Arterial spin labeling MR image denoising and reconstruction using unsupervised deep learning

Arterial spin labeling (ASL) imaging is a powerful magnetic resonance imaging technique that allows to quantitatively measure blood perfusion non-invasively, which has great potential for assessing tissue viability in various clinical settings. However, the clinical applications of ASL are currently limited by its low signal-to-noise ratio (SNR), limited spatial resolution, and long imaging time. In this work, we propose an unsupervised deep learning-based image denoising and reconstruction framework to improve the SNR and accelerate the imaging speed of high resolution ASL imaging. The unique feature of the proposed framework is that it does not require any prior training pairs but only the subject's own anatomical prior, such as T1-weighted images, as network input. The neural network was trained from scratch in the denoising or reconstruction process, with noisy images or sparely sampled k-space data as training labels. Performance of the proposed method was evaluated using in vivo experiment data obtained from 3 healthy subjects on a 3T MR scanner, using ASL images acquired with 44-min acquisition time as the ground truth. Both qualitative and quantitative analyses demonstrate the superior performance of the proposed txtc framework over the reference methods. In summary, our proposed unsupervised deep learning-based denoising and reconstruction framework can improve the image quality and accelerate the imaging speed of ASL imaging.     

Improved k-t BLAST and k-t SENSE using FOCUSS

The dynamic MR imaging of time-varying objects, such as beating hearts or brain hemodynamics, requires a significant reduction of the data acquisition time without sacrificing spatial resolution. The classical approaches for this goal include parallel imaging, temporal filtering and their combinations. Recently, model-based reconstruction methods called k-t BLAST and k-t SENSE have been proposed which largely overcome the drawbacks of the conventional dynamic imaging methods without a priori knowledge of the spectral support. Another recent approach called k-t SPARSE also does not require exact knowledge of the spectral support. However, unlike k-t BLAST/SENSE, k-t SPARSE employs the so-called compressed sensing (CS) theory rather than using training. The main contribution of this paper is a new theory and algorithm that unifies the above mentioned approaches while overcoming their drawbacks. Specifically, we show that the celebrated k-t BLAST/SENSE are the special cases of our algorithm, which is asymptotically optimal from the CS theory perspective. Experimental results show that the new algorithm can successfully reconstruct a high resolution cardiac sequence and functional MRI data even from severely limited k-t samples, without incurring aliasing artifacts often observed in conventional methods.     

Highly undersampled MR image reconstruction using an improved dual-dictionary learning method with self-adaptive dictionaries

Dual-dictionary learning (Dual-DL) method utilizes both a low-resolution dictionary and a high-resolution dictionary, which are co-trained for sparse coding and image updating, respectively. It can effectively exploit a priori knowledge regarding the typical structures, specific features, and local details of training sets images. The prior knowledge helps to improve the reconstruction quality greatly. This method has been successfully applied in magnetic resonance (MR) image reconstruction. However, it relies heavily on the training sets, and dictionaries are fixed and nonadaptive. In this research, we improve Dual-DL by using self-adaptive dictionaries. The low- and high-resolution dictionaries are updated correspondingly along with the image updating stage to ensure their self-adaptivity. The updated dictionaries incorporate both the prior information of the training sets and the test image directly. Both dictionaries feature improved adaptability. Experimental results demonstrate that the proposed method can efficiently and significantly improve the quality and robustness of MR image reconstruction.     

动态磁共振成像中利用时空滤波的非笛卡尔稀疏数据重建新算法

通过非笛卡尔稀疏采样,可以显著缩短磁共振成像数据采集时间,在动态磁共振中具有良好的应用前景.现有的动态图像重建算法主要利用信号在时间域上的相关性完成图像重建,对信号在空间域上的相关性探讨不足.本文提出利用时空滤波的非笛卡尔稀疏数据重建新算法,同时考虑采集信号在时间域和空间域上的相关性.对动态的磁共振数据在时间域上采用改进的Hanning滤波,以克服数据量的不足;在空间域上,引入高频增强约束以突出图像中的细节信息.仿真实验结果显示,该方法重建出时间分辨率良好、细节比较清晰的图像,实现了稀疏采集的非笛卡尔数据在k空间的重建.     

Rapid generation of preview images for real-time 3D MR angiography

In 3D real-time MR angiography the reconstruction of images from large raw datasets via Fourier transforms with minimal delays is problematic. In this study strategies for reconstructing time-resolved three-dimensional (3D) datasets at a rate substantially faster than conventional 3D MR image reconstruction were investigated on general-purpose computer hardware. Moderate quality 'preview images' were generated from k-space subsets to reduce image reconstruction times from more than 50 s to 0.3 s per image volume. A blinded review of 3D TRICKS patient examinations showed that these moderate-quality images were sufficient for providing immediate feedback and guiding the subsequent reconstruction of selected time frames (p < 0.05). Fourier projection (reconstruction from a central k-space slice) was the most efficient reconstruction technique. However, the reduction of the reconstructed volume in all three dimensions resulted in higher contrast and better image quality while allowing reconstruction in near-to-real-time (less than 1 s per image volume). The use of such preview images in a real-time system allows for fast feedback from dynamic 3D datasets, enables scanner interaction with minimal latencies and can substantially reduce the postprocessing times.     

Fast T(2) relaxometry with an accelerated multi-echo spin-echo sequence

A new method has been developed to reduce the number of phase-encoding steps in a multi-echo spin-echo imaging sequence allowing fast T(2) mapping without loss of spatial resolution. In the proposed approach, the k-space data at each echo time were undersampled and a reconstruction algorithm that exploited the temporal correlation of the MR signal in k-space was used to reconstruct alias-free images. A specific application of this algorithm with multiple-receiver acquisition, offering an alternative to existing parallel imaging methods, has also been introduced. The fast T(2) mapping method has been validated in human brain T(2) measurements in a group of nine volunteers with acceleration factors up to 3.4. The results demonstrated that the proposed method exhibited excellent linear correlation with the regular T(2) mapping with full sampling and achieved better image reconstruction and T(2) mapping with respect to SNR and reconstruction artifacts than the selected reference acceleration techniques. The new method has also been applied for quantitative tracking of injected magnetically labeled breast cancer cells in the rat brain with acceleration factors of 1.8 and 3.0. The proposed technique can provide an effective approach for accelerated T(2) quantification, especially for experiments with single-channel coil when parallel imaging is not applicable.     

k-Space tutorial: an MRI educational tool for a better understanding of k-space

A main difference between Magnetic Resonance (MR) imaging and other medical imaging modalities is the control over the data acquisition and how it can be managed to finally show the adequate reconstructed image. With some basic programming adjustments, the user can modify the spatial resolution, field of view (FOV), image contrast, acquisition velocity, artifacts and so many other parameters that will contribute to form the final image. The main character and agent of all this control is called k-space, which represents the matrix where the MR data will be stored previously to a Fourier transformation to obtain the desired image.This work introduces 'k-Space tutorial', a MATLAB-based educational environment to learn how the image and the k-space are related, and how the image can be affected through k-space modifications. This MR imaging educational environment has learning facilities on the basic acceleration strategies that can be encountered in almost all MR scanners: scan percentage, rectangular FOV and partial Fourier imaging. It also permits one to apply low- and high-pass filtering to the k-space, and to observe how the contrast or the details are selected in the reconstructed image. It also allows one to modify the signal-to-noise ratio of the acquisition and create some artifacts on the image as a simulated movement of the patient - with variable intensity level - and some electromagnetic spikes on k-space occurring during data acquisition.     

Exploiting sparsity and low-rank structure for the recovery of multi-slice breast MRIs with reduced sampling error

It has been shown that, magnetic resonance images (MRIs) with sparsity representation in a transformed domain, e.g. spatial finite-differences (FD), or discrete cosine transform (DCT), can be restored from undersampled k-space via applying current compressive sampling theory. The paper presents a model-based method for the restoration of MRIs. The reduced-order model, in which a full-system-response is projected onto a subspace of lower dimensionality, has been used to accelerate image reconstruction by reducing the size of the involved linear system. In this paper, the singular value threshold (SVT) technique is applied as a denoising scheme to reduce and select the model order of the inverse Fourier transform image, and to restore multi-slice breast MRIs that have been compressively sampled in k-space. The restored MRIs with SVT for denoising show reduced sampling errors compared to the direct MRI restoration methods via spatial FD, or DCT. Compressive sampling is a technique for finding sparse solutions to underdetermined linear systems. The sparsity that is implicit in MRIs is to explore the solution to MRI reconstruction after transformation from significantly undersampled k-space. The challenge, however, is that, since some incoherent artifacts result from the random undersampling, noise-like interference is added to the image with sparse representation. These recovery algorithms in the literature are not capable of fully removing the artifacts. It is necessary to introduce a denoising procedure to improve the quality of image recovery. This paper applies a singular value threshold algorithm to reduce the model order of image basis functions, which allows further improvement of the quality of image reconstruction with removal of noise artifacts. The principle of the denoising scheme is to reconstruct the sparse MRI matrices optimally with a lower rank via selecting smaller number of dominant singular values. The singular value threshold algorithm is performed by minimizing the nuclear norm of difference between the sampled image and the recovered image. It has been illustrated that this algorithm improves the ability of previous image reconstruction algorithms to remove noise artifacts while significantly improving the quality of MRI recovery.     

A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data

Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data.

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Graphical abstract Two Real Images and their sparsified images by singularizing operator

     

A neural network approach for image reconstruction in electron magnetic resonance tomography

An object-oriented, artificial neural network (ANN) based, application system for reconstruction of two-dimensional spatial images in electron magnetic resonance (EMR) tomography is presented. The standard back propagation algorithm is utilized to train a three-layer sigmoidal feed-forward, supervised, ANN to perform the image reconstruction. The network learns the relationship between the 'ideal' images that are reconstructed using filtered back projection (FBP) technique and the corresponding projection data (sinograms). The input layer of the network is provided with a training set that contains projection data from various phantoms as well as in vivo objects, acquired from an EMR imager. Twenty five different network configurations are investigated to test the ability of the generalization of the network. The trained ANN then reconstructs two-dimensional temporal spatial images that present the distribution of free radicals in biological systems. Image reconstruction by the trained neural network shows better time complexity than the conventional iterative reconstruction algorithms such as multiplicative algebraic reconstruction technique (MART). The network is further explored for image reconstruction from 'noisy' EMR data and the results show better performance than the FBP method. The network is also tested for its ability to reconstruct from limited-angle EMR data set.     

Measurements of MTF and SNR(f) using a subtraction method in MRI

A method was developed for accurate measurement of the modulation transfer function (MTF) and signal-to-noise ratio in the spatial frequency domain (SNR(f)) of magnetic resonance images (MRI). The MTF was calculated from the complex images of a line object which were obtained by the subtraction of two separately acquired data sets of a specially designed phantom with a sliding sheet. Moreover, the SNR(f) was calculated from the MTF and Wiener spectrum, both of which were determined using the same phantom configuration. The MTFs and SNR(f)s in the conventional spin-echo (SE) and turbo SE, in which the effective echo time was set to the first echo, were evaluated by changing the T2 of the phantom and the echo train length. The MTFs in the positive and negative frequencies indicated the effect of the k-space trajectory for each pulse sequence. SNR(f)s gave spatial frequency information that was not obtained with conventional methods. In this method, the influence of image nonuniformity and unwanted artefacts (edge and ghost) could be eliminated. An analysis of the MTF and the SNR in the spatial frequency domain provides additional information for the assessment of image quality in MRI.     

磁共振成像PROPELLER采样数据重建中的运动估计新算法

PROPELLER（推进器）采样技术能够利用K空间中心重叠采样区域的数据来估计采集过程中受检查者的运动进而加以补偿,对运动伪影的消除效果非常显著。然而,由于其重建时的运动估计是基于最大化频域空间上相关系数的配准算法,该算法为了实现旋转估计与平移估计的分离,在进行旋转估计时,仅仅采用K空间数据的模,在数据量有限的情况下造成估计精度较低,在重建图像上表现为模糊及星条状伪影。本研究基于最大化图像空间上的互信息提出一种PROPELLER采样数据的运动估计新算法,首先由每个K空间带进行傅立叶逆变换后取模重建出系列临时图像,对这些图像进行模糊增强后以互信息作为相似性测度迭代搜索最优的运动参数。实验证明,该方法能显著提高PROPELLER采样数据重建中运动估计与补偿的精度,从而更好地消除伪影,特别是用于有运动时T1加权头部成像时。     

Iterative 4D cardiac micro-CT image reconstruction using an adaptive spatio-temporal sparsity prior

Temporal-correlated image reconstruction, also known as 4D CT image reconstruction, is a big challenge in computed tomography. The reasons for incorporating the temporal domain into the reconstruction are motions of the scanned object, which would otherwise lead to motion artifacts. The standard method for 4D CT image reconstruction is extracting single motion phases and reconstructing them separately. These reconstructions can suffer from undersampling artifacts due to the low number of used projections in each phase. There are different iterative methods which try to incorporate some a priori knowledge to compensate for these artifacts. In this paper we want to follow this strategy. The cost function we use is a higher dimensional cost function which accounts for the sparseness of the measured signal in the spatial and temporal directions. This leads to the definition of a higher dimensional total variation. The method is validated using in vivo cardiac micro-CT mouse data. Additionally, we compare the results to phase-correlated reconstructions using the FDK algorithm and a total variation constrained reconstruction, where the total variation term is only defined in the spatial domain. The reconstructed datasets show strong improvements in terms of artifact reduction and low-contrast resolution compared to other methods. Thereby the temporal resolution of the reconstructed signal is not affected.     

Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography

It is well known that the reconstruction problem in optical tomography is ill-posed. In other words, many different spatial distributions of optical properties inside the medium can lead to the same detector readings on the surface of the medium under consideration. Therefore, the choice of an appropriate method to overcome this problem is of crucial importance for any successful optical tomographic image reconstruction algorithm. In this work we approach the problem within a gradient-based iterative image reconstruction scheme. The image reconstruction is considered to be a minimization of an appropriately defined objective function. The objective function can be separated into a least-square-error term, which compares predicted and actual detector readings, and additional penalty terms that may contain a priori information about the system. For the efficient minimization of this objective function the gradient with respect to the spatial distribution of optical properties is calculated. Besides presenting the underlying concepts in our approach to overcome ill-posedness in optical tomography, we will show numerical results that demonstrate how prior knowledge, represented as penalty terms, can improve the reconstruction results.     

MR-based keyhole SPECT for small animal imaging

The rationale for multi-modality imaging is to integrate the strengths of different imaging technologies while reducing the shortcomings of an individual modality. The work presented here proposes a limited-field-of-view (LFOV) SPECT reconstruction technique that can be implemented on a multi-modality MR/SPECT system that can be used to obtain simultaneous MRI and SPECT images for small animal imaging. The reason for using a combined MR/SPECT system in this work is to eliminate any possible misregistration between the two sets of images when MR images are used as a priori information for SPECT. In nuclear imaging the target area is usually smaller than the entire object; thus, focusing the detector on the LFOV results in various advantages including the use of a smaller nuclear detector (less cost), smaller reconstruction region (faster reconstruction) and higher spatial resolution when used in conjunction with pinhole collimators with magnification. The MR/SPECT system can be used to choose a region of interest (ROI) for SPECT. A priori information obtained by the full field-of-view (FOV) MRI combined with the preliminary SPECT image can be used to reduce the dimensions of the SPECT reconstruction by limiting the computation to the smaller FOV while reducing artifacts resulting from the truncated data. Since the technique is based on SPECT imaging within the LFOV it will be called the keyhole SPECT (K-SPECT) method. At first MRI images of the entire object using a larger FOV are obtained to determine the location of the ROI covering the target organ. Once the ROI is determined, the animal is moved inside the radiofrequency (rf) coil to bring the target area inside the LFOV and then simultaneous MRI and SPECT are performed. The spatial resolution of the SPECT image is improved by employing a pinhole collimator with magnification >1 by having carefully calculated acceptance angles for each pinhole to avoid multiplexing. In our design all the pinholes are focused to the center of the LFOV. K-SPECT reconstruction is accomplished by generating an adaptive weighting matrix using a priori information obtained by simultaneously acquired MR images and the radioactivity distribution obtained from the ROI region of the SPECT image that is reconstructed without any a priori input. Preliminary results using simulations with numerical phantoms show that the image resolution of the SPECT image within the LFOV is improved while minimizing artifacts arising from parts of the object outside the LFOV due to the chosen magnification and the new reconstruction technique. The root-mean-square-error (RMSE) in the out-of-field artifacts was reduced by 60% for spherical phantoms using the K-SPECT reconstruction technique and by 48.5-52.6% for the heart in the case with the MOBY phantom. The K-SPECT reconstruction technique significantly improved the spatial resolution and quantification while reducing artifacts from the contributions outside the LFOV as well as reducing the dimension of the reconstruction matrix.     

Linear motion correction in three dimensions applied to dynamic gadolinium enhanced breast imaging.

Quantitative analysis of dynamic gadolinium-DTPA (diethylenetriamine pentaacetic acid) enhanced magnetic resonance imaging (MRI) is emerging as a highly sensitive tool for detecting malignant breast tissue. Three-dimensional rapid imaging techniques, such as keyhole MRI, yield high temporal sampling rates to accurately track contrast enhancement and washout in lesions over the course of multiple volume acquisitions. Patient motion during the dynamic acquisitions is a limiting factor that degrades the image quality, particularly of subsequent subtraction images used to identify and quantitatively evaluate regions suggestive of malignancy. Keyhole imaging is particularly sensitive to motion since datasets acquired over an extended period are combined in k-space. In this study, motion is modeled as set of translations in each of the three orthogonal dimensions. The specific objective of the study is to develop and implement an algorithm to correct the consequent phase shifts in k-space data prior to offline keyhole reconstruction three-dimensional (3D) volume breast MR acquisitions.     

Diffuse optical tomography with a priori anatomical information

Diffuse optical tomography (DOT) poses a typical ill-posed inverse problem with a limited number of measurements and inherently low spatial resolution. In this paper, we propose a hierarchical Bayesian approach to improve spatial resolution and quantitative accuracy by using a priori information provided by a secondary high resolution anatomical imaging modality, such as magnetic resonance (MR) or x-ray. In such a dual imaging approach, while the correlation between optical and anatomical images may be high, it is not perfect. For example, a tumour may be present in the optical image, but may not be discernable in the anatomical image. The proposed hierarchical Bayesian approach allows incorporation of partial a priori knowledge about the noise and unknown optical image models, thereby capturing the function-anatomy correlation effectively. We present a computationally efficient iterative algorithm to simultaneously estimate the optical image and the unknown a priori model parameters. Extensive numerical simulations demonstrate that the proposed method avoids undesirable bias towards anatomical prior information and leads to significantly improved spatial resolution and quantitative accuracy.     

一种新的仿射参数估计方法在磁共振成像PROPELLER中的应用

本文提出了一种基于频域相位相关算法的仿射参数估计方法,以改进PROPELLER仿射伪影消除中现有方法的不足。首先利用频域相位相关算法求出每个k-空间条的刚性运动参数,然后把刚性运动参数作为初值代入到仿射估计中,进行运动补偿后由网格化重建得到最终结果。实验结果证实该方法对于仿射参数估计的精度更高,稳定性更好,仿射运动伪影消除效果明显优于现有方法。该方法在PROPELLER伪影消除中是一种有效的并且实用的仿射参数估计方法。     

A tool for validating MRI-guided strategies: a digital breathing CT/MRI phantom of the abdominal site

Dynamic magnetic resonance imaging (MRI) is emerging as the elected image modality for organ motion quantification and management in image-guided radiotherapy. However, the lack of validation tools is an open issue for image guidance in the abdominal and thoracic organs affected by organ motion due to respiration. We therefore present an abdominal four-dimensional (4D) CT/MRI digital phantom, including the estimation of MR tissue parameters, simulation of dedicated abdominal MR sequences, modeling of radiofrequency coil response and noise, followed by k-space sampling and image reconstruction. The phantom allows the realistic simulation of images generated by MR pulse sequences with control of scan and tissue parameters, combined with co-registered CT images. In order to demonstrate the potential of the phantom in a clinical scenario, we describe the validation of a virtual T1-weighted 4D MRI strategy. Specifically, the motion extracted from a T2-weighted 4D MRI is used to warp a T1-weighted breath-hold acquisition, with the aim of overcoming trade-offs that limit T1-weighted acquisitions. Such an application shows the applicability of the digital CT/MRI phantom as a validation tool, which should be especially useful for cases unsuited to obtain real imaging data.     

A hierarchical neural network algorithm for robust and automatic windowing of MR images

A novel hierarchical neural network based algorithm for automatic adjustment of display window width and center for a wide range of magnetic resonance (MR) images is presented in this paper. The algorithm consists of a feature generator utilizing both wavelet histogram and compact spatial statistical information computed from a MR image, a competitive layer based neural network for clustering MR images into different subclasses, two pairs of a radial basis function (RBF) network and a bi-modal linear estimator for each subclass, as well as a data fusion process using estimates from both estimators to compute the final display parameters. Both estimators can adapt to new kinds of MR images simply by training them with those images, which make the algorithm adaptive and extendable. The RBF based estimator performs very well for images that are similar to those in the training data set. The bi-modal linear estimator provides reasonable estimations for a wide range of images that may not be included in the training data set. The data fusion step makes the final estimation of the display parameters accurate for trained images and robust for the unknown images. The algorithm has been tested on a wide range of MR images and has shown satisfactory results.