Application of perceptual difference model on regularization techniques of parallel MR imaging

Parallel magnetic resonance imaging through sensitivity encoding using multiple receiver coils has emerged as an effective tool to reduce imaging time or to improve image SNR. The quality of reconstructed images is limited by the inaccurate estimation of the sensitivity map, noise in the acquired k-space data and the ill-conditioned nature of the coefficient matrix. Tikhonov regularization is a popular method to reduce or eliminate the ill-conditioned nature of the problem. In this approach, selection of the regularization map and the regularization parameter is very important. Perceptual difference model (PDM) is a quantitative image quality evaluation tool that has been successfully applied to varieties of MR applications. High correlation between the human rating and PDM score shows that PDM should be suitable to evaluate image quality in parallel MR imaging. By applying PDM, we compared four methods of selecting the regularization map and four methods of selecting the regularization parameter. We found that a regularization map obtained using generalized series (GS) together with a spatially adaptive regularization parameter gave the best reconstructions. PDM was also used as an objective function for optimizing two important parameters in the spatially adaptive method. We conclude that PDM enables one to do comprehensive experiments and that it is an effective tool for designing and optimizing reconstruction methods in parallel MR imaging.     

Estimation and application of spatially variable noise fields in diffusion tensor imaging

Optimal interpretation of magnetic resonance image content often requires an estimate of the underlying image noise, which is typically realized as a spatially invariant estimate of the noise distribution. This is not an ideal practice in diffusion tensor imaging because the noise distribution is usually spatially varying due to the use of fast imaging and noise suppression techniques. A new estimation approach for spatially varying noise fields (NFs) is proposed in this article. The approach is based on a noise invariance property in scenarios in which more than one image, each with potentially different signal levels, is acquired on each slice, as in diffusion-weighted MRI. This technique leads to improved NF estimates in simulations, phantom experiments and in vivo studies when compared to traditional NF estimators that use regional variability or background intensity histograms. The proposed method reduces the NF estimation error by a factor of 100 in simulations, shows a strong linear correlation (R²=0.99) between theoretical and estimated noise changes in phantoms and demonstrates consistent (<5% variability) NF estimates in vivo. The advantages of spatially varying NF estimation are demonstrated for power analysis, outlier detection and tensor estimation.     

Generalized total variation-based MRI Rician denoising model with spatially adaptive regularization parameters

Magnetic resonance imaging (MRI) is an outstanding medical imaging modality but the quality often suffers from noise pollution during image acquisition and transmission. The purpose of this study is to enhance image quality using feature-preserving denoising method. In current literature, most existing MRI denoising methods did not simultaneously take the global image prior and local image features into account. The denoising method proposed in this paper is implemented based on an assumption of spatially varying Rician noise map. A two-step wavelet-domain estimation method is developed to extract the noise map. Following a Bayesian modeling approach, a generalized total variation-based MRI denoising model is proposed based on global hyper-Laplacian prior and Rician noise assumption. The proposed model has the properties of backward diffusion in local normal directions and forward diffusion in local tangent directions. To further improve the denoising performance, a local variance estimator-based method is introduced to calculate the spatially adaptive regularization parameters related to local image features and spatially varying noise map. The main benefit of the proposed method is that it takes full advantage of the global MR image prior and local image features. Numerous experiments have been conducted on both synthetic and real MR data sets to compare our proposed model with some state-of-the-art denoising methods. The experimental results have demonstrated the superior performance of our proposed model in terms of quantitative and qualitative image quality evaluations.     

A dual image approach for bias field correction in magnetic resonance imaging

In this paper, we propose a dual image approach to correcting intensity inhomogeneities for MR images acquired using surface coils. Previous methods are usually not satisfactory due to restricted application domains, considerable human interactions, or some undesirable artifacts. The proposed algorithm provides nice correction results for a variety of surface-coil MR images. It is accomplished by using an additional body-coil MR image of a smaller size captured at the same position as that of the surface-coil image to facilitate the estimation of the bias field function. The correction algorithm consists of aligning the surface-coil image with the body-coil image and fitting a spline surface from a sparse set of data points for the associated bias field function. Experiments on some real images show satisfactory correction results by using the proposed algorithm.     

MRI denoising using progressively distribution-based neural network

Magnetic Resonance (MR) images often suffer from noise pollution during image acquisition and transmission, which limits the accuracy of quantitative measurements from the data. Noise in magnitude MR images is usually governed by Rician distribution, due to the existence of uncorrelated Gaussian noise with zero-mean and equal variance in both the real and imaginary parts of the complex K-space data. Different from the existing MRI denoising methods that utilizing the spatial neighbor information around the pixels or patches, this work turns to capture the pixel-level distribution information by means of supervised network learning. A progressive network learning strategy is proposed via fitting the distribution of pixel-level and feature-level intensities. The proposed network consists of two residual blocks, one is used for fitting pixel domain without batch normalization layer and another one is applied for matching feature domain with batch normalization layer. Experimental results under synthetic, complex-valued and clinical MR brain images demonstrate great potential of the proposed network with substantially improved quantitative measures and visual inspections.     

GPU based parallel framework for receiver coil sensitivity estimation in SENSE reconstruction

Magnetic Resonance Imaging (MRI) uses non-ionizing radiations and is safer as compared to CT and X-ray imaging. MRI is broadly used around the globe for medical diagnostics. One main limitation of MRI is its long data acquisition time. Parallel MRI (pMRI) was introduced in late 1990's to reduce the MRI data acquisition time. In pMRI, data is acquired by under-sampling the Phase Encoding (PE) steps which introduces aliasing artefacts in the MR images. SENSitivity Encoding (SENSE) is a pMRI based method that reconstructs fully sampled MR image from the acquired under-sampled data using the sensitivity information of receiver coils. In SENSE, precise estimation of the receiver coil sensitivity maps is vital to obtain good quality images. Eigen-value method (a recently proposed method in literature for the estimation of receiver coil sensitivity information) does not require a pre-scan image unlike other conventional methods of sensitivity estimation. However, Eigen-value method is computationally intensive and takes a significant amount of time to estimate the receiver coil sensitivity maps. This work proposes a parallel framework for Eigen-value method of receiver coil sensitivity estimation that exploits its inherent parallelism using Graphics Processing Units (GPUs). We evaluated the performance of the proposed algorithm on in-vivo and simulated MRI datasets (i.e. human head and simulated phantom datasets) with Peak Signal-to-Noise Ratio (PSNR) and Artefact Power (AP) as evaluation metrics. The results show that the proposed GPU implementation reduces the execution time of Eigen-value method of receiver coil sensitivity estimation (providing up to 30 times speed up in our experiments) without degrading the quality of the reconstructed image.     

A wavelet-based method for improving signal-to-noise ratio and contrast in MR images

Magnetic resonance (MR) images acquired with fast measurement often display poor signal-to-noise ratio (SNR) and contrast. With the advent of high temporal resolution imaging, there is a growing need to remove these noise artifacts. The noise in magnitude MR images is signal-dependent (Rician), whereas most de-noising algorithms assume additive Gaussian (white) noise. However, the Rician distribution only looks Gaussian at high SNR. Some recent work by Nowak employs a wavelet-based method for de-noising the square magnitude images, and explicitly takes into account the Rician nature of the noise distribution. In this article, we apply a wavelet de-noising algorithm directly to the complex image obtained as the Fourier transform of the raw k-space two-channel (real and imaginary) data. By retaining the complex image, we are able to de-noise not only magnitude images but also phase images. A multiscale (complex) wavelet-domain Wiener-type filter is derived. The algorithm preserves edges better when the Haar wavelet rather than smoother wavelets, such as those of Daubechies, are used. The algorithm was tested on a simulated image to which various levels of noise were added, on several EPI image sequences, each of different SNR, and on a pair of low SNR MR micro-images acquired using gradient echo and spin echo sequences. For the simulated data, the original image could be well recovered even for high values of noise (SNR approximately 0 dB), suggesting that the present algorithm may provide better recovery of the contrast than Nowak's method. The mean-square error, bias, and variance are computed for the simulated images. Over a range of amounts of added noise, the present method is shown to give smaller bias than when using a soft threshold, and smaller variance than a hard threshold; in general, it provides a better bias-variance balance than either hard or soft threshold methods. For the EPI (MR) images, contrast improvements of up to 8% (for SNR = 33 dB) were found. In general, the improvement in contrast was greater the lower the original SNR, for example, up to 50% contrast improvement for SNR of about 20 dB in micro-imaging. Applications of the algorithm to the segmentation of medical images, to micro-imaging and angiography (where the correct preservation of phase is important for flow encoding to be possible), as well as to de-noising time series of functional MR images, are discussed.     

Channel-combination method for phase-based |B1+| mapping techniques

PurposeThe aim of this study was to propose a channel combination method for |B₁⁺| mapping methods using phase difference to reconstruct |B₁⁺| map.Theory and methodsPhase-based |B₁⁺| mapping methods commonly consider the phase difference of two scans to measure |B₁⁺|. Multiple receiver coils acquire a number of images and the phase difference at each channel is theoretically the same in the absence of noise. Affected by noise, phase difference is approximately governed by Gaussian distribution. Considering data from all channels as samples, estimation can be achieved by maximum likelihood method. With this method, all phase differences at each channel are combined into one. In this study, the proposed method is applied with Bloch-Siegert shift |B₁⁺| mapping method. Simulations are performed to illustrate the phase difference distribution and demonstrate the feasibility and facility of the proposed method. Phantom and vivo experiments are carried out at 1.5 T scanner equipped with 8-channel receiver coil. In all experiments, the proposed method is compared with weighted averaging (WA) method.ResultsSimulations revealed appropriateness of approximating the distribution of phase difference to Gaussian distribution. Compared with WA method, the proposed method reduces errors of |B₁⁺| calculation. Phantom and vivo experiments provide further validation.ConclusionConsidering phase noise distribution, the proposed method achieves channel combination by finding the estimation from data acquired by multiple receivers coil. The proposed method reduces |B₁⁺| reconstruction errors caused by noise.     

基于神经网络和小波变换的MRI图像去噪方法

过去10年中,小波变换在图像去噪中取得了很大的成功.人们提出了多种适用于小波去噪的阈值方法,而这些方法就是希望能够正确地反映有噪声小波系数与无噪声小波系数之间的映射关系.基于这种想法,我们提出一种在小波域中利用神经网络寻找这种映射关系的图像去噪新方法.我们把该方法应用于不同噪声分布的磁共振图像的去噪,取得了良好的效果.     

A multi-scale residual network for accelerated radial MR parameter mapping

A deep learning MR parameter mapping framework which combines accelerated radial data acquisition with a multi-scale residual network (MS-ResNet) for image reconstruction is proposed. The proposed supervised learning strategy uses input image patches from multi-contrast images with radial undersampling artifacts and target image patches from artifact-free multi-contrast images. Subspace filtering is used during pre-processing to denoise input patches. For each anatomy and relaxation parameter, an individual network is trained. in vivo T₁ mapping results are obtained on brain and abdomen datasets and in vivo T₂ mapping results are obtained on brain and knee datasets. Quantitative results for the T₂ mapping of the knee show that MS-ResNet trained using either fully sampled or undersampled data outperforms conventional model-based compressed sensing methods. This is significant because obtaining fully sampled training data is not possible in many applications. in vivo brain and abdomen results for T₁ mapping and in vivo brain results for T₂ mapping demonstrate that MS-ResNet yields contrast-weighted images and parameter maps that are comparable to those achieved by model-based iterative methods while offering two orders of magnitude reduction in reconstruction times. The proposed approach enables recovery of high-quality contrast-weighted images and parameter maps from highly accelerated radial data acquisitions. The rapid image reconstructions enabled by the proposed approach makes it a good candidate for routine clinical use.     

A novel, fast entropy-minimization algorithm for bias field correction in MR images

A novel, fast entropy-minimization algorithm for bias field correction in magnetic resonance (MR) images is suggested to correct the intensity inhomogeneity degradation of MR images that has become an increasing problem with the use of phased-array coils. Four important modifications were made to the conventional algorithm: (a) implementation of a modified two-step sampling strategy for stacked 2D image data sets, which included reducing the size of the measured image on each slice with a simple averaging method without changing the number of slices and then using a binary mask generated by a histogram threshold method to define the sampled voxels in the reduced image; (b) improvement of the efficiency of the correction function by using a Legendre polynomial as an orthogonal base function polynomial; (c) use of a nonparametric Parzen window estimator with a Gaussian kernel to calculate the probability density function and Shannon entropy directly from the image data; and (d) performing entropy minimization with a conjugate gradient method. Results showed that this algorithm could correct different types of MR images from different types of coils acquired at different field strengths very efficiently and with decreased computational load.     

Parametric and non-parametric statistical analysis of DT-MRI data

In this work parametric and non-parametric statistical methods are proposed to analyze Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data. A Multivariate Normal Distribution is proposed as a parametric statistical model of diffusion tensor data when magnitude MR images contain no artifacts other than Johnson noise. We test this model using Monte Carlo (MC) simulations of DT-MRI experiments. The non-parametric approach proposed here is an implementation of bootstrap methodology that we call the DT-MRI bootstrap. It is used to estimate an empirical probability distribution of experimental DT-MRI data, and to perform hypothesis tests on them. The DT-MRI bootstrap is also used to obtain various statistics of DT-MRI parameters within a single voxel, and within a region of interest (ROI); we also use the bootstrap to study the intrinsic variability of these parameters in the ROI, independent of background noise. We evaluate the DT-MRI bootstrap using MC simulations and apply it to DT-MRI data acquired on human brain in vivo, and on a phantom with uniform diffusion properties.     

Methods for quantitative image quality evaluation of MRI parallel reconstructions: detection and perceptual difference model

Many reconstruction algorithms are being proposed for parallel magnetic resonance imaging (MRI), which uses multiple coils and subsampled k-space data, and a quantitative method for comparison of algorithms is sorely needed. On such images, we compared three methods for quantitative image quality evaluation: human detection, computer detection model and a computer perceptual difference model (PDM). One-quarter sampling and three different reconstruction methods were investigated: a regularization method developed by Ying et al., a simplified regularization method and an iterative method proposed by Pruessmann et al. Images obtained from a full complement of k-space data were also included as reference images. Detection studies were performed using a simulated dark tumor added on MR images of fresh bovine liver. Human detection depended strongly on reconstruction methods used, with the two regularization methods achieving better performance than the iterative method. Images were also evaluated using detection by a channelized Hotelling observer model and by PDM scores. Both predicted the same trends as observed from human detection. We are encouraged that PDM gives trends similar to that for human detection studies. Its ease of use and applicability to a variety of MRI situations make it attractive for evaluating image quality in a variety of MR studies.     

An anisotropic images segmentation and bias correction method

Intensity inhomogeneities cause considerable difficulty in the quantitative analysis of magnetic resonance (MR) images. Thus, bias field correction is a necessary step before quantitative analysis of MR data can be undertaken. This paper presents an anisotropic approach to bias correction and segmentation for images with intensity inhomogeneities and noise. Intensity-based methods are usually applied to estimate the bias field; however, most of them only concern the intensity information. When the images have noise or slender topological objects, these methods cannot obtain accurate results or bias fields. We use structure information to construct an anisotropic Gibbs field and combine the anisotropic Gibbs field with the Bayesian framework to segment images while estimating the bias fields. Our method is able to capture bias of quite general profiles. Moreover, it is robust to noise and slender topological objects. The proposed method has been used for images of various modalities with promising results.     

Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation.

New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.     

Rician noise reduction in magnetic resonance images using adaptive non-local mean and guided image filtering

This paper proposes a Rician noise reduction method for magnetic resonance (MR) images. The proposed method is based on adaptive non-local mean and guided image filtering techniques. In the first phase, a guidance image is obtained from the noisy image through an adaptive non-local mean filter. Sobel operators are applied to compute the strength of edges which is further used to control the spread of the kernel in non-local mean filtering. In the second phase, the noisy and the guidance images are provided to the guided image filter as input to restore the noise-free image. The improved performance of the proposed method is investigated using the simulated and real data sets of MR images. Its performance is also compared with the previously proposed state-of-the art methods. Comparative analysis demonstrates the superiority of the proposed scheme over the existing approaches.     

基于经验模态分解的高光谱遥感数据去噪方法

经验模态分解(EMD)是一种新的时频分析方法,经EMD分解后的各个固有模态函数(IMF)突出了原始信号的局部特征,从而可以区分噪声和有用信号。基于此,结合高光谱遥感数据的光谱变化特征,提出了一种基于经验模态分解的高光谱遥感数据去噪方法。通过对理论数据的实验表明,数据中的噪声无论是高斯分布还是均匀分布,数据经EMD分解后,噪声都主要集中在前几个特定的IMF,对相应的IMF进行滤波处理后并与其他IMF分量进行重构就可得到去噪信号,与小波去噪结果相比较,这种方法效果更好。最后把该去噪方法应用于野外实测的油膜高光谱数据去噪,实验结果表明,该方法能准确、有效地去除高光谱遥感数据的噪声。     

Non-locally regularized segmentation of multiple sclerosis lesion from multi-channel MRI data

Segmentation of multiple sclerosis (MS) lesion is important for many neuroimaging studies. In this paper, we propose a novel algorithm for automatic segmentation of MS lesions from multi-channel MR images (T1W, T2W and FLAIR images). The proposed method is an extension of Li et al.'s algorithm in [1], which only segments the normal tissues from T1W images. The proposed method is aimed to segment MS lesions, while normal tissues are also segmented and bias field is estimated to handle intensity inhomogeneities in the images. Another contribution of this paper is the introduction of a nonlocal means technique to achieve spatially regularized segmentation, which overcomes the influence of noise. Experimental results have demonstrated the effectiveness and advantages of the proposed algorithm.     

Synthetic T1-weighted brain image generation with incorporated coil intensity correction using DESPOT1

The increased use of phased-array and surface coils in magnetic resonance imaging, the push toward increased field strength and the need for standardized imaging across multiple sites during clinical trials have resulted in the need for methods that can ensure consistency of intensity both within the image and across multiple subjects/sites. Here, we describe a means of addressing these concerns through an extension of the rapid T(1) mapping technique - driven equilibrium single-pulse observation of T(1). The effectiveness of the proposed approach was evaluated using human brain T(1) maps acquired at 1.5 T with a multichannel phased-array coil. Corrected "synthetic" T(1)-weighted images were reconstructed by substituting the T(1) values back into the governing signal intensity equation while assuming a constant value for the equilibrium magnetization. To demonstrate signal normalization across a longitudinal study, we calculated synthetic T(1)-weighted images from data acquired from the same healthy subject at four different time points. Signal intensity profiles between the acquired and synthetic images were compared to determine the improvements with our proposed approach. Following correction, the images demonstrate obvious qualitative improvement with increased signal uniformity across the image. Near-perfect signal normalization was also observed across the longitudinal study, allowing direct comparison between the images. In addition, we observe an increase in contrast-to-noise ratio (compared with regular T(1)-weighted images) for synthetic images created, assuming uniform proton density throughout the volume. The proposed approach permits rapid correction for signal intensity inhomogeneity without significantly lengthening exam time or reducing image signal-to-noise ratio. This technique also provides a robust method for signal normalization, which is useful in multicenter longitudinal MR studies of disease progression, and allows the user to reconstruct T(1)-weighted images with arbitrary T(1) weighting.     

Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics

The statistical properties of background noise such as its standard deviation and mean value are frequently used to estimate the original noise level of the acquired data. This requires the knowledge of the statistical intensity distribution of the background signal, that is, the probability density of the occurrence of a certain signal intensity. The influence of many new MRI techniques and, in particular, of various parallel-imaging methods on the noise statistics has neither been rigorously investigated nor experimentally demonstrated yet. In this study, the statistical distribution of background noise was analyzed for MR acquisitions with a single-channel and a 32-channel coil, with sum-of-squares (SoS) and spatial-matched-filter (SMF) data combination, with and without parallel imaging using k-space and image-domain algorithms, with real-part and conventional magnitude reconstruction and with several reconstruction filters. Depending on the imaging technique, the background noise could be described by a Rayleigh distribution, a noncentral chi-distribution or the positive half of a Gaussian distribution. In particular, the noise characteristics of SoS-reconstructed multichannel acquisitions (with k-space-based parallel imaging or without parallel imaging) differ substantially from those with image-domain parallel imaging or SMF combination. These effects must be taken into account if mean values or standard deviations of background noise are employed for data analysis such as determination of local noise levels. Assuming a Rayleigh distribution as in conventional MR images or a noncentral chi-distribution for all multichannel acquisitions is invalid in general and may lead to erroneous estimates of the signal-to-noise ratio or the contrast-to-noise ratio.