基于梯度阈值自适应处理的红外图像超分辨率重建

超分辨率图像重建中,Huber马尔可夫随机场模型是一种常用的正则化算子.针对Huber函数中固定梯度阈值引起图像重建效果不佳的问题,本文提出一种梯度阈值自适应处理的红外图像超分辨率重建算法.在最大后验概率理论框架下,构造了基于数据项和正则项的正则化模型;通过迭代的方式,利用中间重建结果不断更新正则化参量,解决了Huber马尔可夫随机场模型中梯度阈值不易选择的难题.实验结果表明,改进算法能够根据局部梯度特征自适应选择相应的正则化参量并找到最优解,较好恢复目标细节的同时有效抑制了图像噪音.     

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.     

基于梯度阈值自适应处理的红外图像超分辨率重建

超分辨率图像重建中,Huber马尔可夫随机场模型是一种常用的正则化算子.针对Huber函数中固定梯度阈值引起图像重建效果不佳的问题,本文提出一种梯度阈值自适应处理的红外图像超分辨率重建算法.在最大后验概率理论框架下,构造了基于数据项和正则项的正则化模型;通过迭代的方式,利用中间重建结果不断更新正则化参量,解决了Huber马尔可夫随机场模型中梯度阈值不易选择的难题.实验结果表明,改进算法能够根据局部梯度特征自适应选择相应的正则化参量并找到最优解,较好恢复目标细节的同时有效抑制了图像噪音.     

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.     

A parallel spatial and Bloch manifold regularized iterative reconstruction method for MR Fingerprinting

Magnetic Resonance Fingerprinting (MRF) reconstructs tissue maps based on a sequence of very highly undersampled images. In order to be able to perform MRF reconstruction, state-of-the-art MRF methods rely on priors such as the MR physics (Bloch equations) and might also use some additional low-rank or spatial regularization. However to our knowledge these three regularizations are not applied together in a joint reconstruction. The reason is that it is indeed challenging to incorporate effectively multiple regularizations in a single MRF optimization algorithm. As a result most of these methods are not robust to noise especially when the sequence length is short. In this paper, we propose a family of new methods where spatial and low-rank regularizations, in addition to the Bloch manifold regularization, are applied on the images. We show on digital phantom and NIST phantom scans, as well as volunteer scans that the proposed methods bring significant improvement in the quality of the estimated tissue maps.     

A robust algorithm for high-resolution dynamic MRI based on the partially separable functions model

A recently developed partially separable functions (PSF) model can be used to generate high-resolution dynamic magnetic resonance imaging (MRI). However, this method could not robustly reconstruct high-quality MR images because the estimation of the PSF parameters is often interfered by the noise of the sampled MR data. To improve the robustness of MRI reconstruction using the PSF model, we proposed a new algorithm to estimate the PSF parameters by jointly using robust principal component analysis and modified truncated singular value decomposition regularization methods, instead of using the least square fitting method in the original PSF model. The experiment results of in vivo cardiac MRI demonstrated that the proposed algorithm can robustly reconstruct dynamic MR images with higher signal-to-noise ratio and clearer anatomical structures in comparison with the previous PSF model.     

双树小波变换与小波树稀疏联合的低场CS-MRI算法

压缩感知理论常用在磁共振快速成像上,仅采样少量的K空间数据即可重建出高质量的磁共振图像.压缩感知磁共振成像技术的原理是将磁共振图像重建问题建模成一个包含数据保真项、稀疏先验项和全变分项的线性组合最小化问题,显著减少磁共振扫描时间.稀疏表示是压缩感知理论的一个关键假设,重建结果很大程度上依赖于稀疏变换.本文将双树复小波变换和小波树稀疏联合作为压缩感知磁共振成像中的稀疏变换,提出了基于双树小波变换和小波树稀疏的压缩感知低场磁共振图像重建算法.实验表明,本文所提算法可以在某些磁共振图像客观评价指标中表现出一定的优势.     

Krylov subspace iterative methods for boundary element method based near-field acoustic holography

The reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods. The solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements. These methods will not require the calculation of the singular value decomposition, which can be expensive when the matrix system is considerably large. Krylov subspace methods are iterative methods that have the phenomena known as "semi-convergence," i.e., the optimal regularization solution is obtained after a few iterations. If the iteration is not stopped, the method converges to a solution that generally is totally corrupted by errors on the measurements. For these methods the number of iterations play the role of the regularization parameter. We will focus our attention to the study of the regularizing properties from the Krylov subspace methods like conjugate gradients, least squares QR and the recently proposed Hybrid method. A discussion and comparison of the available stopping rules will be included. A vibrating plate is considered as an example to validate our results.     

Super-resolution image reconstruction based on Tukey data fusion and bilateral-total-variation regularization

Images of high-resolution are desired and often required in most photoelectronic imaging applications, and corresponding image reconstruction algorithm has became the frontier topics. On the basis of stochastic theory, a novel super-resolution image reconstruction algorithm based on Tukey norm data fusion and bilateral total variation regularization is proposed in this paper. The Tukey norm is employed for fusing the data of low-resolution frames and removing outliers in the data, and then aiming at the sickness of super-resolution reconstruction, the bilateral total variation regularization as a priori knowledge about the solution is incorporated to remove the artifacts from the final answer and improve the convergence rate. Simulated and real experiment results show that the proposed algorithm can improve the image resolution greatly and it is immune to noise and errors in motion and blur estimation.     

Image reconstruction algorithm for diffraction enhanced imaging-based computed tomography

A number of reconstruction algorithms for differential phase-contrast computed tomography reconstruct the refractive index decrement using the refraction angles of X-rays. However, these approaches require that the refraction angle at each view be extracted from several raw images captured at the same view, leading to unacceptably long exposure times and huge X-ray doses. We develop an iterative reconstruction algorithm to reconstruct the complex refractive index from raw images gathered only once at each view angle. Using the Tikhonov regularization method as basis, we simultaneously obtain the refractive index decrement and attenuation coefficient by minimizing the cost function. The experimental results show that the proposed algorithm effectively yields reconstructed images of low noise level.     

The reconstruction of particle size distributions from dynamic light scattering data using particle swarm optimization techniques with different objective functions

In this paper, the reconstruction of particle size distributions (PSDs) using particle swarm optimization (PSO) techniques from dynamic light scattering (DLS) data was established. Three different objective functions containing non-smooth constrained objective function, smooth functional objective function of Tikhonov regularization and L objective function, were employed. Simulated results of unimodal, bimodal and bi-dispersed particles show that the PSO technique with non-smooth constrained objective function produces narrower PSDs focusing on peak position in the presence of random noise, the PSO technique with smooth functional of Tikhonov regularization creates relative smooth PSDs, which could be successfully applied to the broad particles inversion, and the PSO technique with L objective function yields smooth PSDs, which saves calculation amount. Experimental results as well as comparisons with CONTIN algorithm and Cumulants method demonstrate the performance of our algorithms. Therefore, the PSO techniques employing the three different objective functions, which only require objective function and need a few initial guesses, may be applied to the reconstruction of PSDs from DLS data.     

The statistical sinogram smoothing via adaptive-weighted total variation regularization for low-dose X-ray CT

Though clinically desired, low-dose X-ray computed tomography (CT) images tend to be degraded by the noise-contaminated sinogram data. Preprocessing the noisy sinogram before filtered back-projection (FBP) is an effective way to solve this problem. This paper presents a statistical sinogram smoothing approach for low-dose CT reconstruction. The approach is obtained by minimizing an energy function consisting of an adaptive-weighted total variation (AWTV) regularization term and a data fidelity term based on the Markov random fields (MRF) framework. The AWTV regularization term can make our algorithm automatically adjust the smoothing degree according to the feature and the level of noise of the smoothed pixel. The experimental results indicate that the proposed approach has the excellent performance in visual effects and quantitative analysis.     

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.     

一种基于约束共轭梯度的闪光照相图像重建算法

 针对闪光照相系统成像信噪比低的特点,提出了正则化预优约束共轭梯度算法（RPCCG）。RPCCG算法在闪光照相重建方程中引入Tikhonov正则化准则,利用预优约束共轭梯度法迭代求图像重建的最优解。数值试验表明,采用最小二乘+平滑准则的RPCCG算法是一种具有较高的抗噪能力的有效闪光照相图像重建算法,具有良好的收敛性和稳定性以及较高的重建精度。     

Total variation based gradient descent algorithm for sparse-view photoacoustic image reconstruction

In photoacoustic imaging (PAI), reconstruction from sparse-view sampling data is a remaining challenge in the cases of fast or real-time imaging. In this paper, we present our study on a total variation based gradient descent (TV-GD) algorithm for sparse-view PAI reconstruction. This algorithm involves the total variation (TV) method in compressed sensing (CS) theory. The objective function of the algorithm is modified by adding the TV value of the reconstructed image. With this modification, the reconstructed image could be closer to the real optical energy distribution map. Additionally in the proposed algorithm, the photoacoustic data is processed and the image is updated individually at each detection point. In this way, the calculation with large matrix can be avoided and a more frequent image update can be obtained. Through the numerical simulations, the proposed algorithm is verified and compared with other reconstruction algorithms which have been widely used in PAI. The peak signal-to-noise ratio (PSNR) of the image reconstructed by this algorithm is higher than those by the other algorithms. Additionally, the convergence of the algorithm, the robustness to noise and the tunable parameter are further discussed. The TV-based algorithm is also implemented in the in vitro experiment. The better performance of the proposed method is revealed in the experiments results. From the results, it is seen that the TV-GD algorithm may be a practical and efficient algorithm for sparse-view PAI reconstruction.     

含噪动态光散射测量数据反演中正则化算法与Chahine算法的比较

采用两种常用的粒度反演方法——正则化和Chahine算法,对90nm与250nm单峰分布、50nm与200nm双峰分布、100nm与300nm双峰分布的模拟动态光散射数据,以及105nm、300nm标准颗粒的实测动态光散射数据进行了反演分析.结果表明:噪声水平的高低是影响粒度分布反演准确性的关键因素之一,反演结果的准确性随噪声水平的增加而降低,噪声水平超过某一阈值后,将无法得到有意义的反演结果;不同反演方法具有不同的抗噪能力,在低噪声水平下反演结果无显著差别,随着噪声水平的增加,反演结果表现出很大差异;正则化方法通过正则参数的选择可以有效抑制噪声影响,表现出强于Chahine算法的抗噪能力;与Chahine算法相比,正则化方法不需要假定初始分布,因此,在噪声较大的实验或生产过程中进行颗粒分布测量时,宜采用正则化方法.     

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.     

总变差约束的数据分离最小图像重建模型及其Chambolle-Pock求解算法

基于优化的迭代法,可以结合压缩感知和低秩矩阵等稀疏优化技术高精度地重建图像.其中,总变差最小（total variation minimization,TV）模型是一种简单有效的优化模型.传统的约束TV模型,使用数据保真项为约束项,TV正则项为目标函数.本文研究TV约束的、数据分离最小（TV constrained,data divergence minimization,TVcDM）新型TV模型及其求解算法.详细推导了TVcDM模型的Chambolle-Pock（CP）算法,验证了模型及算法的正确性;分析了算法的收敛行为;评估了模型的稀疏重建能力;分析了模型参数的选择对重建的影响及算法参数对收敛速率的影响.研究表明,TVcDM模型有高精度稀疏重建能力;TVcDM-CP算法确保收敛,但迭代过程中有振荡现象;TV限对重建有重要影响,参数值过大会引入噪声而过小会模糊图像细节;算法参数的不同选取会导致不同的收敛速率.     

基于加权块稀疏联合非凸低秩约束的高光谱图像去条带方法

针对高光谱图像(hyperspectral images,HSI)去条带易引起影像结构细节丢失问题,提出一种基于加权块稀疏(weighted block sparsity,WBS)正则化联合最小最大非凸惩罚(minimax concave penalty,MCP)约束的HSI去条带方法.本算法采用加权?2,1范数和MC...     

平面近场声全息中正则化参数的确定

近场声全息的逆向重建过程属于线性病态逆问题,必须进行正则化处理。本文对三种基于Tikhonov正则化的参数选择方法,即离差原理法、广义交叉验证法、L曲线法,在不同全息距离、声源频率和信噪比的条件下进行了比较,结果表明,它们在远距离及低噪声环境下难以获得合适的正则化参数。采用等效噪声方差的方法,对其中较为稳定的离差原理进行了改进,使其在较远全息距离及低噪声环境下仍能获得合适的正则化参数。相应的仿真实验表明,改进后的离差原理法在很宽的信噪比(＞6 dB)和较远的全息距离(~10 cm)均能稳定地找到合适的正则化参数。此外,由于该方法无须对全息声压进行平滑处理,其有效重建孔径和全息孔径相等。