Undersampling Artifacts Research Articles

Prior frequency guided diffusion model for limited angle (LA)-CBCT reconstruction

Objective. Cone-beam computed tomography (CBCT) is widely used in image-guided radiotherapy. Reconstructing CBCTs from limited-angle acquisitions (LA-CBCT) is highly desired for improved imaging efficiency, dose reduction, and better mechanical clearance. LA-CBCT reconstruction, however, suffers from severe under-sampling artifacts, making it a highly ill-posed inverse problem. Diffusion models can generate data/images by reversing a data-noising process through learned data distributions; and can be incorporated as a denoiser/regularizer in LA-CBCT reconstruction. In this study, we developed a diffusion model-based framework, prior frequency-guided diffusion model (PFGDM), for robust and structure-preserving LA-CBCT reconstruction. Approach. PFGDM uses a conditioned diffusion model as a regularizer for LA-CBCT reconstruction, and the condition is based on high-frequency information extracted from patient-specific prior CT scans which provides a strong anatomical prior for LA-CBCT reconstruction. Specifically, we developed two variants of PFGDM (PFGDM-A and PFGDM-B) with different conditioning schemes. PFGDM-A applies the high-frequency CT information condition until a pre-optimized iteration step, and drops it afterwards to enable both similar and differing CT/CBCT anatomies to be reconstructed. PFGDM-B, on the other hand, continuously applies the prior CT information condition in every reconstruction step, while with a decaying mechanism, to gradually phase out the reconstruction guidance from the prior CT scans. The two variants of PFGDM were tested and compared with current available LA-CBCT reconstruction solutions, via metrics including peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM). Main results. PFGDM outperformed all traditional and diffusion model-based methods. The mean(s.d.) PSNR/SSIM were 27.97(3.10)/0.949(0.027), 26.63(2.79)/0.937(0.029), and 23.81(2.25)/0.896(0.036) for PFGDM-A, and 28.20(1.28)/0.954(0.011), 26.68(1.04)/0.941(0.014), and 23.72(1.19)/0.894(0.034) for PFGDM-B, based on 120°, 90°, and 30° orthogonal-view scan angles respectively. In contrast, the PSNR/SSIM was 19.61(2.47)/0.807(0.048) for 30° for DiffusionMBIR, a diffusion-based method without prior CT conditioning. Significance. PFGDM reconstructs high-quality LA-CBCTs under very-limited gantry angles, allowing faster and more flexible CBCT scans with dose reductions.

Fast Pure Shift NMR Spectroscopy Using Attention-Assisted Deep Neural Network.

Pure shift NMR spectroscopy enables the robust probing on molecular structure and dynamics, benefiting from great resolution enhancements. Despite extensive application landscapes in various branches of chemistry, the long experimental times induced by the additional time dimension generally hinder its further developments and practical deployments, especially for multi-dimensional pure shift NMR. Herein, this study proposes and implements the fast, reliable, and robust reconstruction for accelerated pure shift NMR spectroscopy with lightweight attention-assisted deep neural network. This deep learning protocol allows one to regain high-resolution signals and suppress undersampling artifacts, as well as furnish high-fidelity signal intensities along with the accelerated pure shift acquisition, benefitting from the introduction of the attention mechanism to highlight the spectral feature and information of interest. Extensive results of simulated and experimental NMR data demonstrate that this attention-assisted deep learning protocol enables the effective recovery of weak signals that are almost drown in the serious undersampling artifacts, and the distinction and recognition of close chemical shifts even though using merely 5.4% data, highlighting its huge potentials on fast pure shift NMR spectroscopy. As a result, this study affords a promising paradigm for the AI-assisted NMR protocols toward broader applications in chemistry, biology, materials, and life sciences, and among others.

Enhancing quality and speed in database-free neural network reconstructions of undersampled MRI with SCAMPI.

We present SCAMPI (Sparsity Constrained Application of deep Magnetic resonance Priors for Image reconstruction), an untrained deep Neural Network for MRI reconstruction without previous training on datasets. It expands the Deep Image Prior approach with a multidomain, sparsity-enforcing loss function to achieve higher image quality at a faster convergence speed than previously reported methods. Two-dimensional MRI data from the FastMRI dataset with Cartesian undersampling in phase-encoding direction were reconstructed for different acceleration rates for single coil and multicoil data. The performance of our architecture was compared to state-of-the-art Compressed Sensing methods and ConvDecoder, another untrained Neural Network for two-dimensional MRI reconstruction. SCAMPI outperforms these by better reducing undersampling artifacts and yielding lower error metrics in multicoil imaging. In comparison to ConvDecoder, the U-Net architecture combined with an elaborated loss-function allows for much faster convergence at higher image quality. SCAMPI can reconstruct multicoil data without explicit knowledge of coil sensitivity profiles. Moreover, it is a novel tool for reconstructing undersampled single coil k-space data. Our approach avoids overfitting to dataset features, that can occur in Neural Networks trained on databases, because the network parameters are tuned only on the reconstruction data. It allows better results and faster reconstruction than the baseline untrained Neural Network approach.

Computationally Efficient Algorithm for Modeling Grain Growth Using Hillert's Mean-Field Approach.

To investigate the interconnected effects of manufacturing processes on microstructure evolution during hot-rolling, a through process model is required. A novel numerical implementation of the mean-field approach was introduced to efficiently describe the grain growth of larger systems and extended durations. In this approach, each grain is embedded within an average medium and interacts with the average medium, thus avoiding the complexities of individual grain interactions. The proposed upsampling approach dynamically adjusts the simulation grain ensemble, ensuring efficiency and accuracy regardless of the initial number of grains present. This adaptation prevents undersampling artifacts during grain growth. The accuracy of the model is verified against analytical solutions and experimental data, demonstrating high agreement. Moreover, the effects of different initial conditions are successfully investigated, demonstrating the model's versatility. Due to its simplicity and efficiency, the model can be seamlessly integrated into other microstructure evolution models.

Accelerated MRI reconstructions via variational network and feature domain learning

We introduce three architecture modifications to enhance the performance of the end-to-end (E2E) variational network (VarNet) for undersampled MRI reconstructions. We first implemented the Feature VarNet, which propagates information throughout the cascades of the network in an N-channel feature-space instead of a 2-channel feature-space. Then, we add an attention layer that utilizes the spatial locations of Cartesian undersampling artifacts to further improve performance. Lastly, we combined the Feature and E2E VarNets into the Feature-Image (FI) VarNet, to facilitate cross-domain learning and boost accuracy. Reconstructions were evaluated on the fastMRI dataset using standard metrics and clinical scoring by three neuroradiologists. Feature and FI VarNets outperformed the E2E VarNet for 4×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document}, 5×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} and 8×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} Cartesian undersampling in all studied metrics. FI VarNet secured second place in the public fastMRI leaderboard for 4×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} Cartesian undersampling, outperforming all open-source models in the leaderboard. Radiologists rated FI VarNet brain reconstructions with higher quality and sharpness than the E2E VarNet reconstructions. FI VarNet excelled in preserving anatomical details, including blood vessels, whereas E2E VarNet discarded or blurred them in some cases. The proposed FI VarNet enhances the reconstruction quality of undersampled MRI and could enable clinically acceptable reconstructions at higher acceleration factors than currently possible.

Constrained alternating minimization for parameter mapping (CAMP)

ObjectiveTo improve image quality in highly accelerated parameter mapping by incorporating a linear constraint that relates consecutive images. ApproachIn multi-echo T1 or T2 mapping, scan time is often shortened by acquiring undersampled but complementary measures of k-space at each TE or TI. However, residual undersampling artifacts from the individual images can then degrade the quality of the final parameter maps.In this work, a new reconstruction method, dubbed Constrained Alternating Minimization for Parameter mapping (CAMP), is introduced. This method simultaneously extracts T2 or T1* maps in addition to an image for each TE or TI from accelerated datasets, leveraging the constraints of the decay to improve the reconstructed image quality. The model enforces exponential decay through a linear constraint, resulting in a biconvex objective function that lends itself to alternating minimization. The method was tested in four in vivo volunteer experiments and validated in phantom studies and healthy subjects, using T2 and T1 mapping, with accelerations of up to 12. Main resultsCAMP is demonstrated for accelerated radial and Cartesian acquisitions in T2 and T1 mapping. The method is even applied to generate an entire T2 weighted image series from a single TSE dataset, despite the blockwise k-space sampling at each echo time. Experimental undersampled phantom and in vivo results processed with CAMP exhibit reduced artifacts without introducing bias. SignificanceFor a wide array of applications, CAMP linearizes the model cost function without sacrificing model accuracy so that the well-conditioned and highly efficient reconstruction algorithm improves the image quality of accelerated parameter maps.

Emerging Trends in Magnetic Resonance Fingerprinting for Quantitative Biomedical Imaging Applications: A Review.

Magnetic resonance imaging (MRI) stands as a vital medical imaging technique, renowned for its ability to offer high-resolution images of the human body with remarkable soft-tissue contrast. This enables healthcare professionals to gain valuable insights into various aspects of the human body, including morphology, structural integrity, and physiological processes. Quantitative imaging provides compositional measurements of the human body, but, currently, either it takes a long scan time or is limited to low spatial resolutions. Undersampled k-space data acquisitions have significantly helped to reduce MRI scan time, while compressed sensing (CS) and deep learning (DL) reconstructions have mitigated the associated undersampling artifacts. Alternatively, magnetic resonance fingerprinting (MRF) provides an efficient and versatile framework to acquire and quantify multiple tissue properties simultaneously from a single fast MRI scan. The MRF framework involves four key aspects: (1) pulse sequence design; (2) rapid (undersampled) data acquisition; (3) encoding of tissue properties in MR signal evolutions or fingerprints; and (4) simultaneous recovery of multiple quantitative spatial maps. This paper provides an extensive literature review of the MRF framework, addressing the trends associated with these four key aspects. There are specific challenges in MRF for all ranges of magnetic field strengths and all body parts, which can present opportunities for further investigation. We aim to review the best practices in each key aspect of MRF, as well as for different applications, such as cardiac, brain, and musculoskeletal imaging, among others. A comprehensive review of these applications will enable us to assess future trends and their implications for the translation of MRF into these biomedical imaging applications.

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.

Compressed SVD-based L + S model to reconstruct undersampled dynamic MRI data using parallel architecture.

Magnetic Resonance Imaging (MRI) is a highly demanded medical imaging system due to high resolution, large volumetric coverage, and ability to capture the dynamic and functional information of body organs e.g. cardiac MRI is employed to assess cardiac structure and evaluate blood flow dynamics through the cardiac valves. Long scan time is the main drawback of MRI, which makes it difficult for the patients to remain still during the scanning process. By collecting fewer measurements, MRI scan time can be shortened, but this undersampling causes aliasing artifacts in the reconstructed images. Advanced image reconstruction algorithms have been used in literature to overcome these undersampling artifacts. These algorithms are computationally expensive and require a long time for reconstruction which makes them infeasible for real-time clinical applications e.g. cardiac MRI. However, exploiting the inherent parallelism in these algorithms can help to reduce their computation time. Low-rank plus sparse (L+S) matrix decomposition model is a technique used in literature to reconstruct the highly undersampled dynamic MRI (dMRI) data at the expense of long reconstruction time. In this paper, Compressed Singular Value Decomposition (cSVD) model is used in L+S decomposition model (instead of conventional SVD) to reduce the reconstruction time. The results provide improved quality of the reconstructed images. Furthermore, it has been observed that cSVD and other parts of the L+S model possess highly parallel operations; therefore, a customized GPU based parallel architecture of the modified L+S model has been presented to further reduce the reconstruction time. Four cardiac MRI datasets (three different cardiac perfusion acquired from different patients and one cardiac cine data), each with different acceleration factors of 2, 6 and 8 are used for experiments in this paper. Experimental results demonstrate that using the proposed parallel architecture for the reconstruction of cardiac perfusion data provides a speed-up factor up to 19.15× (with memory latency) and 70.55× (without memory latency) in comparison to the conventional CPU reconstruction with no compromise on image quality. The proposed method is well-suited for real-time clinical applications, offering a substantial reduction in reconstruction time.

Intravoxel incoherent motion magnetic resonance imaging reconstruction from highly under-sampled diffusion-weighted PROPELLER acquisition data via physics-informed residual feedback unrolled network

Objective. The acquisition of diffusion-weighted images for intravoxel incoherent motion (IVIM) imaging is time consuming. This work aims to accelerate the scan through a highly under-sampling diffusion-weighted turbo spin echo PROPELLER (DW-TSE-PROPELLER) scheme and to develop a reconstruction method for accurate IVIM parameter mapping from the under-sampled data. Approach . The proposed under-sampling DW-TSE-PROPELLER scheme for IVIM imaging is that a few blades per b-value are acquired and rotated along the b-value dimension to cover high-frequency information. A physics-informed residual feedback unrolled network (PIRFU-Net) is proposed to directly estimate distortion-free and artifact-free IVIM parametric maps (i.e., the perfusion-free diffusion coefficient D and the perfusion fraction f) from highly under-sampled DW-TSE-PROPELLER data. PIRFU-Net used an unrolled convolution network to explore data redundancy in the k-q space to remove under-sampling artifacts. An empirical IVIM physical constraint was incorporated into the network to ensure that the signal evolution curves along the b-value follow a bi-exponential decay. The residual between the realistic and estimated measurements was fed into the network to refine the parametric maps. Meanwhile, the use of synthetic training data eliminated the need for genuine DW-TSE-PROPELLER data. Main results . The experimental results show that the DW-TSE-PROPELLER acquisition was six times faster than full k-space coverage PROPELLER acquisition and within a clinically acceptable time. Compared with the state-of-the-art methods, the distortion-free D and f maps estimated by PIRFU-Net were more accurate and had better-preserved tissue boundaries on a simulated human brain and realistic phantom/rat brain/human brain data. Significance . Our proposed method greatly accelerates IVIM imaging. It is capable of directly and simultaneously reconstructing distortion-free, artifact-free, and accurate D and f maps from six-fold under-sampled DW-TSE-PROPELLER data.

Mitigating Under-Sampling Artifacts in 3D Photoacoustic Imaging Using Res-UNet Based on Digital Breast Phantom.

In recent years, photoacoustic (PA) imaging has rapidly grown as a non-invasive screening technique for breast cancer detection using three-dimensional (3D) hemispherical arrays due to their large field of view. However, the development of breast imaging systems is hindered by a lack of patients and ground truth samples, as well as under-sampling problems caused by high costs. Most research related to solving these problems in the PA field were based on 2D transducer arrays or simple regular shape phantoms for 3D transducer arrays or images from other modalities. Therefore, we demonstrate an effective method for removing under-sampling artifacts based on deep neural network (DNN) to reconstruct high-quality PA images using numerical digital breast simulations. We constructed 3D digital breast phantoms based on human anatomical structures and physical properties, which were then subjected to 3D Monte-Carlo and K-wave acoustic simulations to mimic acoustic propagation for hemispherical transducer arrays. Finally, we applied a 3D delay-and-sum reconstruction algorithm and a Res-UNet network to achieve higher resolution on sparsely-sampled data. Our results indicate that when using a 757 nm laser with uniform intensity distribution illuminated on a numerical digital breast, the imaging depth can reach 3 cm with 0.25 mm spatial resolution. In addition, the proposed DNN can significantly enhance image quality by up to 78.4%, as measured by MS-SSIM, and reduce background artifacts by up to 19.0%, as measured by PSNR, even at an under-sampling ratio of 10%. The post-processing time for these improvements is only 0.6 s. This paper suggests a new 3D real time DNN method addressing the sparse sampling problem based on numerical digital breast simulations, this approach can also be applied to clinical data and accelerate the development of 3D photoacoustic hemispherical transducer arrays for early breast cancer diagnosis.

A 3D Drizzle Algorithm for JWST and Practical Application to the MIRI Medium Resolution Spectrometer

We describe an algorithm for application of the classic “drizzle” technique to produce 3D spectral cubes using data obtained from the slicer-type integral field unit (IFU) spectrometers on board the James Webb Space Telescope. This algorithm relies upon the computation of overlapping volume elements (composed of two spatial dimensions and one spectral dimension) between the 2D detector pixels and the 3D data cube voxels, and is greatly simplified by treating the spatial and spectral overlaps separately at the cost of just 0.03% in spectrophotometric fidelity. We provide a matrix-based formalism for the computation of spectral radiance, variance, and covariance from arbitrarily dithered data and comment on the performance of this algorithm for the Mid-Infrared Instrument’s Medium Resolution IFU Spectrometer. We derive a series of simplified scaling relations to account for covariance between cube spaxels in spectra extracted from such cubes, finding multiplicative factors ranging from 1.5–3 depending on the wavelength range and kind of data cubes produced. Finally, we discuss how undersampling produces periodic amplitude modulations in the extracted spectra in addition to those naturally produced by fringing within the instrument; reducing such undersampling artifacts below 1% requires a four-point dithering strategy and spectral extraction radii of 1.5 times the point-spread function FWHM or greater.

Analysis of temporal encoding efficiency of MR fingerprinting sequences.

MR Fingerprinting (MRF) relies on highly-undersampled images to simultaneously estimate multiple tissue parameters of interest. While a good understanding of the encoding principle behind MRF exists, we want to shed light on the question of when parameters are encoded during an MRF acquisition. We analyze the importance of each time point by leaving it out during matching (leave-one-out, LOO) assuming linear reconstruction is applied and study its influence on the reconstructed parameter map. To accelerate the analysis, we treat LOO as a small perturbation (LOOP) to the full matching problem and derive an analytical formula by leveraging Stolk and Sbrizzi's analysis on the interplay of k-space sampling and transient state dynamics. To study the influence of geometry and parameter distribution, we deploy LOOP on randomly sliced 3D brain geometries with randomized T1/T2 values to identify primary encoding regions independent of geometry. LOOP can be evaluated orders of magnitude faster than conventional matching and visualizes temporal encoding efficiency. We use the findings to accelerate an MRF sequence by truncation as well as to remove undersampling artifacts through an iterative omission scheme in an ill-working MRF sequence in both in-silico and in-vivo experiments. LOOP is an analytical approach to quantify and visualize parameter encoding in MRF.

Systematic review of reconstruction techniques foraccelerated quantitative MRI.

To systematically review the techniques that address undersampling artifacts in accelerated quantitative magnetic resonance imaging (qMRI). A literature search was conducted using the Embase, Medline, Web of Science Core Collection, Coherence Central Register of Controlled Trials, and Google Scholar databases for studies, published before July 2022 proposing reconstruction techniques for accelerated qMRI. Studies are reviewed according to inclusion criteria, and included studies are categorized based on the methodology used. A total of 292 studies included in the review are categorized. A technical overview of each category is provided, and the categories are described in a unified mathematical framework. The distribution of the reviewed studies over time, application domain, and parameters of interest is illustrated. An increasing trend in the number of articles that propose new techniques for accelerated qMRI reconstruction indicates the importance of acceleration in qMRI. The techniques are mostly validated for relaxometry parameters and brain scans. The categories of techniques are compared based on theoretical grounds, highlighting existing trends and potential gaps in the field.

Feasibility of CycleGAN enhanced low dose CBCT imaging for prostate radiotherapy dose calculation

Daily cone beam computed tomography (CBCT) imaging during the course of fractionated radiotherapy treatment can enable online adaptive radiotherapy but also expose patients to a non-negligible amount of radiation dose. This work investigates the feasibility of low dose CBCT imaging capable of enabling accurate prostate radiotherapy dose calculation with only 25% projections by overcoming under-sampling artifacts and correcting CT numbers by employing cycle-consistent generative adversarial networks (cycleGAN). Uncorrected CBCTs of 41 prostate cancer patients, acquired with ∼350 projections (CBCTorg), were retrospectively under-sampled to 25% dose images (CBCTLD) with only ∼90 projections and reconstructed using Feldkamp–Davis–Kress. We adapted a cycleGAN including shape loss to translate CBCTLD into planning CT (pCT) equivalent images (CBCTLD_GAN). An alternative cycleGAN with a generator residual connection was implemented to improve anatomical fidelity (CBCTLD_ResGAN). Unpaired 4-fold cross-validation (33 patients) was performed to allow using the median of 4 models as output. Deformable image registration was used to generate virtual CTs (vCT) for Hounsfield units (HU) accuracy evaluation on 8 additional test patients. Volumetric modulated arc therapy plans were optimized on vCT, and recalculated on CBCTLD_GAN and CBCTLD_ResGAN to determine dose calculation accuracy. CBCTLD_GAN, CBCTLD_ResGAN and CBCTorg were registered to pCT and residual shifts were analyzed. Bladder and rectum were manually contoured on CBCTLD_GAN, CBCTLD_ResGAN and CBCTorg and compared in terms of Dice similarity coefficient (DSC), average and 95th percentile Hausdorff distance (HDavg, HD95). The mean absolute error decreased from 126 HU for CBCTLD to 55 HU for CBCTLD_GAN and 44 HU for CBCTLD_ResGAN. For PTV, the median differences of D 98%, D 50% and D 2% comparing both CBCTLD_GAN to vCT were 0.3%, 0.3%, 0.3%, and comparing CBCTLD_ResGAN to vCT were 0.4%, 0.3% and 0.4%. Dose accuracy was high with both 2% dose difference pass rates of 99% (10% dose threshold). Compared to the CBCTorg-to-pCT registration, the majority of mean absolute differences of rigid transformation parameters were less than 0.20 mm/0.20°. For bladder and rectum, the DSC were 0.88 and 0.77 for CBCTLD_GAN and 0.92 and 0.87 for CBCTLD_ResGAN compared to CBCTorg, and HDavg were 1.34 mm and 1.93 mm for CBCTLD_GAN, and 0.90 mm and 1.05 mm for CBCTLD_ResGAN. The computational time was ∼2 s per patient. This study investigated the feasibility of adapting two cycleGAN models to simultaneously remove under-sampling artifacts and correct image intensities of 25% dose CBCT images. High accuracy on dose calculation, HU and patient alignment were achieved. CBCTLD_ResGAN achieved better anatomical fidelity.

A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI

Radial sampling is a fast magnetic resonance imaging technique. Further imaging acceleration can be achieved with undersampling but how to reconstruct a clear image with fast algorithm is still challenging. Previous work has shown the advantage of removing undersampling image artifacts using the tight-frame sparse reconstruction model. This model was further solved with a projected fast iterative soft-thresholding algorithm (pFISTA). However, the convergence of this algorithm under radial sampling has not been clearly set up. In this work, the authors derived a theoretical convergence condition for this algorithm. This condition was approximated by estimating the maximal eigenvalue of reconstruction operators through the power iteration. Based on the condition, an optimal step size was further suggested to allow the fastest convergence. Verifications were made on the prospective in vivo data of static brain imaging and dynamic contrast-enhanced liver imaging, demonstrating that the recommended parameter allowed fast convergence in radial MRI.

Motion estimation based on projective information disentanglement for 3D reconstruction of rotational coronary angiography

The 2D projection space-based motion compensation reconstruction (2D-MCR) is a kind of representative method for 3D reconstruction of rotational coronary angiography owing to its high efficiency. However, due to the lack of accurate motion estimation of the overlapping projection pixels, existing 2D-MCR methods may still have a certain level of under-sampling artifacts or lose accuracy for cases with strong cardiac motion. To overcome this, in this study, we proposed a motion estimation approach based on projective information disentanglement (PID-ME) for 3D reconstruction of rotational coronary angiography. The reconstruction method adopts the framework of 2D-MCR, which is referred to as 2D-PID-MCR. The PID-ME consists of two parts: generation of the reference projection sequence based on the fast simplified distance driven projector (FSDDP) algorithm, motion estimation and correction based on the projective average minimal distance measure (PAMD) model. The FSDDP algorithm generates the reference projection sequence faster and accelerates the whole reconstruction greatly. The PAMD model can disentangle the projection information effectively and estimate the motion of both overlapping and non-overlapping projection pixels accurately. The main contribution of this study is the construction of 2D-PID-MCR to overcome the inherent limitations of the existing 2D-MCR method. Simulated and clinical experiments show that the PID-ME, consisting of FSDDP and PAMD, can estimate the motion of the projection sequence data accurately and efficiently. Our 2D-PID-MCR method outperforms the state-of-the-art approaches in terms of accuracy and real-time performance.

Deep supervised dictionary learning by algorithm unrolling-Application to fast 2D dynamic MR image reconstruction.

Unrolled neural networks (NNs) have been extensively applied to different image reconstruction problems across all imaging modalities. A key component of the latter is that they allow for physics-informed learning of the regularization method, which is parametrized by the NN. However, due to the lack of understanding of deep NNs from a theoretical point of view, unrolled NNs are still black-boxes when the regularizers are given by deep NNs, for example, U-Nets. Dictionarylearning (DL) is a well-established regularization method, which is based on learning a transform to sparsely approximate the signals of interest. Typically, DL-based image reconstruction either employs a dictionary, which was pretrained on a set of patches which were extracted from ground-truth images or a dictionary which is jointly trained during the reconstruction. However, in both cases, the used DL-algorithms are not designed to take into account the reconstruction problem or the underlying physical model, which describes the imaging process. In this work, we propose a DL-algorithm based on unrolled NNs to overcome these limitations. We construct an unrolled NN, which corresponds to an unrolled DL-based reconstruction algorithm and train the unrolled NN to optimize its weights, that is, the atoms of the dictionary, by back-propagation in a supervised manner. Further, we propose a new way to employ a 2D dictionary in the spatio-temporal domain. We tested and evaluated the method on an accelerated cardiac cine MR image reconstruction problem using 216/36/36 dynamic images for training, validation, and testing and compared it to two well-known state-of-the-art approaches for cardiac cine MRI based on deep iterative CNNs. Further, we analyze the obtained dictionaries in terms of dictionary-coherence and structure of the atoms. Last, we compare the reported methods in terms of stability by applying them to an entirely different dataset consisting of 49 different testimages. The investigated physics-informed DL-approach yields significantly more accurate reconstructions compared to the DL-method, which uses dictionaries obtained by decoupled pretraining, thereby providing an improvement of up to 4.90 dB in terms of PSNR and 5% in terms of SSIM. Further, the proposed spatio-temporal 2D dictionary outperforms the 1D and 3D dictionaries by preventing smoothing of image details while still accurately removing undersampling artifacts and noise resulting in an increase of up to 1.10 dB in terms of PSNR and 4% in terms of SSIM. Although being surpassed by the CNNs on the first dataset, the proposed NNs-based DL method is more stable compared to the latter approach and yields comparable results on the second dataset. Last, it has the advantage of being entirely interpretable in eachcomponent. The presented physics-informed NN can be used as training algorithm for a classical and interpretable data-driven regularization method based on a learned dictionary, which can then not only be linked to the considered data but also to the reconstruction method that the NNdefines.

A Genetic Algorithm Optimized Undersampling Method for Seismic Sparse Acquisition and Reconstruction

The irregular observation region poses challenges to seismic acquisition systems design. The commonly-used parallel-type acquisition system requires that the geophones are located at equally spaced positions and therefore is hard to implement in an irregular observation region. An acquisition system which allows implementation of sparse and irregular observation (e.g., the node-type geometry) followed by a reconstruction procedure is a solution. It can not only fit in irregular observation regions but also make a significant reduction in seismic acquisition costs. The seismic sparse acquisition can be mathematically modeled as a undersampling operator in the seismic reconstruction problem. A suboptimal undersampling pattern will lead to an inferior reconstruction result. To optimize the seismic sparse acquisition, I propose a undersampling method based on bionic intelligence in this study. In the proposed method, a Shannon entropy maximum model is proposed to improve the observed ergodicity and reduce the undersampling artifacts. To solve the maximum problem, an improved version of genetic algorithm is presented. The proposed method is applicable to irregular observation regions and can optimize the subsequent reconstruction performance. I provide the detailed algorithm framework and discuss the undersampling artifacts of different undersampling methods. The application to synthetic and field seismic data validates the effectiveness of the proposed method.

Cycloidal-spiral sampling for three-modal x-ray CT flyscans with two-dimensional phase sensitivity.

We present a flyscan compatible acquisition scheme for three-modal X-Ray Computed Tomography (CT) with two-dimensional phase sensitivity. Our approach is demonstrated using a "beam tracking" setup, through which a sample's attenuation, phase (refraction) and scattering properties can be measured from a single frame, providing three complementary contrast channels. Up to now, such setups required the sample to be stepped at each rotation angle to sample signals at an adequate rate, to prevent resolution losses, anisotropic resolution, and under-sampling artefacts. However, the need for stepping necessitated a step-and-shoot implementation, which is affected by motors' overheads and increases the total scan time. By contrast, our proposed scheme, by which continuous horizontal and vertical translations of the sample are integrated with its rotation (leading to a "cycloidal-spiral" trajectory), is fully compatible with continuous scanning (flyscans). This leads to greatly reduced scan times while largely preserving image quality and isotropic resolution.