Wavelet-based edge correlation incorporated iterative reconstruction for undersampled MRI

Undersampling k-space is an effective way to decrease acquisition time for MRI. However, aliasing artifacts introduced by undersampling may blur the edges of magnetic resonance images, which often contain important information for clinical diagnosis. Moreover, k-space data is often contaminated by the noise signals of unknown intensity. To better preserve the edge features while suppressing the aliasing artifacts and noises, we present a new wavelet-based algorithm for undersampled MRI reconstruction. The algorithm solves the image reconstruction as a standard optimization problem including a ?₂ data fidelity term and ?₁ sparsity regularization term. Rather than manually setting the regularization parameter for the ?₁ term, which is directly related to the threshold, an automatic estimated threshold adaptive to noise intensity is introduced in our proposed algorithm. In addition, a prior matrix based on edge correlation in wavelet domain is incorporated into the regularization term. Compared with nonlinear conjugate gradient descent algorithm, iterative shrinkage/thresholding algorithm, fast iterative soft-thresholding algorithm and the iterative thresholding algorithm using exponentially decreasing threshold, the proposed algorithm yields reconstructions with better edge recovery and noise suppression.     

Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization

Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges.     

Improved grid-noise removal in single-frame digital moiré 3D shape measurement

A single-frame grid-noise removal technique was developed for application in single-frame digital-moiré 3D shape measurement. The ability of the stationary wavelet transform (SWT) to prevent oscillation artifacts near discontinuities, and the ability of the Fourier transform (FFT) applied to wavelet coefficients to separate grid-noise from useful image information, were combined in a new technique, SWT-FFT, to remove grid-noise from moiré-pattern images generated by digital moiré. In comparison to previous grid-noise removal techniques in moiré, SWT-FFT avoids the requirement for mechanical translation of optical components and capture of multiple frames, to enable single-frame moiré-based measurement. Experiments using FFT, Discrete Wavelet Transform (DWT), DWT-FFT, and SWT-FFT were performed on moiré-pattern images containing grid noise, generated by digital moiré, for several test objects. SWT-FFT had the best performance in removing high-frequency grid-noise, both straight and curved lines, minimizing artifacts, and preserving the moiré pattern without blurring and degradation. SWT-FFT also had the lowest noise amplitude in the reconstructed height and lowest roughness index for all test objects, indicating best grid-noise removal in comparison to the other techniques.     

Visually weighted reconstruction of compressive sensing MRI

Compressive sensing (CS) enables the reconstruction of a magnetic resonance (MR) image from undersampled data in k-space with relatively low-quality distortion when compared to the original image. In addition, CS allows the scan time to be significantly reduced. Along with a reduction in the computational overhead, we investigate an effective way to improve visual quality through the use of a weighted optimization algorithm for reconstruction after variable density random undersampling in the phase encoding direction over k-space. In contrast to conventional magnetic resonance imaging (MRI) reconstruction methods, the visual weight, in particular, the region of interest (ROI), is investigated here for quality improvement. In addition, we employ a wavelet transform to analyze the reconstructed image in the space domain and fully utilize data sparsity over the spatial and frequency domains. The visual weight is constructed by reflecting the perceptual characteristics of the human visual system (HVS), and then applied to ?₁ norm minimization, which gives priority to each coefficient during the reconstruction process. Using objective quality assessment metrics, it was found that an image reconstructed using the visual weight has higher local and global quality than those processed by conventional methods.     

Exploiting rank deficiency and transform domain sparsity for MR image reconstruction

The reconstruction of magnetic resonance (MR) images from the partial samples of their k-space data using compressed sensing (CS)-based methods has generated a lot of interest in recent years. To reconstruct the MR images, these techniques exploit the sparsity of the image in a transform domain (wavelets, total variation, etc.). In a recent work, it has been shown that it is also possible to reconstruct MR images by exploiting their rank deficiency. In this work, it will be shown that, instead of exploiting the sparsity of the image or rank deficiency alone, better reconstruction results can be achieved by combining transform domain sparsity with rank deficiency.To reconstruct an MR image using its transform domain sparsity and its rank deficiency, this work proposes a combined l₁-norm (of the transform coefficients) and nuclear norm (of the MR image matrix) minimization problem. Since such an optimization problem has not been encountered before, this work proposes and derives a first-order algorithm to solve it.The reconstruction results show that the proposed approach yields significant improvements, in terms of both visual quality as well as the signal to noise ratio, over previous works that reconstruct MR images either by exploiting rank deficiency or by the standard CS-based technique popularly known as the ‘Sparse MRI.’     

Reconstruction of dynamic contrast enhanced magnetic resonance imaging of the breast with temporal constraints

A number of methods using temporal and spatial constraints have been proposed for reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. The complex data can be constrained or regularized in a number of different ways, for example, the time derivative of the magnitude and phase image voxels can be constrained separately or jointly. Intuitively, the performance of different regularizations will depend on both the data and the chosen temporal constraints. Here, a complex temporal total variation (TV) constraint was compared to the use of separate real and imaginary constraints, and to a magnitude constraint alone. Projection onto Convex Sets (POCS) with a gradient descent method was used to implement the diverse temporal constraints in reconstructions of DCE MRI data. For breast DCE data, serial POCS with separate real and imaginary TV constraints was found to give relatively poor results while serial/parallel POCS with a complex temporal TV constraint and serial POCS with a magnitude-only temporal TV constraint performed well with an acceleration factor as large as R=6. In the tumor area, the best method was found to be parallel POCS with complex temporal TV constraint. This method resulted in estimates for the pharmacokinetic parameters that were linearly correlated to those estimated from the fully-sampled data, with K^trans,R=6=0.97 K^trans,R=1+0.00 with correlation coefficient r=0.98, k_ep,R=6=0.95 k_ep,R=1+0.00 (r=0.85). These results suggest that it is possible to acquire highly undersampled breast DCE-MRI data with improved spatial and/or temporal resolution with minimal loss of image quality.     

Smoothly Clipped Absolute Deviation (SCAD) regularization for compressed sensing MRI Using an augmented Lagrangian scheme

PurposeCompressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l₁ norm while approaching an l₀ norm.Materials and MethodsThe CS-MR image reconstruction was formulated as an equality-constrained optimization problem using a variable splitting technique and solved using an augmented Lagrangian (AL) method developed to accelerate the optimization of constrained problems. The performance of the resulting SCAD-based algorithm was evaluated for discrete gradients and wavelet sparsifying transforms and compared with its l₁-based counterpart using phantom and clinical studies. The k-spaces of the datasets were retrospectively undersampled using different sampling trajectories. In the AL framework, the CS-MRI problem was decomposed into two simpler sub-problems, wherein the linearization of the SCAD norm resulted in an adaptively weighted soft thresholding rule with a sparsity enhancing effect.ResultsIt was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l₁-based counterpart.ConclusionThe SCAD regularization improves the performance of l₁-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI.     

Wavelet-based detection of coherent structures and self-affinity in financial data

As a linear superposition of translated and dilated versions of a chosen analyzing wavelet function, the wavelet transform lends itself to the analysis of underlying multi-scale structure in nonstationary time series. In this work, we use the discrete wavelet transform (DWT) to investigate scaling and search for the presence of coherent structures in financial data. Quantitative measurements are given by the DWT of the original time series and wavelet coefficient variance. We find that variations and correlations in the transform coefficients are able to indicate the presence of structure and that measurements based on the DWT allow us to observe scaling directly in the nonstationary time series. Received 5 September 2000     

Noise estimation in parallel MRI: GRAPPA and SENSE

Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE and GRAPPA are the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. The reconstruction process carried out by both methods yields to a variance of noise value which is dependent on the position within the final image. Hence, the traditional noise estimation methods – based on a single noise level for the whole image – fail. In this paper we propose a novel methodology to estimate the spatial dependent pattern of the variance of noise in SENSE and GRAPPA reconstructed images. In both cases, some additional information must be known beforehand: the sensitivity maps of each receiver coil in the SENSE case and the reconstruction coefficients for GRAPPA.     

基于深度神经网络的时空编码磁共振成像超分辨率重建方法

单扫描时空编码磁共振成像是一种新型超快速磁共振成像技术,它对磁场不均匀和化学位移伪影有较强的抵抗性,但是其固有的空间分辨率较低,因此通常需要进行超分辨率重建,以在不增加采样点数的情况下提高时空编码磁共振图像的空间分辨率.然而,现有的重建方法存在迭代求解时间长、重建结果有混叠伪影残留等问题.为此,本文提出了一种基于深度神经网络的单扫描时空编码磁共振成像超分辨率重建方法.该方法采用模拟样本训练深度神经网络,再利用训练好的网络模型对实际采样信号进行重建.数值模拟、水模和活体鼠脑的实验结果表明,该方法能快速重建出无残留混叠伪影、纹理信息清楚的超分辨率时空编码磁共振图像.适当增加训练样本数量以及在训练样本中加入适当的随机噪声水平,有助于改善重建效果.     

Optimization of hyperparameters for SMS reconstruction

PurposeSimultaneous multi-slice (SMS) imaging accelerates MRI data acquisition by exciting multiple image slices with a single radiofrequency pulse. Overlapping slices encoded in acquired signal are separated using a mathematical model, which requires estimation of image reconstruction kernels using calibration data. Several parameters used in SMS reconstruction impact the quality and fidelity of final images. Therefore, finding an optimal set of reconstruction parameters is critical to ensure that accelerated acquisition does not significantly degrade resulting image quality.MethodsGradient-echo echo planar imaging data were acquired with a range of SMS acceleration factors from a cohort of five volunteers with no known neurological pathology. Images were collected using two available phased-array head coils (a 48-channel array and a reduced diameter 32-channel array) that support SMS. Data from these coils were identically reconstructed offline using a range of coil compression factors and reconstruction kernel parameters. A hybrid space (k-x), externally-calibrated coil-by-coil slice unaliasing approach was used for image reconstruction. The image quality of the resulting reconstructed SMS images was assessed by evaluating correlations with identical echo-planar reference data acquired without SMS. A finger tapping functional MRI (fMRI) experiment was also performed and group analysis results were compared between data sets reconstructed with different coil compression levels.ResultsBetween the two RF coils tested in this study, the 32-channel coil with smaller dimensions clearly outperformed the larger 48-channel coil in our experiments. Generally, a large calibration region (144–192 samples) and small kernel sizes (2–4 samples) in k_y direction improved image quality. Use of regularization in the kernel fitting procedure had a notable impact on the fidelity of reconstructed images and a regularization value 0.0001 provided good image quality. With optimal selection of other hyperparameters in the hybrid space SMS unaliasing algorithm, coil compression caused small reduction in correlation between single-band and SMS unaliased images. Similarly, group analysis of fMRI results did not show a significant influence of coil compression on resulting image quality.ConclusionsThis study demonstrated that the hyperparameters used in SMS reconstruction need to be fine-tuned once the experimental factors such as the RF receive coil and SMS factor have been determined. A cursory evaluation of SMS reconstruction hyperparameter values is therefore recommended before conducting a full-scale quantitative study using SMS technologies.     

Composite pulses for RF phase encoded MRI: A simulation study

BackgroundIn B₁ encoded MRI, a realistic non-linear phase RF encoding coil will generate an inhomogeneous B₁ field that leads to spatially dependent flip angles. The non-linearity of the B₁ phase gradient can be compensated for in the reconstruction, but B₁ inhomogeneity remains a problem. The effect of B₁ inhomogeneity on tip angles for conventional, B₀ encoded MRI, may be minimized using composite pulses. The objective of this study was to explore the feasibility of using composite pulses with non-linear RF phase encoding coils and to identify the most appropriate composite pulse scheme.MethodsRF encoded signals were simulated via the Bloch equation for various symmetric, asymmetric and antisymmetric composite pulses. The simulated signals were reconstructed using a constrained least squares method.ResultsRoot mean square reconstruction errors varied from 6% (for an asymmetric composite pulse) to 9.7% (for an antisymmetric composite pulse).ConclusionAn asymmetric composite pulse scheme created images with fewer artifacts than other composite pulse schemes in inhomogeneous B₀ and B₁ fields making it the best choice for decreasing the effects of spatially varying flip angles. This is contrary to the conclusion that antisymmetric composite pulses are the best ones to use for spin echo sequences in conventional, B₀ encoded, MRI.     

多通道相位图像的改进型自适应重建算法

自适应重建(Adaptive Reconstruction,AR)算法被广泛应用于磁共振图像的多通道合并问题上.AR算法不需要直接采集各个线圈的灵敏度信息,而是通过通道间信号及噪声相关矩阵,估算出各个通道的灵敏度,从而保证了合并的幅值图像具有较高的信噪比(Signal-to-Noise Ratio,SNR).然而,由于AR算法没有针对相位图像的合并问题进行优化,导致重建出的相位图像具有不确定性.另外,受各通道之间相位偏移及低信噪比相位图像的影响,重建结果可能包含伪影.该文提出了一种改进型AR算法,估算并移除了各通道之间的相位偏移,同时对多通道数据的相位进行质量评估及通道重排,用以进行后续自适应重建.仿体及在体实验表明,该方法可以有效提升AR算法稳定性、消除重建图像中存在的伪影,同时保持合并后幅值图像及相位图像的高信噪比.     

基于平稳小波变换的时域光学相干层析系统

以平衡检测原理为基础,利用中心波长为700 nm的宽带低相干白光光源,在自由空间中搭建了分辨率为0.93 m的基于平稳小波变换（SWT）的时域光学相干层析（TDOCT）系统,并将其应用于塑料薄片与透明胶纸多层薄膜结构的无损评价。针对现有算法重构效果不够理想的问题,通过对OCT成像过程中的图像增强手段的对比,提出利用SWT分解算法处理多层薄膜结构的光学相干层析二维图像。由薄膜检测的实验结果可知,从SWT细节系数中可以提取更显著的多层薄膜界面干涉信号,从而提高多层薄膜界面的增强效果。     

Non-Iterative Regularized reconstruction Algorithm for Non-CartesiAn MRI: NIRVANA

We introduce a novel noniterative algorithm for the fast and accurate reconstruction of nonuniformly sampled MRI data. The proposed scheme derives the reconstructed image as the nonuniform inverse Fourier transform of a compensated dataset. We derive each sample in the compensated dataset as a weighted linear combination of a few measured k-space samples. The specific k-space samples and the weights involved in the linear combination are derived such that the reconstruction error is minimized. The computational complexity of the proposed scheme is comparable to that of gridding. At the same time, it provides significantly improved accuracy and is considerably more robust to noise and undersampling. The advantages of the proposed scheme makes it ideally suited for the fast reconstruction of large multidimensional datasets, which routinely arise in applications such as f-MRI and MR spectroscopy. The comparisons with state-of-the-art algorithms on numerical phantoms and MRI data clearly demonstrate the performance improvement.     

一种以超分辨率理论为基础的磁共振眼球成像方法

磁共振成像（MRI）是一种无电离辐射的非介入性的眼内肿瘤检测方法,但分辨率和运动伪影是成像过程中不易克服的困难．以往的扫描方法或是不可避免的引入运动伪影,或是需要受试者做精确的配合,增加了成像的难度,给受试者带来不舒适的体验．本文提出了一种以超分辨率理论为基础的新的磁共振眼球成像方法,使用一种特制的眼球线圈,对眼部区域扫描一系列动态的图像,使得不同方向上的采集分辨率互补．最后经过预处理、配准、超分辨率重建等操作,得到高质量的磁共振眼球图像．实验结果表明,这种方法可以在不需要受试者做额外配合工作的情况下,得到更加清晰的磁共振眼球图像．     

Robust GRAPPA reconstruction using sparse multi-kernel learning with least squares support vector regression

Accuracy of interpolation coefficients fitting to the auto-calibrating signal data is crucial for k-space-based parallel reconstruction. Both conventional generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction that utilizes linear interpolation function and nonlinear GRAPPA (NLGRAPPA) reconstruction with polynomial kernel function are sensitive to interpolation window and often cannot consistently produce good results for overall acceleration factors. In this study, sparse multi-kernel learning is conducted within the framework of least squares support vector regression to fit interpolation coefficients as well as to reconstruct images robustly under different subsampling patterns and coil datasets. The kernel combination weights and interpolation coefficients are adaptively determined by efficient semi-infinite linear programming techniques. Experimental results on phantom and in vivo data indicate that the proposed method can automatically achieve an optimized compromise between noise suppression and residual artifacts for various sampling schemes. Compared with NLGRAPPA, our method is significantly less sensitive to the interpolation window and kernel parameters.     

Remote-sensing image encryption in hybrid domains

Remote-sensing technology plays an important role in military and industrial fields. Remote-sensing image is the main means of acquiring information from satellites, which always contain some confidential information. To securely transmit and store remote-sensing images, we propose a new image encryption algorithm in hybrid domains. This algorithm makes full use of the advantages of image encryption in both spatial domain and transform domain. First, the low-pass subband coefficients of image DWT (discrete wavelet transform) decomposition are sorted by a PWLCM system in transform domain. Second, the image after IDWT (inverse discrete wavelet transform) reconstruction is diffused with 2D (two-dimensional) Logistic map and XOR operation in spatial domain. The experiment results and algorithm analyses show that the new algorithm possesses a large key space and can resist brute-force, statistical and differential attacks. Meanwhile, the proposed algorithm has the desirable encryption efficiency to satisfy requirements in practice.     

Evaluation of B0-correction of relative CBF maps using tagging distance dependent Z-spectrum (TADDZ)

Arterial spin labeling (ASL) MRI, based on endogenous contrast from blood water, is used in research and diagnosis of cerebral vascular conditions. However, artifacts due to imperfect imaging conditions such as B₀-inhomogeneity (ΔB₀) could lead to variations in the quantification of relative cerebral blood flow (CBF). In this study, we evaluate a new approach using tagging distance dependent Z-spectrum (TADDZ) data, similar to the ΔB₀ corrections in the chemical exchange saturation transfer (CEST) experiments, to remove the imaging plane B₀ inhomogeneity induced CBF artifacts in ASL MRI. Our results indicate that imaging-plane B₀-inhomogeneity can lead to variations and errors in the relative CBF maps especially under small tagging distances. Along with an acquired B₀ map, TADDZ data helps to eliminate B₀-inhomogeneity induced artifacts in the resulting relative CBF maps. We demonstrated the effective use of TADDZ data to reduce variation while subjected to systematic changes in ΔB₀. In addition, TADDZ corrected ASL MRI, with improved consistency, was shown to outperform conventional ASL MRI by differentiating the subtle CBF difference in Alzheimer's disease (AD) mice brains with different APOE genotypes.     

Parallel imaging with 3D TPI trajectory: SNR and acceleration benefits

Three-dimensional (3D) twisted projection imaging (TPI) trajectory has a unique advantage in sodium (²³Na) imaging on clinical MRI scanners at 1.5 or 3 T, generating a high signal-to-noise ratio (SNR) with a short acquisition time (∼10 min). Parallel imaging with an array of coil elements transits SNR benefits from small coil elements to acquisition efficiency by sampling partial k-space. This study investigates the feasibility of parallel sodium imaging with emphases on SNR and acceleration benefits provided by the 3D TPI trajectory. Computer simulations were used to find available acceleration factors and noise amplification. Human head studies were performed on clinical 1.5/3-T scanners with four-element coil arrays to verify simulation outcomes. In in vivo studies, proton (¹H) data, however, were acquired for concept–proof purpose. The sensitivity encoding (SENSE) method with the conjugate gradient algorithm was used to reconstruct images from accelerated TPI-SENSE data sets. Self-calibration was employed to estimate coil sensitivities. Noise amplification in TPI-SENSE was evaluated using multiple noise trials. It was found that the acceleration factor was as high as 5.53 (corresponding to acceleration number 2×3, ring-by-rotation), with a small image error of 6.9% when TPI projections were reduced in both polar (ring) and azimuthal (rotation) directions. The average noise amplification was as low as 98.7%, or 27% lower than Cartesian SENSE at that acceleration factor. The 3D nature of both TPI trajectory and coil sensitivities might be responsible for the high acceleration and low noise amplification. Consequently, TPI-SENSE may have potential advantages for parallel sodium imaging.