Assessment of averaging spatially correlated noise for 3-D radial imaging

Any measurement of signal intensity obtained from an image will be corrupted by noise. If the measurement is from one voxel, an error bound associated with noise can be assigned if the standard deviation of noise in the image is known. If voxels are averaged together within a region of interest (ROI) and the image noise is uncorrelated, the error bound associated with noise will be reduced in proportion to the square root of the number of voxels in the ROI. However, when 3-D-radial images are created the image noise will be spatially correlated. In this paper, an equation is derived and verified with simulated noise for the computation of noise averaging when image noise is correlated, facilitating the assessment of noise characteristics for different 3-D-radial imaging methodologies. It is already known that if the radial evolution of projections are altered such that constant sampling density is produced in k-space, the signal-to-noise ratio (SNR) inefficiency of standard radial imaging (SR) can effectively be eliminated (assuming a uniform transfer function is desired). However, it is shown in this paper that the low-frequency noise power reduction of SR will produce beneficial (anti-) correlation of noise and enhanced noise averaging characteristics. If an ROI contains only one voxel a radial evolution altered uniform k-space sampling technique such as twisted projection imaging (TPI) will produce an error bound ~35% less with respect to noise than SR, however, for an ROI containing 16 voxels the SR methodology will facilitate an error bound ~20% less than TPI. If a filtering transfer function is desired, it is shown that designing sampling density to create the filter shape has both SNR and noise correlation advantages over sampling k-space uniformly. In this context SR is also beneficial. Two sets of 48 images produced from a saline phantom with sodium MRI at 4.7T are used to experimentally measure noise averaging characteristics of radial imaging and good agreement with theory is obtained.     

多准则图象重建的神经网络模型及实现

本文提出一种采用Ｈｏｐｆｉｅｌｅ神经网络（Ｈｏｐｆｉｅｌｄ Ｎｅｉｒａｌ Ｎｅｔｗｏｒｋ简称ＨＮＮ）优化的图象重建算法。将图象重建问题转化为ＨＮＮ优化问题,取重建图象的峰值函数最小以及原始投影与再投影之间的误差平方和最小作为图象重建的优化目标,作为能量函数构造连续型ＨＮＮ模型,由ＨＮＮ能量函数极小化可得到重建问题的优化解。这种方法具有简单、计算量小、收敛快、便于并行计算等特点。对照ＡＲＴ算法,用计算机模拟产生的无噪声投影数据检验新算法,验证了新算法的优越性。     

Filter-based coded-excitation system for high-speed ultrasonic imaging

We have recently presented a new algorithm for high-speed parallel processing of ultrasound pulse-echo data for real-time three-dimensional (3-D) imaging. The approach utilizes a discretized linear model of the echo data received from the region of interest (ROI) using a conventional beam former. The transmitter array elements are fed with binary codes designed to produce distinct impulse responses from different directions in ROI. Image reconstruction in ROI is achieved with a regularized pseudoinverse operator derived from the linear receive signal model. The reconstruction operator can be implemented using a transversal filter bank with every filter in the bank designed to extract echoes from a specific direction in the ROI. The number of filters in the bank determines the number of image lines acquired simultaneously. In this paper, we present images of a cyst phantom reconstructed based on our formulation. A number of issues of practical significance in image reconstruction are addressed. Specifically, an augmented model is introduced to account for imperfect blocking of echoes from outside the ROI. We have also introduced a column-weighting algorithm for minimizing the number of filter coefficients. In addition, a detailed illustration of a full image reconstruction using subimage acquisition and compounding is given. Experimental results have shown that the new approach is valid for phased-array pulse-echo imaging of speckle-generating phantoms typically used in characterizing medical imaging systems. Such coded-excitation-based image reconstruction from speckle-generating phantoms, to the best of our knowledge, have not been reported previously.     

Exact (spiral + circles) scan region-of-interest cone beam reconstruction via backprojection

We present a (spiral + circles) scan cone beam reconstruction algorithm in which image reconstruction proceeds via backprojection in the object space. In principle, the algorithm can reconstruct sectional region-of-interest (ROI) in a long object. The approach is a generalization of the cone beam backprojection technique developed by Kudo and Saito in two aspects: the resource-demanding normalization step in the Kudo and Saito's algorithm is eliminated through the technique of data combination that we published earlier, and the elimination of the restriction that the detector be big enough to capture the entire cone beam projection of the ROI. Restricting the projection data to the appropriate angular range required by data combination can be accomplished by a masking process. Because of the simplification resulting from the elimination of the normalization step, the most time-consuming operations of the algorithm can be approximated by the efficient step of line-by-line ramp filtering the cone beam image in the direction of the scan path, plus a correction image. The correction image, which can be computed exactly, is needed because data combination is not properly matched at the mask boundary when ramp filtering is involved. Empirical two-dimensional (2-D) point spread function (PSF) is developed to improve matching with the correction image which is computed with finite samplings. The use of transition region to further improve matching is introduced. The results of testing the algorithm on simulated phantoms are presented.     

Two-dimensional restoration of single photon emission computed tomography images using the Kalman filter

The discrete filtered backprojection (DFBP) algorithm used for the reconstruction of single photon emission computed tomography (SPECT) images affects image quality because of the operations of filtering and discretization. The discretization of the filtered backprojection process can cause the modulation transfer function (MTF) of the SPECT imaging system to be anisotropic and nonstationary, especially near the edges of the camera's field of view. The use of shift-invariant restoration techniques fails to restore large images because these techniques do not account for such variations in the MTF. This study presents the application of a two-dimensional (2D) shift-variant Kalman filter for post-reconstruction restoration of SPECT slices. This filter was applied to SPECT images of a hollow cylinder phantom; a resolution phantom; and a large, truncated cone phantom containing two types of cold spots, a sphere, and a triangular prism. The images were acquired on an ADAC GENESYS camera. A comparison was performed between results obtained by the Kalman filter and those obtained by shift-invariant filters. Quantitative analysis of the restored images performed through measurement of root mean squared errors shows a considerable reduction in error of Kalman-filtered images over images restored using shift-invariant methods.     

Temporal integration method for image-processing-basedsuper-high-resolution image acquisition

The authors propose an image processing-based approach towards the development of a super-high-resolution image acquisition system. Imaging methods based on this approach can be classified into two main categories: a spatial integration imaging method and a temporal integration imaging method. With regard to the spatial integration imaging method, the authors have previously presented a method for acquiring an improved-resolution image by integrating multiple images taken simultaneously with multiple different cameras. They develop their work, aiming at a particular class of application where a user indicates a region of interest (ROI) on an observed image in advance, and apply a prototypal temporal integration imaging method. The prototypal temporal integration imaging method does not involve global image segmentation, but uses a subpixel registration algorithm which describes an image warp within the ROI, with subpixel accuracy, as a deformation of quadrilateral patches. The method then performs a subpixel registration by warping an observed image with the warping function recovered from the deformed quadrilateral patches. Experimental simulations demonstrate that the temporal integration imaging is promising as a basic means of high resolution imaging     

一种基于勒让德拟合的SAR 后向投影自聚焦算法

对于合成孔径雷达(SAR)成像来说,后向投影(Back Projection, BP)算法是一种十分重要的时域成像方法。然而现有的自聚焦算法都是基于频域成像算法开发的,无法直接用于BP 聚焦图像的误差相位估计。针对这一问题,该文提出一种适用于BP 图像的自聚焦算法。该算法以图像锐度函数为目标函数,以待估计的相位校正值为自变量,通过坐标下降最优化算法循环迭代获得它们的最优估计。在问题求解中,该算法利用勒让德多项式来拟合目标函数,使得每次迭代的最优解可以解析地获得,避免了低效的线搜索过程。基于仿真数据和实测数据的实验验证了该算法的精确性和有效性。      

A New Method for Electric Impedance Imaging Using an Eddy Current With a Tetrapolar Circuit

A new contactless technique for electrical impedance imaging, using an eddy current managed along with the tetrapolar circuit method, is proposed. The eddy current produced by a magnetic field is superimposed on a constant current that is normally used in the tetrapolar circuit method, and thus is used to control the current distribution in the body. By changing the current distribution, a set of voltage differences is measured with a pair of electrodes. This set of voltage differences is used in the image reconstruction of the resistivity distribution. The least square error minimization method is used in the reconstruction algorithm. The principle of this method is explained theoretically. A backprojection algorithm was used to get 2-D images. Based on this principle, a measurement system was developed and model experiments were conducted with a saline-filled phantom. The estimated shape of each model in the reconstructed image was similar to that of the corresponding model. From the results of these experiments, it is confirmed that the proposed method is applicable to the realization of electrical conductivity imaging.     

Image reconstruction for hybrid true-color micro-CT

X-ray micro-CT is an important imaging tool for biomedical researchers. Our group has recently proposed a hybrid "true-color" micro-CT system to improve contrast resolution with lower system cost and radiation dose. The system incorporates an energy-resolved photon-counting true-color detector into a conventional micro-CT configuration, and can be used for material decomposition. In this paper, we demonstrate an interior color-CT image reconstruction algorithm developed for this hybrid true-color micro-CT system. A compressive sensing-based statistical interior tomography method is employed to reconstruct each channel in the local spectral imaging chain, where the reconstructed global gray-scale image from the conventional imaging chain served as the initial guess. Principal component analysis was used to map the spectral reconstructions into the color space. The proposed algorithm was evaluated by numerical simulations, physical phantom experiments, and animal studies. The results confirm the merits of the proposed algorithm, and demonstrate the feasibility of the hybrid true-color micro-CT system. Additionally, a "color diffusion" phenomenon was observed whereby high-quality true-color images are produced not only inside the region of interest, but also in neighboring regions. It appears harnessing that this phenomenon could potentially reduce the color detector size for a given ROI, further reducing system cost and radiation dose.     

一种微波光子雷达ISAR成像新方法

微波光子雷达发射信号带宽大、波长短,能够实现分辨率更高的逆合成孔径雷达(ISAR)成像。但带宽大、波长小的回波信号也导致传统成像算法对目标转动分量的近似不成立,使得传统算法无法应用。在微波光子雷达成像中,目标转动分量在回波包络中形成空变的距离弯曲项,在方位相位中形成空变的2次相位误差,导致ISAR图像散焦。该文针对微波光子雷达系统提出一种新的ISAR成像算法,该算法同时考虑了目标转动分量对回波包络和相位的影响,以包络相关值为目标函数值迭代估计目标转速,根据转速估计值,在距离向进行重采样对齐包络,在方位向构造空变的方位补偿函数校正转动相位。仿真和实测数据的处理结果证明了该算法的有效性。     

Estimation of images and nonrigid deformations in gated emission CT

In this paper, we propose and test a new iterative algorithm to simultaneously estimate the nonrigid motion vector fields and the emission images for a complete cardiac cycle in gated cardiac emission tomography. We model the myocardium as an elastic material whose motion does not generate large amounts of strain. As a result, our method is based on minimizing an objective function consisting of the negative logarithm of a maximum likelihood image reconstruction term, the standard biomechanical model of strain energy, and an image matching term that ensures a measure of agreement of intensities between frames. Simulations are obtained using data for the four-dimensional (4-D) NCAT phantom. The data models realistic noise levels in a typical gated myocardial perfusion SPECT study. We show that our simultaneous algorithm produces images with improved spatial resolution characteristics and noise properties compared with those obtained from postsmoothed 4-D maximum likelihood methods. The simulations also demonstrate improved motion estimates over motion estimation using independently reconstructed images.     

Optimal Two-Stage Search for Sparse Targets Using Convex Criteria

We consider the problem of estimating and detecting sparse signals over a large area of an image or other medium. We introduce a novel cost function that captures the tradeoff between allocating energy to signal regions, called regions of interest (ROI), versus exploration of other regions. We show that minimizing our cost guarantees reduction of both the error probability over the unknown ROI and the mean square error (MSE) in estimating the ROI content. Two solutions to the resource allocation problem, subject to a total resource constraint, are derived. Asymptotic analysis shows that the estimated ROI converges to the true ROI. We show that our adaptive sampling method outperforms exhaustive search and are nearly optimal in terms of MSE performance. An illustrative example of our method in radar imaging is given.      

Blind restoration of turbulence degraded images based on two-channel alternating minimization algorithm

Due to the atmospheric turbulence and the system noise, images are blurred in the astronomical or space object detection. Wavefront aberrations and system noise make the capability of detecting objects decrease greatly. A two-channel image restoration method based on alternating minimization is proposed to restore the turbulence degraded images. The images at different times are regarded as separate channels, then the object and the point spread function (PSF) are reconstructed in an alternative way. There are two optimization parameters in the algorithm:the object and the PSF. Each optimization step is transformed into a constraint problem by variable splitting and processed by the augmented Lagrangian method. The results of simulation and actual experiment verify that the two-channel image restoration method can always converge rapidly within five iterations, and values of normalized root mean square error (NRMSE) remain below 3% after five iterations. Standard deviation data show that optimized alternating minimization (OAM) has strong stability and adaptability to different turbulent levels and noise levels. Restored images are approximate to the ideal imaging by visual assessment, even though atmospheric turbulence and systemnoise have a strong impact on imaging. Additionally, the method can remove noise effectively during the process of image restoration.     

Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm

Time-resolved cardiac imaging is particularly interesting in the interventional setting since it would provide both image guidance for accurate procedural planning and cardiac functional evaluations directly in the operating room. Imaging the heart in vivo using a slowly rotating C-arm system is extremely challenging due to the limitations of the data acquisition system and the high temporal resolution required to avoid motion artifacts. In this paper, a data acquisition scheme and an image reconstruction method are proposed to achieve time-resolved cardiac cone-beam computed tomography imaging with isotropic spatial resolution and high temporal resolution using a slowly rotating C-arm system. The data are acquired within 14 s using a single gantry rotation with a short scan angular range. The enabling image reconstruction method is the prior image constrained compressed sensing (PICCS) algorithm. The prior image is reconstructed from data acquired over all cardiac phases. Each cardiac phase is then reconstructed from the retrospectively gated cardiac data using the PICCS algorithm. To validate the method, several studies were performed. Both numerical simulations using a hybrid motion phantom with static background anatomy as well as physical phantom studies have been used to demonstrate that the proposed method enables accurate reconstruction of image objects with a high isotropic spatial resolution. A canine animal model scanned in vivo was used to further validate the method.     

Terahertz composite imaging method

In order to improve the imaging quality of terahertz(THz) spectroscopy, Terahertz Composite Imaging Method(TCIM) is proposed. The traditional methods of improving THz spectroscopy image quality are mainly from the aspects of de-noising and image enhancement. TCIM breaks through this limitation. A set of images, reconstructed in a single data collection, can be utilized to construct two kinds of composite images. One algorithm, called Function Superposition Imaging Algorithm(FSIA), is to construct a new gray image utilizing multiple gray images through a certain function. The features of the Region Of Interest (ROI) are more obvious after operating, and it has capability of merging ROIs in multiple images. The other, called Multi-characteristics Pseudo-color Imaging Algorithm(McPcIA), is to construct a pseudo-color image by combining multiple reconstructed gray images in a single data collection. The features of ROI are enhanced by color differences. Two algorithms can not only improve the contrast of ROIs, but also increase the amount of information resulting in analysis convenience. The experimental results show that TCIM is a simple and effective tool for THz spectroscopy image analysis.     

基于几何投影的线扩展函数算法研究

线扩展函数测试是光学成像系统成像质量评价中最重要的一部分,线扩展函数测量精度的高低直接影响到系统调制传递函数(MTF)曲线的测量精度.为了提高线扩展函数的测量精度,提出了一种基于几何投影的线扩展函数测试算法.从算法的原理分析入手,通过感兴趣区域(ROI)截取、狭缝确认及投影计算,拟合得到线扩展函数曲线.用中波红外探测器...     

基于全变分α散度最小化的PET优质重建

为了获得优质的PET成像,本文提出一种基于全变分阿尔法散度最小化的PET重建新方法.新方法通过引入阿尔法散度度量投影数据和估计值之间的偏差;通过增加全变分正则化修正阿尔法散度最小化解的一致性.针对新构建的PET重建目标函数的求解,本文提出一种基于次梯度理论的交替式迭代策略,期间运用自适应非单调线性搜索来保证算法的收敛性.仿真和临床PET数据实验表明,本文方法在噪声抑制和边缘保持方面均优于传统的PET重建方法.     

Scatter correction method for X-ray CT using primary modulation: theory and preliminary results

An X-ray system with a large area detector has high scatter-to-primary ratios (SPRs), which result in severe artifacts in reconstructed computed tomography (CT) images. A scatter correction algorithm is introduced that provides effective scatter correction but does not require additional patient exposure. The key hypothesis of the algorithm is that the high-frequency components of the X-ray spatial distribution do not result in strong high-frequency signals in the scatter. A calibration sheet with a checkerboard pattern of semitransparent blockers (a "primary modulator") is inserted between the X-ray source and the object. The primary distribution is partially modulated by a high-frequency function, while the scatter distribution still has dominant low-frequency components, based on the hypothesis. Filtering and demodulation techniques suffice to extract the low-frequency components of the primary and hence obtain the scatter estimation. The hypothesis was validated using Monte Carlo (MC) simulation, and the algorithm was evaluated by both MC simulations and physical experiments. Reconstructions of a software humanoid phantom suggested system parameters in the physical implementation and showed that the proposed method reduced the relative mean square error of the reconstructed image in the central region of interest from 74.2% to below 1%. In preliminary physical experiments on the standard evaluation phantom, this error was reduced from 31.8% to 2.3%, and it was also demonstrated that the algorithm has no noticeable impact on the resolution of the reconstructed image in spite of the filter-based approach. Although the proposed scatter correction technique was implemented for X-ray CT, it can also be used in other X-ray imaging applications, as long as a primary modulator can be inserted between the X-ray source and the imaged object.     

Inexact alternating direction method based on Newton descent algorithm with application to Poisson image deblurring

The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based regularizers involving the popular total variation semi-norm have become standard techniques for Poisson image restoration due to its edge-preserving ability. Various efficient algorithms have been developed for solving the corresponding minimization problem with non-smooth regularization terms. In this paper, motivated by the idea of the alternating direction minimization algorithm and the Newton’s method with upper convergent rate, we further propose inexact alternating direction methods utilizing the proximal Hessian matrix information of the objective function, in a way reminiscent of Newton descent methods. Besides, we also investigate the global convergence of the proposed algorithms under certain conditions. Finally, we illustrate that the proposed algorithms outperform the current state-of-the-art algorithms through numerical experiments on Poisson image deblurring.     

基于Labview的光声信号采集和成像系统

为了实现光声信号的快速采集和图像重建,采用基于Labview软件平台的光声信号采集和成像系统进行光声信号采集,并调用Matlab程序对采集到的数据进行处理,最后利用滤波反投影重建算法,实现了对模拟组织样品的光声层析成像。成像系统的分辨率为0.15mm,重建图像与实物十分吻合。实验表明,该系统具有快速、方便、直观等特点,有望发展成为一种低成本的实用的临床诊断仪器。