (SIM) has been widely used in live-cell superresolution (SR) imaging. However, conventional physical model-based SIM SR reconstruction algorithms are prone to artifacts in handling raw images with low signal-to-noise ratios (SNRs). Deep-learning (DL)-based methods can address this challenge but may lead to degradation and hallucinations. By combining the physical inversion model with a total deep variation (TDV) regularization, we propose a hybrid restoration method (TDV-SIM) that outperforms conventional or DL methods in suppressing artifacts and hallucinations while maintaining resolutions. We demonstrate the performance superiority of TDV-SIM in restoring actin filaments, endoplasmic reticulum, and mitochondrial cristae from extremely low SNR raw images. Thus TDV-SIM represents the ideal method for prolonged live-cell SR imaging with minimal exposure and photodamage. Overall, TDV-SIM proves the power of integrating model-based reconstruction methods with DL ones, possibly leading to the rapid exploration of similar strategies in high-fidelity reconstructions of other microscopy methods.

Efficient Approximation of Jacobian Matrices Involving a Non-Uniform Fast Fourier Transform (NUFFT).

There is growing interest in learning Fourier domain sampling strategies (particularly for magnetic resonance imaging, MRI) using optimization approaches. For non-Cartesian sampling, the system models typically involve non-uniform fast Fourier transform (NUFFT) operations. Commonly used NUFFT algorithms contain frequency domain interpolation, which is not differentiable with respect to the sampling pattern, complicating the use of gradient methods. This paper describes an efficient and accurate approach for computing approximate gradients involving NUFFTs. Multiple numerical experiments validate the improved accuracy and efficiency of the proposed approximation. As an application to computational imaging, the NUFFT Jacobians were used to optimize non-Cartesian MRI sampling trajectories via data-driven stochastic optimization. Specifically, the sampling patterns were learned with respect to various model-based image reconstruction (MBIR) algorithms. The proposed approach enables sampling optimization for image sizes that are infeasible with standard auto-differentiation methods due to memory limits. The synergistic acquisition and reconstruction design leads to remarkably improved image quality. In fact, we show that model-based image reconstruction methods with suitably optimized imaging parameters can perform nearly as well as CNN-based methods.

OTRE: Where Optimal Transport Guided Unpaired Image-to-Image Translation Meets Regularization by Enhancing.

Non-mydriatic retinal color fundus photography (CFP) is widely available due to the advantage of not requiring pupillary dilation, however, is prone to poor quality due to operators, systemic imperfections, or patient-related causes. Optimal retinal image quality is mandated for accurate medical diagnoses and automated analyses. Herein, we leveraged the Optimal Transport (OT) theory to propose an unpaired image-to-image translation scheme for mapping low-quality retinal CFPs to high-quality counterparts. Furthermore, to improve the flexibility, robustness, and applicability of our image enhancement pipeline in the clinical practice, we generalized a state-of-the-art model-based image reconstruction method, regularization by denoising, by plugging in priors learned by our OT-guided image-to-image translation network. We named it as regularization by enhancing (RE). We validated the integrated framework, OTRE, on three publicly available retinal image datasets by assessing the quality after enhancement and their performance on various downstream tasks, including diabetic retinopathy grading, vessel segmentation, and diabetic lesion segmentation. The experimental results demonstrated the superiority of our proposed framework over some state-of-the-art unsupervised competitors and a state-of-the-art supervised method.

Sparse-View Cone Beam CT Reconstruction Using Data-Consistent Supervised and Adversarial Learning From Scarce Training Data

Reconstruction of CT images from a limited set of projections through an object is important in several applications ranging from medical imaging to industrial settings. As the number of available projections decreases, traditional reconstruction techniques such as the FDK algorithm and model-based iterative reconstruction methods perform poorly. Recently, data-driven methods such as deep learning-based reconstruction have garnered a lot of attention in applications because they yield better performance when enough training data is available. However, even these methods have their limitations when there is a scarcity of available training data. This work focuses on image reconstruction in such settings, i.e., when both the number of available CT projections and the training data is extremely limited. We adopt a sequential reconstruction approach over several stages using an adversarially trained shallow network for ‘destreaking’ followed by a data-consistency update in each stage. To deal with the challenge of limited data, we use image subvolumes to train our method, and patch aggregation during testing. To deal with the computational challenge of learning on 3D datasets for 3D reconstruction, we use a hybrid 3D-to-2D mapping network for the ‘destreaking’ part. Comparisons to other methods over several test examples indicate that the proposed method has much potential, when both the number of projections and available training data are highly limited.