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Purpose Nyquist ghost artifacts in echo planar imaging (EPI) are originated from phase mismatch between the even and odd echoes. However, conventional correction methods using reference scans often produce erroneous results especially in high-field MRI due to the nonlinear and time-varying local magnetic field changes. Recently, it was shown that the problem of ghost correction can be reformulated as k-space interpolation problem that can be solved using structured low-rank Hankel matrix approaches. Another recent work showed that data driven Hankel matrix decomposition can be reformulated to exhibit similar structures as deep convolutional neural network. By synergistically combining these findings, we propose a k-space deep learning approach that immediately corrects the phase mismatch without a reference scan in both accelerated and non-accelerated EPI acquisitions. Theory and methods To take advantage of the even and odd-phase directional redundancy, the k-space data are divided into 2 channels configured with even and odd phase encodings. The redundancies between coils are also exploited by stacking the multi-coil k-space data into additional input channels. Then, our k-space ghost correction network is trained to learn the interpolation kernel to estimate the missing virtual k-space data. For the accelerated EPI data, the same neural network is trained to directly estimate the interpolation kernels for missing k-space data from both ghost and subsampling. Results Reconstruction results using 3T and 7T in vivo data showed that the proposed method outperformed the image quality compared to the existing methods, and the computing time is much faster. Conclusions The proposed k-space deep learning for EPI ghost correction is highly robust and fast, and can be combined with acceleration, so that it can be used as a promising correction tool for high-field MRI without changing the current acquisition protocol.

Purpose Magnetic resonance imaging (MRI) artifacts are originated from various sources including instability of an magnetic resonance (MR) system, patient motion, inhomogeneities of gradient fields, and so on. Such MRI artifacts are usually considered as irreversible, so additional artifact-free scan or navigator scan is necessary. To overcome these limitations, this article proposes a novel compressed sensing-based approach for removal of various MRI artifacts. Theory Recently, the annihilating filter based low-rank Hankel matrix approach was proposed. The annihilating filter based low-rank Hankel matrix exploits the duality between the low-rankness of weighted Hankel structured matrix and the sparsity of signal in a transform domain. Because MR artifacts usually appeared as sparse k-space components, the low-rank Hankel matrix from underlying artifact-free k-space data can be exploited to decompose the sparse outliers. Methods The sparse + low-rank decomposition framework using Hankel matrix was proposed for removal of MRI artifacts. Alternating direction method of multipliers algorithm was employed for the minimization of associated cost function with the initialized matrices from a factorization-based matrix completion. Results Experimental results demonstrated that the proposed algorithm can correct MR artifacts including herringbone (crisscross), motion, and zipper artifacts without image distortion. Conclusion The proposed method may be a robust correction solution for various MRI artifacts that can be represented as sparse outliers. Magn Reson Med 78:327-340, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Purpose MR measurements from an echo-planar imaging (EPI) sequence produce Nyquist ghost artifacts that originate from inconsistencies between odd and even echoes. Several reconstruction algorithms have been proposed to reduce such artifacts, but most of these methods require either additional reference scans or multipass EPI acquisition. This article proposes a novel and accurate single-pass EPI ghost artifact correction method that does not require any additional reference data. Theory and Methods After converting a ghost correction problem into separate k-space data interpolation problems for even and odd phase encoding, our algorithm exploits an observation that the differential k-space data between the even and odd echoes is a Fourier transform of an underlying sparse image. Accordingly, we can construct a rank-deficient Hankel structured matrix, whose missing data can be recovered using an annihilating filter-based low rank Hankel structured matrix completion approach. Results The proposed method was applied to EPI data for both single and multicoil acquisitions. Experimental results using in vivo data confirmed that the proposed method can completely remove ghost artifacts successfully without prescan echoes. Conclusion Owing to the discovery of the annihilating filter relationship from the intrinsic EPI image property, the proposed method successfully suppresses ghost artifacts without a prescan step. Magn Reson Med 76:1775–1789, 2016. © 2016 International Society for Magnetic Resonance in Medicine

Purpose MR parameter mapping is one of clinically valuable MR imaging techniques. However, increased scan time makes it difficult for routine clinical use. This article aims at developing an accelerated MR parameter mapping technique using annihilating filter based low-rank Hankel matrix approach (ALOHA). Theory When a dynamic sequence can be sparsified using spatial wavelet and temporal Fourier transform, this results in a rank-deficient Hankel structured matrix that is constructed using weighted k-t measurements. ALOHA then utilizes the low rank matrix completion algorithm combined with a multiscale pyramidal decomposition to estimate the missing k-space data. Methods Spin-echo inversion recovery and multiecho spin echo pulse sequences for T1 and T2 mapping, respectively, were redesigned to perform undersampling along the phase encoding direction according to Gaussian distribution. The missing k-space is reconstructed using ALOHA. Then, the parameter maps were constructed using nonlinear regression. Results Experimental results confirmed that ALOHA outperformed the existing compressed sensing algorithms. Compared with the existing methods, the reconstruction errors appeared scattered throughout the entire images rather than exhibiting systematic distortion along edges and the parameter maps. Conclusion Given that many diagnostic errors are caused by the systematic distortion of images, ALOHA may have a great potential for clinical applications. Magn Reson Med 76:1848–1864, 2016. © 2016 International Society for Magnetic Resonance in Medicine

Recently, balanced steady-state free precession (bSSFP) readout has been proposed for arterial spin labeling (ASL) perfusion imaging to reduce susceptibility artifacts at a relatively high spatial resolution and signal-to-noise ratio (SNR). However, the main limitation of bSSFP-ASL is the low spatial coverage. In this work, methods to increase the spatial coverage of bSSFP-ASL are proposed for distortion-free, high-resolution, whole-brain perfusion imaging. Three strategies of (i) segmentation, (ii) compressed sensing (CS) and (iii) a hybrid approach combining the two methods were tested to increase the spatial coverage of pseudo-continuous ASL (pCASL) with three-dimensional bSSFP readout. The spatial coverage was increased by factors of two, four and six using each of the three approaches, whilst maintaining the same total scan time (5.3 min). The number of segments and/or CS acceleration rate (R) correspondingly increased to maintain the same bSSFP readout time (1.2 s). The segmentation approach allowed whole-brain perfusion imaging for pCASL-bSSFP with no penalty in SNR and/or total scan time. The CS approach increased the spatial coverage of pCASL-bSSFP whilst maintaining the temporal resolution, with minimal impact on the image quality. The hybrid approach provided compromised effects between the two methods. Balanced SSFP-based ASL allows the acquisition of perfusion images with wide spatial coverage, high spatial resolution and SNR, and reduced susceptibility artifacts, and thus may become a good choice for clinical and neurological studies. Copyright © 2015 John Wiley & Sons, Ltd.

Purpose: In digital breast tomosynthesis (DBT), scatter correction is highly desirable, as it improves image quality at low doses. Because the DBT detector panel is typically stationary during the source rotation, antiscatter grids are not generally compatible with DBT; thus, a software-based scatter correction is required. This work proposes a fully iterative scatter correction method that uses a novel fast Monte Carlo simulation (MCS) with a tissue-composition ratio estimation technique for DBT imaging. Methods: To apply MCS to scatter estimation, the material composition in each voxel should be known. To overcome the lack of prior accurate knowledge of tissue composition for DBT, a tissue-composition ratio is estimated based on the observation that the breast tissues are principally composed of adipose and glandular tissues. Using this approximation, the composition ratio can be estimated from the reconstructed attenuation coefficients, and the scatter distribution can then be estimated by MCS using the composition ratio. The scatter estimation and image reconstruction procedures can be performed iteratively until an acceptable accuracy is achieved. For practical use, (i) the authors have implemented a fast MCS using a graphics processing unit (GPU), (ii) the MCS is simplified to transport only x-rays in the energy range of 10–50 keV, modeling Rayleigh and Compton scattering and the photoelectric effect using the tissue-composition ratio of adipose and glandular tissues, and (iii) downsampling is used because the scatter distribution varies rather smoothly. Results: The authors have demonstrated that the proposed method can accurately estimate the scatter distribution, and that the contrast-to-noise ratio of the final reconstructed image is significantly improved. The authors validated the performance of the MCS by changing the tissue thickness, composition ratio, and x-ray energy. The authors confirmed that the tissue-composition ratio estimation was quite accurate under a variety of conditions. Our GPU-based fast MCS implementation took approximately 3 s to generate each angular projection for a 6 cm thick breast, which is believed to make this process acceptable for clinical applications. In addition, the clinical preferences of three radiologists were evaluated; the preference for the proposed method compared to the preference for the convolution-based method was statistically meaningful (p < 0.05, McNemar test). Conclusions: The proposed fully iterative scatter correction method and the GPU-based fast MCS using tissue-composition ratio estimation successfully improved the image quality within a reasonable computational time, which may potentially increase the clinical utility of DBT.

Cardiac T(2) mapping is a promising method for quantitative assessment of myocardial edema and iron overload. We have developed a new multiecho fast spin echo (ME-FSE) pulse sequence for breath-hold T(2) mapping with acceptable spatial resolution. We propose to further accelerate this new ME-FSE pulse sequence using k-t focal underdetermined system solver adapted with a framework that uses both compressed sensing and parallel imaging (e.g., sensitivity encoding) to achieve higher spatial resolution. We imaged 12 control subjects in midventricular short-axis planes and compared the accuracy of T(2) measurements obtained using ME-FSE with generalized autocalibrating partially parallel acquisitions and ME-FSE with k-t focal underdetermined system solver. For image reconstruction, we used a bootstrapping two-step approach, where in the first step fast Fourier transform was used as the sparsifying transform and in the final step principal component analysis was used as the sparsifying transform. When compared with T(2) measurements obtained using generalized autocalibrating partially parallel acquisitions, T(2) measurements obtained using k-t focal underdetermined system solver were in excellent agreement (mean difference = 0.04 msec; upper/lower 95% limits of agreement were 2.26/-2.19 msec, respectively). The proposed accelerated ME-FSE pulse sequence with k-t focal underdetermined system solver is a promising investigational method for rapid T(2) measurement of the heart with relatively high spatial resolution (1.7 × 1.7 mm(2) ).

A compressed sensing dynamic MR technique called k-t FOCUSS (k-t FOCal Underdetermined System Solver) has been recently proposed. It outperforms the conventional k-t BLAST/SENSE (Broad-use Linear Acquisition Speed-up Technique/SENSitivity Encoding) technique by exploiting the sparsity of x-f signals. This paper applies this idea to radial trajectories for high-resolution cardiac cine imaging. Radial trajectories are more suitable for high-resolution dynamic MRI than Cartesian trajectories since there is smaller tradeoff between spatial resolution and number of views if streaking artifacts due to limited views can be resolved. As shown for Cartesian trajectories, k-t FOCUSS algorithm efficiently removes artifacts while preserving high temporal resolution. k-t FOCUSS algorithm applied to radial trajectories is expected to enhance dynamic MRI quality. Rather than using an explicit gridding method, which transforms radial k-space sampling data to Cartesian grid prior to applying k-t FOCUSS algorithms, we use implicit gridding during FOCUSS iterations to prevent k-space sampling errors from being propagated. In addition, motion estimation and motion compensation after the first FOCUSS iteration were used to further sparsify the residual image. By applying an additional k-t FOCUSS step to the residual image, improved resolution was achieved. In vivo experimental results show that this new method can provide high spatiotemporal resolution even from a very limited radial data set.

A model-based dynamic MRI called k-t BLAST/SENSE has drawn significant attention from the MR imaging community because of its improved spatio-temporal resolution. Recently, we showed that the k-t BLAST/SENSE corresponds to the special case of a new dynamic MRI algorithm called k-t FOCUSS that is optimal from a compressed sensing perspective. The main contribution of this article is an extension of k-t FOCUSS to a more general framework with prediction and residual encoding, where the prediction provides an initial estimate and the residual encoding takes care of the remaining residual signals. Two prediction methods, RIGR and motion estimation/compensation scheme, are proposed, which significantly sparsify the residual signals. Then, using a more sophisticated random sampling pattern and optimized temporal transform, the residual signal can be effectively estimated from a very small number of k-t samples. Experimental results show that excellent reconstruction can be achieved even from severely limited k-t samples without aliasing artifacts. Magn Reson Med 61:103–116, 2009.

Purpose: Material decomposition using multienergy photon counting x-ray detectors (PCXD) has been an active research area over the past few years. Even with some success, the problem of optimal energy selection and three material decomposition including malignant tissue is still on going research topic, and more systematic studies are required. This paper aims to address this in a unified statistical framework in a mammographic environment. Methods: A unified statistical framework for energy level optimization and decomposition of three materials is proposed. In particular, an energy level optimization algorithm is derived using the theory of the minimum variance unbiased estimator, and an iterative algorithm is proposed for material composition as well as system parameter estimation under the unified statistical estimation framework. To verify the performance of the proposed algorithm, the authors performed simulation studies as well as real experiments using physical breast phantom andex vivo breast specimen. Quantitative comparisons using various performance measures were conducted, and qualitative performance evaluations for ex vivo breast specimen were also performed by comparing the ground-truth malignant tissue areas identified by radiologists. Results: Both simulation and real experiments confirmed that the optimized energy bins by the proposed method allow better material decomposition quality. Moreover, for the specimen thickness estimation errors up to 2 mm, the proposed method provides good reconstruction results in both simulation and realex vivo breast phantom experiments compared to existing methods. Conclusions: The proposed statistical framework of PCXD has been successfully applied for the energy optimization and decomposition of three material in a mammographic environment. Experimental results using the physical breast phantom andex vivo specimen support the practicality of the proposed algorithm.