Exploiting the wavelet structure in compressed sensing MRI

Sparsity has been widely utilized in magnetic resonance imaging (MRI) to reduce k-space sampling. According to structured sparsity theories, fewer measurements are required for tree sparse data than the data only with standard sparsity. Intuitively, more accurate image reconstruction can be achieved with the same number of measurements by exploiting the wavelet tree structure in MRI. A novel algorithm is proposed in this article to reconstruct MR images from undersampled k-space data. In contrast to conventional compressed sensing MRI (CS-MRI) that only relies on the sparsity of MR images in wavelet or gradient domain, we exploit the wavelet tree structure to improve CS-MRI. This tree-based CS-MRI problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved by an iterative scheme. Simulations and in vivo experiments demonstrate the significant improvement of the proposed method compared to conventional CS-MRI algorithms, and the feasibleness on MR data compared to existing tree-based imaging algorithms.     

A Robust Point Spread Function Estimation for Out-of-Focus Blurred and Noisy Images Based on a Distribution of Gradient Vectors on the Polar Plane

The estimation of the point spread function (PSF) is a very important and indispensable task for practical image restoration. Various PSF estimation algorithms have been developed, especially for the out-of-focus blur. However, a majority of them are useless in an extremely noisy environment. This paper describes a new robust PSF estimation algorithm based on a distribution of gradient vectors on the logarithmic amplitude spectrum mapped to the polar plane. The proposed algorithm can estimate the out-of-focus PSF accurately and robustly, even for an image highly corrupted by noise. The effectiveness of the proposed algorithm is verified by applying it to the PSF estimation for out-of-focus blurred and noisy images.     

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.’     

基于哈特曼-夏克波前传感器的模糊图像复原方法

离焦模糊图像的清晰度较低,因此必须对其进行复原。传统方法通常采用圆盘或高斯函数来近似离焦造成的点扩散函数,复原效果不够理想。为此,提出利用哈特曼-夏克波前传感器探测离焦波前,根据所得波前计算光学系统的点扩散函数,并采用Richardson-Lucy算法对模糊图像进行复原。搭建了实验用的光学系统,采集了离焦模糊图像以及相应的波前信息,获得了清晰的复原图像,并利用客观图像评价方法对退化图像和复原图像进行了评价,同时与传统方法得到的复原图像进行了比较。实验结果表明,该方法能精确重建点扩散函数,有效提高图像的质量。     

Resolution enhancement in MRI

We consider the problem of super-resolution reconstruction (SRR) in MRI. Subpixel-shifted MR images were taken in several fields of view (FOVs) to reconstruct a high-resolution image. A novel algorithm is presented. The algorithm can be applied locally and guarantees perfect reconstruction in the absence of noise. Results that demonstrate resolution improvement are given for phantom studies (mathematical model) as well as for MRI studies of a phantom carried out with a GE clinical scanner. The method raises questions that are discussed in the last section of the paper. Open questions should be answered in order to apply this method for clinical purposes.     

Singular Value Decomposition Using Jacobi Algorithm in pMRI and CS

Parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) have been recently used to accelerate data acquisition process in MRI. Matrix inversion (for rectangular matrices) is required to reconstruct images from the acquired under-sampled data in various pMRI algorithms (e.g., SENSE, GRAPPA) and CS. Singular value decomposition (SVD) provides a mechanism to accurately estimate pseudo-inverse of a rectangular matrix. This work proposes the use of Jacobi SVD algorithm to reconstruct MR images from the acquired under-sampled data both in pMRI and in CS. The use of Jacobi SVD algorithm is proposed in advance MRI reconstruction algorithms, including SENSE, GRAPPA, and low-rank matrix estimation in L + S model for matrix inversion and estimation of singular values. Experiments are performed on 1.5T human head MRI data and 3T cardiac perfusion MRI data for different acceleration factors. The reconstructed images are analyzed using artifact power and central line profiles. The results show that the Jacobi SVD algorithm successfully reconstructs the images in SENSE, GRAPPA, and L + S algorithms. The benefit of using Jacobi SVD algorithm for MRI image reconstruction is its suitability for parallel computation on GPUs, which may be a great help in reducing the image reconstruction time.     

单幅模糊图像点扩散函数估计的梯度倒谱分析方法研究

针对单幅图像复原算法引入先验信息导致复杂度高、运算效率低的问题, 提出了单幅模糊图像点扩散函数估计的梯度倒谱分析方法. 首先给出了单幅模糊图像梯度倒谱估计其点扩散函数的基本原理, 利用相位恢复策略复原了二维点扩散函数相位信息, 实现了点扩散函数的快速估计; 其次, 为鉴别点扩散函数估计精度, 建立了图像梯度保真约束的全变分正则化图像复原模型, 并采用快速稳定收敛的交替方向策略优化能量函数; 通过对仿真和实拍单幅模糊图像进行的测试实验结果表明, 该方法快速准确地估计出点扩散函数, 克服了传统复原算法收敛速度慢的缺点, 有效抑制了振铃效应、保护了边缘信息, 为大尺寸单幅图像复原的工程化实现提供了理论和技术基础. 关键词： 图像复原 点扩散函数 梯度倒谱分析 全变分     

基于随机点扩散函数的多帧湍流退化图像自适应复原方法

针对湍流退化图像随机性的问题,提出了一种基于随机点扩散函数的多帧湍流退化图像自适应复原方法。首先介绍了随机点扩散函数的图像退化模型,并分析了点扩散函数随机性对图像复原造成的影响,建立了基于随机点扩散函数的多帧图像退化模型。在此基础上,建立了基于多帧退化图像的全变分复原模型,利用前向后向算子分裂法对模型进行求解,提高了算法的运算效率。然后,提出了一种新的自适应正则化参数选取方法,该方法利用全变分复原模型的目标函数计算正则化参数,当正则化参数收敛时,复原图像的峰值信噪比达到最大值,因此利用目标函数的相对差值作为自适应算法迭代终止的条件,可以获得最佳复原效果。最后通过实验分析,算法中退化图像的帧数应不大于10帧。实验结果表明:当取10帧退化图像时,AFBS算法运算时间与单帧的FBS算法相当,信噪比增益为1.4 dB。本文算法对图像噪声有明显的抑制作用,对湍流退化图像可以获得较好的复原效果。     

Magnetic resonance imaging segmentation techniques using batch-type learning vector quantization algorithms

In this article, we propose batch-type learning vector quantization (LVQ) segmentation techniques for the magnetic resonance (MR) images. Magnetic resonance imaging (MRI) segmentation is an important technique to differentiate abnormal and normal tissues in MR image data. The proposed LVQ segmentation techniques are compared with the generalized Kohonen's competitive learning (GKCL) methods, which were proposed by Lin et al. [Magn Reson Imaging 21 (2003) 863-870]. Three MRI data sets of real cases are used in this article. The first case is from a 2-year-old girl who was diagnosed with retinoblastoma in her left eye. The second case is from a 55-year-old woman who developed complete left side oculomotor palsy immediately after a motor vehicle accident. The third case is from an 84-year-old man who was diagnosed with Alzheimer disease (AD). Our comparisons are based on sensitivity of algorithm parameters, the quality of MRI segmentation with the contrast-to-noise ratio and the accuracy of the region of interest tissue. Overall, the segmentation results from batch-type LVQ algorithms present good accuracy and quality of the segmentation images, and also flexibility of algorithm parameters in all the comparison consequences. The results support that the proposed batch-type LVQ algorithms are better than the previous GKCL algorithms. Specifically, the proposed fuzzy-soft LVQ algorithm works well in segmenting AD MRI data set to accurately measure the hippocampus volume in AD MR images.     

Dynamic MRI reconstruction from highly undersampled (k,t)-space data using weighted Schatten p-norm regularizer of tensor

Combination of the low-rankness and sparsity has been successfully used to reconstruct desired dynamic magnetic resonance image (MRI) from highly-undersampled (k, t)-space data. However, nuclear norm, as a convex relaxation of the rank function, can cause the solution deviating from the original solution of low-rank problem. Moreover, equally treating different rank component is not flexible to deal with real applications. In this paper, an efficient reconstruction model is proposed to efficiently reconstruct dynamic MRI. First, we treat dynamic MRI as a 3rd-order tensor, and formulate the low-rankness via non-convex Schatten p-norm of matrices unfolded from the tensor. Secondly, we assign different weight for each rank component in Schatten p-norm. Furthermore, we combine the proposed weighted Schatten p-norm of a tensor as low-rank regularizer, and spatiotemporal total variation as sparse regularizer to formulate the reconstruction model for dynamic MRI. Thirdly, to efficiently solve the formulated reconstruction model, we derive an algorithm based on Bregman iterations with alternating direction multiplier. Over two public data sets of dynamic MRI, experiments demonstrate that the proposed method achieves much better quality.     

Single image motion deblurring: An accurate PSF estimation and ringing reduction

In this paper we have proposed a single image motion deblurring algorithm that is based on a novel use of dual Fourier spectrum combined with bit plane slicing algorithm and Radon transform (RT) for accurate estimation of PSF parameters such as, blur length and blur angle. Even after very accurate PSF estimation, the deconvolution algorithms tend to introduce ringing artifacts at boundaries and near strong edges. To prevent this post deconvolution effect, a post processing method is also proposed in the framework of traditional Richardson–Lucy (RL) deconvolution algorithm. Experimental results evaluated on the basis of both qualitative and quantitative (PSNR, SSIM) metrics, verified on the dataset of both grayscale and color blurred images show that the proposed method outperforms the existing algorithms for removal of uniform blur. A comparison with state-of-the-art methods proves the usefulness of the proposed algorithm for deblurring real-life images/photographs.     

基于指数律分布的图像快速盲复原算法

针对现有图像盲复原迭代算法多存在耗时较长和难以保证收敛性等问题,提出一种改进的快速算法.首先根据指数律重建原始图像的频谱,然后利用原始图像和降质图像的频谱关系,采用多方向综合估计方法得到点扩散函数.多方向综合估计方法可降低估计误差,增加算法的稳定性.最后利用得到的点扩散函数和维纳滤波法进行图像重建.与现有算法的对比实验结果表明,针对适合大量成像系统的G类点扩散函数,本算法可以得到更准确的点扩散函数估计,且降低了振铃效应的影响,取得更好的图像复原效果.     

旋转不变的非局域均值算法在磁共振图像去噪中的应用

磁共振成像（MRI）实验时常采用多次扫描累加平均提高图像信噪比（SNR）,但当扫描过程中运动引起图像变形时,简单地累加平均就无法奏效.为此,本研究组曾提出一种匹配加权平均方法（MWA）提高图像的信噪比.在此基础上,该文提出一种旋转不变的非局域均值算法（RINLM）,即选取圆形邻域区域并将其划分为一系列以中心像素为圆心的等面积圆环,再计算模式的相似性.RINLM算法可以更好地利用图像中旋转的冗余信息、找到更多的相似结构,提高算法的去噪性能.我们把该方法应用于低信噪比图像序列的平均和去噪中,可以更好地处理旋转的局部运动.与非局域均值算法（NLM）相比,RINLM算法可以进一步提高图像的信噪比;与MWA方法相比,其与RINLM算法的结合可以进一步提高磁共振图像序列信噪比,更好的保持图像边缘信息.     

Parametric blur estimation for blind restoration of atmospherically degraded images: Class G

Iterative methods are typically utilized for blind image restoration (BIR); however, they are relatively slow, uncertain, and occasionally ill-behaved. This study presents a non-iterative algorithm to estimate the parameters of point spread functions (PSFs), particularly, Class G. We propose a curve model to approximate the normalized spectrum amplitude of the original image in accordance with the decay law of the natural image spectrum. The blur PSF is estimated by comparing the original image spectrum with the degraded one. Then, the image is restored by applying the estimated PSF and the Wiener filter. Experimental results demonstrate that the proposed algorithm can obtain a more accurate PSF and reduce ringing artifacts compared with the existing algorithms. The quality of the restored images is enhanced significantly.     

A general strategy for anisotropic diffusion in MR image denoising and enhancement

Anisotropic diffusion (AD) has proven to be very effective in the denoising of magnetic resonance (MR) images. The result of AD filtering is highly dependent on several parameters, especially the conductance parameter. However, there is no automatic method to select the optimal parameter values. This paper presents a general strategy for AD filtering of MR images using an automatic parameter selection method. The basic idea is to estimate the parameters through an optimization step on a synthetic image model, which is different from traditional analytical methods. This approach can be easily applied to more sophisticated diffusion models for better denoising results. We conducted a systematic study of parameter selection for the AD filter, including the dynamic parameter decreasing rate, the parameter selection range for different noise levels and the influence of the image contrast on parameter selection. The proposed approach was validated using both simulated and real MR images. The model image generated using our approach was shown to be highly suitable for the purpose of parameter optimization. The results confirm that our method outperforms most state-of-the-art methods in both quantitative measurement and visual evaluation. By testing on real images with different noise levels, we demonstrated that our method is sufficiently general to be applied to a variety of MR images.     

空间变化PSF非盲去卷积图像复原法综述

传统的图像复原一般认为点扩散函数(PSF)是空间不变的,实际光学系统由于受到像差等因素的影响,并非严格的线性空间不变系统,基于空间变化PSF的非盲去卷积图像复原法逐渐体现其优越性。空间变化PSF的非盲去卷积图像复原法先准确估计图像空间变化的PSF,再利用非盲去卷积算法对图像进行复原,有利于恢复出高质量图像。本文从算法的角度综述了近几年提出的基于空间变化PSF的非盲去卷积图像复原方法,并对比了基于强边缘预测估计PSF的非盲去卷积法、基于模糊噪声图像对PSF估计非盲去卷积法等算法的优缺点,各算法分别在PSF估计精确度、振铃效应抑制效果、适用范围等方面体现出各自的优劣。空间变化PSF的非盲去卷积图像复原法的研究,有利于推进图像复原技术向更高水平发展,使光学系统往轻小型化方向发展,从而在多个科学领域发挥其重要作用。     

Brain MRI tissue classification based on local Markov random fields

A new method for tissue classification of brain magnetic resonance images (MRI) of the brain is proposed. The method is based on local image models where each models the image content in a subset of the image domain. With this local modeling approach, the assumption that tissue types have the same characteristics over the brain needs not to be evoked. This is important because tissue type characteristics, such as T1 and T2 relaxation times and proton density, vary across the individual brain and the proposed method offers improved protection against intensity non-uniformity artifacts that can hamper automatic tissue classification methods in brain MRI. A framework in which local models for tissue intensities and Markov Random Field (MRF) priors are combined into a global probabilistic image model is introduced. This global model will be an inhomogeneous MRF and it can be solved by standard algorithms such as iterative conditional modes. The division of the whole image domain into local brain regions possibly having different intensity statistics is realized via sub-volume probabilistic atlases. Finally, the parameters for the local intensity models are obtained without supervision by maximizing the weighted likelihood of a certain finite mixture model. For the maximization task, a novel genetic algorithm almost free of initialization dependency is applied. The algorithm is tested on both simulated and real brain MR images. The experiments confirm that the new method offers a useful improvement of the tissue classification accuracy when the basic tissue characteristics vary across the brain and the noise level of the images is reasonable. The method also offers better protection against intensity non-uniformity artifact than the corresponding method based on a global (whole image) modeling scheme.     

Undersampled MRI reconstruction with patch-based directional wavelets

Compressed sensing has shown great potential in reducing data acquisition time in magnetic resonance imaging (MRI). In traditional compressed sensing MRI methods, an image is reconstructed by enforcing its sparse representation with respect to a preconstructed basis or dictionary. In this paper, patch-based directional wavelets are proposed to reconstruct images from undersampled k-space data. A parameter of patch-based directional wavelets, indicating the geometric direction of each patch, is trained from the reconstructed image using conventional compressed sensing MRI methods and incorporated into the sparsifying transform to provide the sparse representation for the image to be reconstructed. A reconstruction formulation is proposed and solved via an efficient alternating direction algorithm. Simulation results on phantom and in vivo data indicate that the proposed method outperforms conventional compressed sensing MRI methods in preserving the edges and suppressing the noise. Besides, the proposed method is not sensitive to the initial image when training directions.     

Application of multi-frame approach in single-frame blind deconvolution

A new single-frame blind deconvolution algorithm for the linear shift-invariant imaging system is presented. The algorithm processes the partial images segmented from one single degraded image by multi-frame approach to recover the point spread function (PSF). Then a deconvolution method is employed to restore the whole image with the recovered PSF. In addition, in order to improve the fidelity and resolution of the recovered PSF, the coprimeness of the partial images is utilized. Results of simulated and real atmospheric turbulence degraded images using the algorithm are reported.     

多帧距离选通图像点扩散函数估计的超分辨率重建

为了解决水下激光距离选通图像成像过程中退化模型复杂的难题,提出了利用连续帧图像估计点扩散函数的距离选通超分辨成像方法。首先,从连续帧图像中选取一帧为参考帧作为初始清晰图像,下一帧图像为模糊图像,用梯度约束的方法求出点扩散函数,用于优化清晰图像;然后,依次将后续帧图像当作模糊图像与清晰图像交替迭代求取点扩散函数并优化更新清晰图像;最后获得的清晰图像与参考帧图像用乘法更新的方法估计点扩散函数,结合凸集投影法算法进行超分辨率成像重建。仿真实验结果表明,改进的算法重建图像分辨率和质量明显优于原始的算法。