基于凸集投影的稀疏磁共振图像重建新算法

目的:只将稀疏MRI数据重建公式中的正则化项作为最小化的目标函数,避免在迭代过程中系统矩阵参与运算,以降低算法的运算量,提高稀疏MRI数据重建的速度.方法:本文中所用的正则化函数是图像全变分与小波系数L1范数的组合,其最小化问题是用次梯度优化算法来求解的.在每一步迭代过程中,首先求出正则化项的次梯度,用次梯度优化算法求解得到中间图像并对其进行傅立叶变换,再根据凸集投影原理,直接将在相位编码方向上随机降采样的K空间数据替换到中间图像频域值的相应位置上,然后对替换后得到的频域值进行反傅立叶变换并将求得的图像作为下一次迭代过程的初始图像.结果:在正则化函数和迭代步数均相同的条件下,本文方法重建的图像质量与NCG-SMRI方法的相当,但重建速度是NCG-SMRI方法的2倍多.结论:实验表明,在不降低重建图像的质量的前提下,本文方法可以提高稀疏MRI数据的重建速度,能进一步满足临床上对MRI重建速度的要求.     

基于结构自适应归一化卷积的磁共振图像超分辨率重建

目的 探讨一种针对磁共振图像超分辨率重建的有效算法.方法 根据图像间存在的微小结构差异,应用结构自适应归一化卷积算法,对重复扫描获取的磁共振图像进行超分辨率重建,同时运用其他4种常用超分辨率重建算法进行相同处理,计算峰值信噪比,比较重建效果.结果 结构自适应归一化卷积算法与其他算法相比,能够更好地保留磁共振图像的边缘和...     

基于结构自适应归一化卷积的磁共振图像超分辨率重建

目的 探讨一种针对磁共振图像超分辨率重建的有效算法.方法 根据图像间存在的微小结构差异,应用结构自适应归一化卷积算法,对重复扫描获取的磁共振图像进行超分辨率重建,同时运用其他4种常用超分辨率重建算法进行相同处理,计算峰值信噪比,比较重建效果.结果 结构自适应归一化卷积算法与其他算法相比,能够更好地保留磁共振图像的边缘和细节特征.结论 结构自适应归一化卷积算法结合了局部结构信息,可获得质量较好的高分辨率磁共振图像.     

基于自适应T型和菱形搜索算法的CT图像的MAP重建

图像的超分辨率重建就是从一个低分辨率序列中重建出一幅高分辨率的图像.而运动估计则直接影响超分辨率重建的效果.我们提出一种基于物体边缘的自适应运动估计方法,对物体的边缘部分采用菱形搜索的方法,保证运动估计的精确度.对物体内部和背景部分采用自适应T型搜索和菱形搜索相结合的方法.保证运动估计的快速性.将这种运动估计的结果应用到最大后验概率(MAP)重建的过程中,可以保证图像重建算法的可靠性.通过对CT投影数据的分析并进行MAP重建,可以获得良好的高分辨率图像.     

基于L_P范数的磁感应断层成像图像重建算法

磁感应断层成像(MIT)图像重建是一个典型的病态问题,且其数值解不稳定。为了改善解的病态性而又能提高重建图像的质量,本文在变差正则化算法的基础上提出一种新的基于LP范数的变差正则化算法。该算法不仅有效地克服了MIT重建图像数值解的不稳定性,还提高了重建图像的质量,增强了重建图像的空间分辨能力。仿真实验结果表明,该算法所获得的重建图像质量好于Tikhonov正则化算法和变差正则化算法,为MIT提供了一种新的有效方法。     

基于医学图像的超分辨率重建算法综述

随着临床对医学图像高分辨率的要求,基于低分辨率医学图像的超分辨率重建算法已成为研究热点,该类方法在不需要改进硬件设备的情况下,可以显著提高图像分辨率,因此对其进行综述具有重要意义。针对医学图像领域中特有的超分辨率重建算法,首先分析了该类算法的研究现状,并将其分为三类:基于插值的超分辨率重建、基于重构的超分辨率重建和基于学习的超分辨率重建。同时,基于MR图像、CT图像、超声图像等细分医学图像领域,深入分析了超分辨率重建算法的研究进展,并对不同类型的算法进行了归纳总结和比对分析。其次,对超分辨率重建算法所对应的评价标准也进行了介绍。最后,展望了超分辨率重建技术在医学图像领域的发展趋势。当前应用于医学图像领域的超分辨重建算法已经发展到一定水平,逐步突破基于单一方法的研究形式,通过与机器学习和稀疏表示等理论的深度融合,形成了更高效的算法。     

基于遗传算法的电阻抗图像重建

电阻抗图像重建是一个严重病态的非态线性的逆问题， Newton-Raphson迭代算法是目前理论上最为完善的静态电阻抗图像重建算法，它是一种基于最小化目标函数的搜索算法，在实际阻抗图像重建过程中对噪声非常敏感，即使使用正则化技术其稳定性和图像重建精度仍较差，本文提出一种基于遗传算法的图像重建新方法。实验结果表明这种方法具有较强的抗噪能力，其重建的静态电阻抗图像精度和空间分辨率都大大好于改进的Newton-Raphson重建算法。     

基于改进型迭代NR的磁感应断层成像图像重建算法

在磁感应断层成像中,图像重建是一个典型的病态问题,其数值解存在不稳定性。针对此问题,提出一种基于加权矩阵和L1范数正则化的改进型迭代Newton-Raphson(NR)算法。该算法通过在目标函数的误差项中引入加权矩阵,同时在L2范数正则化惩罚项的基础上引入L1范数正则化,改善图像重建解的病态性。设置3种典型的模型,分别对有无噪声的数据进行分析,将本算法与Tikhonov正则化算法和迭代NR算法进行对比。在无噪声数据分析中,所提算法相对Tikhonov正则化算法和迭代NR算法的相对图像误差减小0.11~0.14,相关系数提高13%~17%。在有噪声数据中,所提算法相对于Tikhonov正则化算法和迭代NR算法的相对图像误差减小0.06~0.09,相关系数提高7%~10%。提出的算法成像性能较好,且抗噪性能较强,为进一步的实验重建精确性提供理论依据。     

自适应图像全变差约束的有限角度CT重建算法

针对有限投影角度的CT图像重建问题,提出一种改进的基于自适应图像全变差（Total p Variation, TpV）约束的代数迭代重建算法。改进算法采用两相式重建结构,首先利用代数重建技术（ART）算法重建中间图像并做非负修正,然后利用自适应TpV正则项约束图像稀疏特性,进一步优化重建结果,其中正则项可根据图像区域特性自适应的调整决定平滑强度的参数p,两项交替进行直到满足收敛要求。本文应用经典的Shepp-Logan体模对改进算法进行仿真重建,以重建图像及其局部放大图作为主观分析依据,以profile图和归一化绝对距离值作为客观评估标准,与经典的ART-TV算法进行比较,对比分析重建结果发现:本文算法重建图像不仅与真实体模更接近,重建误差更小,而且能更好地保护图像的边缘特性。     

基于正则化的磁共振相控阵线圈图像均匀性校正算法

由于能提供更大的扫描视野,更高的信噪比和缩短扫描时间,相控阵线圈已经被广泛使用在磁共振成像(MRI)设备中。相控阵线圈的图像重建合成最常用的是SOS算法,但是SOS算法通常会造成图像的灰度不均匀。这样不仅会直接影响医生诊断的准确性,同时对图像自动分割等后处理技术的使用也会产生不良影响。本文提出一种改进的基于正则化的最小二乘化方法,用于MRI相控阵图像的合成。在该方法中利用均匀的大体线圈和相控阵线圈进行预扫描获得线圈敏感图,通过引入正则函数来控制重建图像的噪声。此外,在正则函数中还使用大体线圈的预扫描图像作为参考图像。使用水模和志愿者成像数据验证,该方法能够有效提高相控阵线圈重建图像的均匀性。     

A fast image reconstruction algorithm based on penalized-likelihood estimate

Statistical iterative methods for image reconstruction like maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurately modeling the counting statistics and the photon transport during acquisition. They are rapidly becoming the standard for image reconstruction in emission computed tomography. The maximum likelihood approach provides images with superior noise characteristics compared to the conventional filtered back projection algorithm. But a major drawback of the statistical iterative image reconstruction is its high computational cost. In this paper, a fast algorithm is proposed as a modified OS-EM (MOS-EM) using a penalized function, which is applied to the least squares merit function to accelerate image reconstruction and to achieve better convergence. The experimental results show that the algorithm can provide high quality reconstructed images with a small number of iterations.     

Development and evaluation of an exact fan-beam reconstruction algorithm using an equal weighting scheme via locally compensated filtered backprojection (LCFBP)

A novel exact fan-beam image reconstruction formula is presented and validated using both phantom data and clinical data. This algorithm takes the form of the standard ramp filtered backprojection (FBP) algorithm plus local compensation terms. This algorithm will be referred to as a locally compensated filtered backprojection (LCFBP). An equal weighting scheme is utilized in this algorithm in order to properly account for redundantly measured projection data. The algorithm has the desirable property of maintaining a mathematically exact result for: the full scan mode (2pi), the short scan mode (pi+ full fan angle), and the supershort scan mode [less than (pi+ full fan angle)]. Another desirable feature of this algorithm is that it is derivative-free. This feature is beneficial in preserving the spatial resolution of the reconstructed images. The third feature is that an equal weighting scheme has been utilized in the algorithm, thus the new algorithm has better noise properties than the standard filtered backprojection image reconstruction with a smooth weighting function. Both phantom data and clinical data were utilized to validate the algorithm and demonstrate the superior noise properties of the new algorithm.     

Regularized iterative weighted filtered backprojection for helical cone-beam CT

Contemporary reconstruction methods employed for clinical helical cone-beam computed tomography (CT) are analytical (noniterative) but mathematically nonexact, i.e., the reconstructed image contains so called cone-beam artifacts, especially for higher cone angles. Besides cone artifacts, these methods also suffer from windmill artifacts: alternating dark and bright regions creating spiral-like patterns occurring in the vicinity of high z-direction derivatives. In this article, the authors examine the possibility to suppress cone and windmill artifacts by means of iterative application of nonexact three-dimensional filtered backprojection, where the analytical part of the reconstruction brings about accelerated convergence. Specifically, they base their investigations on the weighted filtered backprojection method [Stierstorfer et al., Phys. Med. Biol. 49, 2209-2218 (2004)]. Enhancement of high frequencies and amplification of noise is a common but unwanted side effect in many acceleration attempts. They have employed linear regularization to avoid these effects and to improve the convergence properties of the iterative scheme. Artifacts and noise, as well as spatial resolution in terms of modulation transfer functions and slice sensitivity profiles have been measured. The results show that for cone angles up to +/-2.78 degrees, cone artifacts are suppressed and windmill artifacts are alleviated within three iterations. Furthermore, regularization parameters controlling spatial resolution can be tuned so that image quality in terms of spatial resolution and noise is preserved. Simulations with higher number of iterations and long objects (exceeding the measured region) verify that the size of the reconstructible region is not reduced, and that the regularization greatly improves the convergence properties of the iterative scheme. Taking these results into account, and the possibilities to extend the proposed method with more accurate modeling of the acquisition process, the authors believe that iterative improvement with non-exact methods is a promising technique for medical CT applications.     

Fundamental study on diffuse reflective optical tomography

We report a simulation study on diffuse reflective optical computed tomography, in which continuous-wave sources and detectors are placed on the plane surface of a semi-infinite body. We adopted a simple Tikhonov regularization in the inverse problem and demonstrated the feasibility of three-dimensional reconstruction of the absorption coefficient change. The spatial resolution of the reconstructed image was shown to be degrading markedly with the depth. The regularization parameter should be chosen appropriately considering the trade-off between the reconstructed image noise and the spatial resolution. We analysed the dependence of the spatial resolution of the reconstructed image on the regularization parameter and the depth, and also the behaviour of the reconstructed image noise on the regularization parameter and the depth.     

Image reconstruction with shift-variant filtration and its implication for noise and resolution properties in fan-beam computed tomography

In computed tomography (CT), the fan-beam filtered backprojection (FFBP) algorithm is used widely for image reconstruction. It is known that the FFBP algorithm can significantly amplify data noise and aliasing artifacts in situations where the focal lengths are comparable to or smaller than the size of the field of measurement (FOM). In this work, we propose an algorithm that is less susceptible to data noise, aliasing, and other data inconsistencies than is the FFBP algorithm while retaining the favorable resolution properties of the FFBP algorithm. In an attempt to evaluate the noise properties in reconstructed images, we derive analytic expressions for image variances obtained by use of the FFBP algorithm and the proposed algorithm. Computer simulation studies are conducted for quantitative evaluation of the spatial resolution and noise properties of images reconstructed by use of the algorithms. Numerical results of these studies confirm the favorable spatial resolution and noise properties of the proposed algorithm and verify the validity of the theoretically predicted image variances. The proposed algorithm and the derived analytic expressions for image variances can have practical implications for both estimation and detection/classification tasks making use of CT images, and they can readily be generalized to other fan-beam geometries.     

Fast imaging of high-resolution two-dimensional effective attenuation profile from diffuse reflectance

Biological tissue is non-homogeneous in nature. It is difficult to measure its optical properties due to non-uniformity throughout the tissue being tested. To obtain the spatial distribution of optical parameters, conventional approaches use an array of light sources and detectors to reconstruct the image, thus, there is very limited spatial resolution. In contrast, solutions that provide high resolution have a high computational complexity. In this paper, we propose a fast, simple scheme to resolve the effective attenuation profile from the spatial diffuse reflectance. Rather than giving one single value for the absorption and reduced scattering coefficients, a novel algorithm is proposed for the reconstruction of an effective attenuation profile in 2-dimension from a diffuse reflectance curve. This technique is applied to the reconstruction of a 2-D effective attenuation profile. By obtaining the diffuse reflectance image from a camera and using the algorithm developed here, fast imaging of the effective attenuation profile with relatively high spatial resolution can be achieved.     

High-resolution three-dimensional blood flow tomography in the subdiffuse regime using laser speckle contrast imaging

Significance: Visualizing high-resolution hemodynamics in cerebral tissue over a large field of view (FOV), provides important information in studying disease states affecting the brain. Current state-of-the-art optical blood flow imaging techniques either lack spatial resolution or are too slow to provide high temporal resolution reconstruction of flow map over a large FOV.Aim: We present a high spatial resolution computational optical imaging technique based on principles of laser speckle contrast imaging (LSCI) for reconstructing the blood flow maps in complex tissue over a large FOV provided that the three-dimensional (3D) vascular structure is known or assumed.Approach: Our proposed method uses a perturbation Monte Carlo simulation of the high-resolution 3D geometry for both accurately deriving the speckle contrast forward model and calculating the Jacobian matrix used in our reconstruction algorithm to achieve high resolution. Given the convex nature of our highly nonlinear problem, we implemented a mini-batch gradient descent with an adaptive learning rate optimization method to iteratively reconstruct the blood flow map. Specifically, we implemented advanced optimization techniques combined with efficient parallelization and vectorization of the forward and derivative calculations to make reconstruction of the blood flow map feasible with reconstruction times on the order of tens of minutes.Results: We tested our reconstruction algorithm through simulation of both a flow phantom model as well as an anatomically correct murine cerebral tissue and vasculature captured via two-photon microscopy. Additionally, we performed a noise study, examining the robustness of our inverse model in presence of 0.1% and 1% additive noise. In all cases, the blood flow reconstruction error was <2% for most of the vasculature, except for the peripheral vasculature which suffered from insufficient photon sampling. Descending vasculature and deeper structures showed slightly higher sensitivity to noise compared with vasculature with a horizontal orientation at the more superficial layers. Our results show high-resolution reconstruction of the blood flow map in tissue down to 500μm and beyond.Conclusions: We have demonstrated a high-resolution computational imaging technique for visualizing blood flow map in complex tissue over a large FOV. Once a high-resolution structural image is captured, our reconstruction algorithm only requires a few LSCI images captured through a camera to reconstruct the blood flow map computationally at a high resolution. We note that the combination of high temporal and spatial resolution of our reconstruction algorithm makes the solution well-suited for applications involving fast monitoring of flow dynamics over a large FOV, such as in functional neural imaging.     

High temporal resolution for multislice helical computed tomography

Multislice helical computed tomography (CT) substantially reduces scanning time. However, the temporal resolution of individual images is still insufficient for imaging rapidly moving organs such as the heart and adjacent pulmonary vessels. It may, in some cases, be worse than with current single-slice helical CT. The purpose of this study is to describe a novel image reconstruction algorithm to improve temporal resolution in multislice helical CT, and to evaluate its performance against existing algorithms. The proposed image reconstruction algorithm uses helical interpolation followed by data weighting based on the acquisition time. The temporal resolution, the longitudinal (z-axis) spatial resolution, the image noise, and the in-plane image artifacts created by a moving phantom were compared with those from the basic multislice helical reconstruction (helical filter interpolation, HFI) algorithm and the basic single-slice helical reconstruction algorithm (180 degrees linear interpolation, 180LI) using computer simulations. Computer simulation results were verified with CT examinations of the heart and lung vasculature using a 0.5 second multislice scanner. The temporal resolution of HFI algorithm varies from 0.28 and 0.86 s, depending on helical pitch. The proposed method improves the resolution to a constant value of 0.29 s, independent of pitch, allowing moving objects to be imaged with reduced blurring or motion artifacts. The spatial (z) resolution was slightly worse than with the HFI algorithm; the image noise was worse than with the HFI algorithm but was comparable to axial (step-and-shoot) CT. The proposed method provided sharp images of the moving objects, portraying the anatomy accurately. The proposed algorithm for multislice helical CT allowed us to obtain CT images with high temporal resolution. It may improve the image quality of clinical cardiac, lung, and vascular CT imaging.     

Half-scan fan-beam computed tomography with improved noise and resolution properties

Half-scan strategy can be used for reducing scanning time and radiation dose delivered to the patient in fan-beam computed tomography (CT). In helical CT, the data weighting/interpolation functions are often devised based upon half-scan configurations. The half-scan fan-beam filtered backprojection (FFBP) algorithm is generally used for image reconstruction from half-scan data. It can, however, be susceptible to sample aliasing and data noise for configurations with short focal lengths and/or large fan-angles, leading to nonuniform resolution and noise properties in reconstructed images. Uniform resolution and noise properties are generally desired because they may lead to an increased utility of reconstructed images in estimation and/or detection/classification tasks. In this work, we propose an algorithm for reconstruction of images with uniform noise and resolution properties in half-scan CT. In an attempt to evaluate the image-noise properties, we derive analytic expressions for image variances obtained by use of the half-scan algorithms. We also perform numerical studies to assess quantitatively the resolution and noise properties of the algorithms. The results in these studies confirm that the proposed algorithm yields images with more uniform spatial resolution and with lower and more uniform noise levels than does the half-scan FFBP algorithm. Empirical results obtained in noise studies also verify the validity of the derived expressions for image variances. The proposed algorithm would be particularly useful for image reconstruction from data acquired by use of configurations with short focal lengths and large field of measurement, which may be encountered in compact micro-CT and radiation therapeutic CT applications. The analytic results of the image-noise properties can be used for image-quality assessment in detection/classification tasks by use of model-observers.     

Effect of compensation for scattering angular uncertainty in analytical Compton camera reconstruction

In Compton cameras, the measured scattering angle is associated with an uncertainty which becomes larger as the incident gamma-ray energy decreases. Since this uncertainty degrades the spatial resolution of reconstructed images, Hirasawa and Tomitani (2003 Phys. Med. Biol. 48 1009-26) previously revised their analytical reconstruction algorithm to compensate for it. As the new algorithm improved the spatial resolution in effect, they expected an enhancement of the statistical noise. In this paper, the effect of this compensation has been analysed in view of spatial resolution (the FWHM of the noise-free reconstructed image for a point source distribution), statistical noise (the relative standard deviation of reconstructed images for an isotropic source distribution) and image quality (the roughness of reconstructed images for a phantom). The results describe not only the effect of the compensation, but also the relation between the statistical noise and three parameters, i.e., the incident gamma-ray energy, the spatial resolution and the measured total event numbers, in reconstruction with compensation. This relation should be taken into account for the design of Compton cameras with good quality images, i.e., useful image, output.