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.     

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.     

Joint Reconstruction of Multi-contrast Images and Multi-channel Coil Sensitivities

Magnetic resonance imaging (MRI) has an important feature that it provides multiple images with different contrasts for complementary diagnostic information. However, a large amount of data is needed for multi-contrast images depiction, and thus, the scan is time-consuming. Many methods based on parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) are applied to accelerate multi-contrast MR imaging. Nevertheless, the image reconstructed by sophisticated pMRI methods contains residual aliasing artifact that degrades the quality of the image when the acceleration factor is high. Other methods based on CS always suffer the regularization parameter-selecting problem. To address these issues, a new method is presented for joint multi-contrast image reconstruction and coil sensitivity estimation. The coil sensitivities can be shared during the reconstruction due to the identity of coil sensitivity profiles of different contrast images for imaging stationary tissues. The proposed method uses the coil sensitivities as sharable information during the reconstruction to improve the reconstruction quality. As a result, the residual aliasing artifact can be effectively removed in the reconstructed multi-contrast images even if the acceleration factor is high. Besides, as there is no regularization term in the proposed method, the troublesome regularization parameter selection in the CS can also be avoided. Results from multi-contrast in vivo experiments demonstrated that multi-contrast images can be jointly reconstructed by the proposed method with effective removal of the residual aliasing artifact at a high acceleration factor.     

Optimization of sensitivity encoding with arbitrary k-space trajectories

Sensitivity encoding (SENSE) is a magnetic resonance technique that unifies gradient and receive coil encoding. SENSE reconstructs the image by solving a large, ill-conditioned inverse problem, which generally requires regularization and preconditioning. The present study suggests a simple heuristic for determining the regularization parameter. Also discussed are the use of density weighting and intensity correction as preconditioners and the role that coil sensitivity estimation has in regularization. A modification to the intensity correction is proposed for use with a phase constraint.     

Adaptive fixed-point iterative shrinkage/thresholding algorithm for MR imaging reconstruction using compressed sensing

Recently compressed sensing (CS) has been applied to under-sampling MR image reconstruction for significantly reducing signal acquisition time. To guarantee the accuracy and efficiency of the CS-based MR image reconstruction, it necessitates determining several regularization and algorithm-introduced parameters properly in practical implementations. The regularization parameter is used to control the trade-off between the sparsity of MR image and the fidelity measures of k-space data, and thus has an important effect on the reconstructed image quality. The algorithm-introduced parameters determine the global convergence rate of the algorithm itself. These parameters make CS-based MR image reconstruction a more difficult scheme than traditional Fourier-based method while implemented on a clinical MR scanner. In this paper, we propose a new approach that reveals that the regularization parameter can be taken as a threshold in a fixed-point iterative shrinkage/thresholding algorithm (FPIST) and chosen by employing minimax threshold selection method. No extra parameter is introduced by FPIST. The simulation results on synthetic and real complex-valued MRI data show that the proposed method can adaptively choose the regularization parameter and effectively achieve high reconstruction quality. The proposed method should prove very useful for practical CS-based MRI applications.     

Removal of stripe noise with spatially adaptive unidirectional total variation

Multi-detectors imaging system often suffers from the problem of the stripe noise, which greatly degrades the quality of the resulting images. To better remove stripe noise and preserve the edge and texture information, a robust destriping algorithm with spatially adaptive unidirectional total variation (SAUTV) model is introduced. The spatial information of the striping noise is detected by using the stripe indicator called difference eigenvalue, and a weighted parameter determined by the difference eigenvalue information is added to constrain the regularization strength of the UTV regularization. The proposed algorithm can effectively remove the stripe noise and preserve the edge and detailed information. Moreover, it becomes more robust with the change of the regularization parameter. Split Bregman method is utilized to efficiently solve the resulting minimization problem. Comparative results on simulated and real striped images taken with two kinds of imaging systems are reported.     

基于自适应正则化的超分辨率重建方法

传统正则化超分辨重建得到的图像往往存在过度平滑或伪信息残留的问题,结合超分辨重建模型对重建图像伪信息的产生进行了分析,针对传统方法的不足提出了基于图像区域信息自适应的正则化方法,通过图像的区域信息将图像划分为平滑区与非平滑区域,对不同区域选用不同的先验模型进行约束。同时考虑人眼的视觉感知特性,结合区域信息实现正则化参数的自适应选取。实验结果表明该方法在抑制重建图像伪信息的同时能有效保护细节,效果要优于传统方法与单一的先验模型约束,对于红外与可见光图像重建效果的提升提供了一定的理论参考。     

Blind image deconvolution with spatially adaptive total variation regularization

A blind deconvolution algorithm with spatially adaptive total variation regularization is introduced. The spatial information in different image regions is incorporated into regularization by using the edge indicator called difference eigenvalue to distinguish edges from flat areas. The proposed algorithm can effectively reduce the noise in flat regions as well as preserve the edge and detailed information. Moreover, it becomes more robust with the change of the regularization parameter. Comparative results on simulated and real degraded images are reported.     

Content-based adaptive image denoising using spatial information

The maximum a posteriori (MAP) model is widely used in image processing fields, such as denoising, deblurring, segmentation, reconstruction, and others. However, the existing methods usually employ a fixed prior item and regularization parameter for the whole image and ignore the local spatial adaptive properties. Though the non-local total variation model has shown great promise because of exploiting the correlation in the image, the computation cost and memory load are the issues. In this paper, a content-based local spatial adaptive denoising algorithm is proposed. To realize the local spatial adaptive process of the prior model and regularization parameter, first the degraded image is divided into several same-sized blocks and the Tchebichef moment is used to analyze the local spatial properties of each block. Different property prior items and regularization parameters are then applied adaptively to different properties’ blocks. To reduce the computational load in denoising process, the split Bregman iteration algorithm is employed to optimize the non-local total variation model and accelerate the speed of the image denoising. Finally, a set of experiments and performance evaluation using recent image quality assessment index are provided to assess the effectiveness of the proposed method.     

Sparsity-constrained SENSE reconstruction: An efficient implementation using a fast composite splitting algorithm

Parallel imaging and compressed sensing have been arguably the most successful and widely used techniques for fast magnetic resonance imaging (MRI). Recent studies have shown that the combination of these two techniques is useful for solving the inverse problem of recovering the image from highly under-sampled k-space data. In sparsity-enforced sensitivity encoding (SENSE) reconstruction, the optimization problem involves data fidelity (L2-norm) constraint and a number of L1-norm regularization terms (i.e. total variation or TV, and L1 norm). This makes the optimization problem difficult to solve due to the non-smooth nature of the regularization terms. In this paper, to effectively solve the sparsity-regularized SENSE reconstruction, we utilize a new optimization method, called fast composite splitting algorithm (FCSA), which was developed for compressed sensing MRI. By using a combination of variable splitting and operator splitting techniques, the FCSA algorithm decouples the large optimization problem into TV and L1 sub-problems, which are then, solved efficiently using existing fast methods. The operator splitting separates the smooth terms from the non-smooth terms, so that both terms are treated in an efficient manner. The final solution to the SENSE reconstruction is obtained by weighted solutions to the sub-problems through an iterative optimization procedure. The FCSA-based parallel MRI technique is tested on MR brain image reconstructions at various acceleration rates and with different sampling trajectories. The results indicate that, for sparsity-regularized SENSE reconstruction, the FCSA-based method is capable of achieving significant improvements in reconstruction accuracy when compared with the state-of-the-art reconstruction method.     

The quantification of structure-borne transmission paths by inverse methods. Part 2: Use of regularization techniques

The inversion of an ill-conditioned matrix of measured data lies at the heart of procedures for the quantification of structure-borne sources and transmission paths. In an earlier paper the use of over-determination, singular value decomposition and the rejection of small singular values was discussed. In the present paper alternative techniques for regularizing the matrix inversion are considered. Such techniques have been used in the field of digital image processing and more recently in relation to nearfield acoustic holography. The application to structure-borne sound transmission involves matrices, which vary much more with frequency and from one element to another. In this study Tikhonov regularization is used with the ordinary cross-validation method for selecting the regularization parameter. An iterative inversion technique is also studied. Here a form of cross-validation is developed allowing an optimum value of the iteration parameter to be selected. Simulations are carried out using a rectangular plate structure to assess the relative merits of these techniques. Experiments are also performed to validate the results. Both techniques are found to give considerably improved results compared to singular value rejection.     

A two-compartment gel phantom for optimization and quality assurance in clinical BOLD fMRI

Clinical applications of blood oxygen level-dependent (BOLD) functional magnetic resonance imaging (fMRI) depend heavily on robust paradigms, imaging methods and analysis procedures. In this work, as a means to optimize and perform quality assurance of the entire imaging and analysis chain, a phantom that provides a well known and reproducible signal change similar to a block type fMRI experiment is presented. It consists of two gel compartments with slightly different T2 that dynamically enter and leave the imaged volume. The homogeneous gel in combination with a cylindrical geometry results in a well-defined T*2 difference causing a signal difference between the two compartments in T*2-weighted MR images. From time series data obtained with the phantom, maps of percent signal change (PSC) and t-values are calculated. As an example of image parameter optimisation, the phantom is demonstrated to be useful for accurate determination of the influence of echo time (TE) on BOLD fMRI results, taking the t-value as a measure of sensitivity. In addition, the phantom is proposed as a tool for quality assurance (QA) since reproducible time series and t-maps are obtained in a series of independent repeat experiments. The phantom is relatively simple to build and can therefore be used by any clinical fMRI center.     

Accelerated 3D Coronary Vessel Wall MR Imaging Based on Compressed Sensing with a Block-Weighted Total Variation Regularization

Coronary vessel wall magnetic resonance (MR) imaging is important for heart disease diagnosis but often suffers long scan time. Compressed sensing (CS) has been previously used to accelerate MR imaging by reconstructing an MR image from undersampled k-space data using a regularization framework. However, the widely used regularizations in the current CS methods often lead to smoothing effects and thus are unable to reconstruct the coronary vessel walls with sufficient resolution. To address this issue, a novel block-weighted total variation regularization is presented to accelerate the coronary vessel wall MR imaging. The proposed regularization divides the image into two parts: a region-of-interest (ROI) which contains the coronary vessel wall, and the other region with less concerned features. Different penalty weights are given to the two regions. As a result, the small details within ROI do not suffer from over-smoothing while the noise outside the ROI can be significantly suppressed. Results with both numerical simulations and in vivo experiments demonstrated that the proposed method can reconstruct the coronary vessel wall from undersampled k-space data with higher qualities than the conventional CS with the total variation or the edge-preserved total variation.     

Low-field magnetic resonance imaging using multiplicative regularization

In this paper we present a magnetic resonance imaging (MRI) technique that is based on multiplicative regularization. Instead of adding a regularizing objective function to a data fidelity term, we multiply by such a regularizing function. By following this approach, no regularization parameter needs to be determined for each new data set that is acquired. Reconstructions are obtained by iteratively updating the images using short-term conjugate gradient-type update formulas and Polak-Ribière update directions. We show that the algorithm can be used as an image reconstruction algorithm and as a denoising algorithm. We illustrate the performance of the algorithm on two-dimensional simulated low-field MR data that is corrupted by noise and on three-dimensional measured data obtained from a low-field MR scanner. Our reconstruction results show that the algorithm effectively suppresses noise and produces accurate reconstructions even for low-field MR signals with a low signal-to-noise ratio.     

A four-element phased array coil for high resolution and parallel MR imaging of the knee

A four-element phased array coil for MR imaging of the knee was designed, built and tested for clinical use at 1.5 Tesla. In routine imaging, it provides over twofold increase in signal-to-noise (SNR) compared to two commercially available knee coils, and supports higher spatial image resolution. The phased array knee coil was also tested for its compatibility with parallel MR imaging that reduces imaging time by several folds over conventional MR technique. Results obtained using SiMultaneous Acquisition of Spatial Harmonics (SMASH) technique shows that our phased array knee coil can be used with parallel MR imaging. These improvements may enhance knee diagnosis with higher image quality and reduced scan time.     

基于空间自适应非凸正则项全变差相干斑噪声抑制

全变差正则化方法是相干斑噪声抑制研究的热点.非凸正则项能够更好地保持图像的边缘、纹理细节信息;空间自适应正则化参数可以根据像素点所在的区域,合理地控制噪声抑制程度,从而提高噪声抑制效果.本文结合非凸正则项和空间自适应正则化参数提出了一种新的全变差相干斑噪声抑制模型,并且给出了一种模型求解的数值算法.数值试验结果表明该模型能够获得更好的相干斑噪声抑制效果.     

Compressed MRI reconstruction exploiting a rotation-invariant total variation discretization

Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration.     

Hopfield neural network-based image restoration with adaptive mixed-norm regularization

To overcome the shortcomings of traditional image restoration model and total variation image restoration model, we propose a novel Hopfield neural network-based image restoration algorithm with adaptive mixed-norm regularization. The new error function of image restoration combines the L2-norm and L1- norm regularization types. A method of calculating the adaptive scale control parameter is introduced. Experimental results demonstrate that the proposed algorithm is better than other algorithms with single norm regularization in the improvement of signal-to-noise ratio （ISNR） and vision effect.     

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.