Fourier-based reconstruction for fully 3-D PET: optimization of interpolation parameters

Fourier-based approaches for three-dimensional (3-D) reconstruction are based on the relationship between the 3-D Fourier transform (FT) of the volume and the two-dimensional (2-D) FT of a parallel-ray projection of the volume. The critical step in the Fourier-based methods is the estimation of the samples of the 3-D transform of the image from the samples of the 2-D transforms of the projections on the planes through the origin of Fourier space, and vice versa for forward-projection (reprojection). The Fourier-based approaches have the potential for very fast reconstruction, but their straightforward implementation might lead to unsatisfactory results if careful attention is not paid to interpolation and weighting functions. In our previous work, we have investigated optimal interpolation parameters for the Fourier-based forward and back-projectors for iterative image reconstruction. The optimized interpolation kernels were shown to provide excellent quality comparable to the ideal sinc interpolator. This work presents an optimization of interpolation parameters of the 3-D direct Fourier method with Fourier reprojection (3D-FRP) for fully 3-D positron emission tomography (PET) data with incomplete oblique projections. The reprojection step is needed for the estimation (from an initial image) of the missing portions of the oblique data. In the 3D-FRP implementation, we use the gridding interpolation strategy, combined with proper weighting approaches in the transform and image domains. We have found that while the 3-D reprojection step requires similar optimal interpolation parameters as found in our previous studies on Fourier-based iterative approaches, the optimal interpolation parameters for the main 3D-FRP reconstruction stage are quite different. Our experimental results confirm that for the optimal interpolation parameters a very good image accuracy can be achieved even without any extra spectral oversampling, which is a common practice to decrease errors caused by interpolation in Fourier reconstruction.     

Study on infrared image super-resolution reconstruction based on an improved POCS algorithm

Aiming at the disadvantages of the traditional projection onto convex sets of blurry edges and lack of image details, this paper proposes an improved projection onto convex sets (POCS) method to enhance the quality of image super-resolution reconstruction (SRR). In traditional POCS method, bilinear interpolation easily blurs the image. In order to improve the initial estimation of high-resolution image (HRI) during reconstruction of POCS algorithm, the initial estimation of HRI is obtained through iterative curvature-based interpolation (ICBI) instead of bilinear interpolation. Compared with the traditional POCS algorithm, the experimental results in subjective evaluation and objective evaluation demonstrate the effectiveness of the proposed method. The visual effect is improved significantly and image detail information is preserved better.     

基于频域插值的信道化原型滤波器设计

针对信道化原型滤波器设计复杂度较高的问题,提出一种满足线性相位要求的原型滤波器频域插值设计算法。该算法采用无约束迭代优化办法获得了阻带衰减较高的低阶滤波器模型,然后根据所推导的频域插值模型构建满足线性相位特性的原型滤波器频谱,最后通过快速傅里叶逆变换获得了满足信道化滤波器组完全重构特性要求的原型滤波器。所提设计算法将频域插值与迭代优化相结合,有效地解决了设计高阻带衰减的原型滤波器时待优化参数数目较大的问题,并且不会产生镜像频谱,省去了镜像抑制滤波器的设计。仿真结果表明,所提算法相比传统的时域插值设计算法具有显著的性能改善,并且降低了设计复杂度。     

A Method for Stop-Action Imaging of the Heart Using Gated Computed Tomography

A new method for the reconstruction of limited angle projection data in rotary fan-beam X-ray computed tomography (CT) is presented. Missing views resulting from ECG-gated cardiac CT are estimated, and the standard fan-beam reconstruction algorithm is used to convolve and backproject both measured and estimated views. The estimation of the missing views takes place in three stages: first, the projection data is augmented by incorporating into each missing view the line integrals that do not pass through the heart, and which otherwise would be considered missing due to ECG-gating; second, line integrals corresponding to source positions in the range 180°±fan angle away from missing view angles are reflected; third, those line integrals that remain missing are estimated by interpolation. This method has been applied to ECG-gated cardiac imaging in dogs without requiring extensive interpolation; end-systolic and end-diastolic images were generated with short-interval gating (?cycle) and total scan time (breath holding period) of 12 s. An important advantage of this method over other proposed limited angle reconstruction techniques is that it uses the existing fan-beam convolution-backprojection algorithm for image reconstruction.     

Hardware Implementation on the Weight Calculation of Iterative Algorithm for CT Image Reconstruction

The weight calculation in an iterative algorithm is the most computationally costly task in computed tomography image reconstruction. In this letter, a fast algorithm to speed up the weight calculation is proposed. The classic square pixel rotation approximate calculation method for computing the weights in the iterative algorithm is first analyzed and then improved by replacing the square pixel model with a circular pixel model and the square rotation approximation with a segmentation method of a circular area. Software simulation and hardware implementation results show that our proposed scheme can not only improve the definition of the reconstructed image but also accelerate the reconstruction.     

Iterative tomographic image reconstruction using Fourier-based forward and back-projectors

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the computation time in iterative reconstruction. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.     

ECG-correlated imaging of the heart with subsecond multislice spiral CT

The new spiral multislice computed tomography (CT) scanners and the significant increase in rotation speed offer great potential for cardiac imaging with X-ray CT. We have therefore developed the dedicated cardiac reconstruction algorithms 180 degrees multislice cardio interpolation (MCI) and 180 degrees multislice cardio delta (MCD) and here offer further details and validation. The algorithm 180 degreesMCI is an electrocardiogram (ECG)-correlated filtering (or weighting) algorithm in both the cardiac phase and in the z-position. Effective scan times (absolute temporal resolution) of as low as t(eff) = 56 ms are possible, assuming M 4 simultaneously measured slices at a rotation time of t(rot) = 0.5 s and S < or = d < or = 3S for the table feed d per rotation, where S denotes the collimated slice thickness. The relative temporal resolution w (fraction of the heart cycle depicted in the image), which is the more important parameter in cardiac imaging, will then be as low as w = 12.5% of the heart cycle. The second approach, 180 degreesMCD, is an ECG-correlated partial scan reconstruction of 180 degrees + delta data with delta < phi (fan-angle). Its absolute temporal resolution lies in the order of 250 ms (for the central ray, i.e., for the center of rotation), and the relative temporal resolution w increases with increasing heart rate, e.g., from typically w = 25% at fH = 60 min(-1) to w = 50% at fH = 120 min(-1), assuming again t(rot) = 0.5 s. For validation purposes, we have done simulations of a virtual cardiac motion phantom, measurements of a dedicated cardiac calibration and motion phantom, and we have reconstructed patient data with simultaneously acquired ECG. Both algorithms significantly improve the image quality compared with the standard reconstruction algorithms 180 degrees multislice linear interpolation (MLI) and 180 degrees multislice filtered interpolation (MFI). However, 180 degreesMCI is clearly superior to 180 degreesMCD for all heart rates. This is best illustrated by multiplanar reformations (MPR) or other three-dimensional (3-D) displays of the volume. 180 degreesMCI, due to its higher temporal resolution, is best for spatial and temporal four-dimensional (4-D) tracking of the anatomy. A tunable scanner rotation time to avoid resonance behavior of the heart rate and the scanner's rotation and shorter rotation times would be of further benefit.     

Improved iterative image reconstruction with automatic noise artifact suppression

A method for stabilizing iterative image reconstruction techniques has been developed for improving the image quality of position emission tomography. A damping matrix is introduced, which suppresses noisy correction on a pixel-by-pixel basis, depending on the statistical precision of the iterative correction. The precision is evaluated by comparing a certain number of correction submatrices, each of which is formed from a subset of the projection data. Simulation studies showed that statistical noise is effectively suppressed, while the image of the source object is reconstructed with high resolution, as long as the signal level is higher than the local noise level. In the application to the MLE (maximum likelihood estimator), the minimum RMS error of the image was reduced to 84% for 500 k total counts, and the RMS error increased more slowly with further iterations as compared with the simple MLE. The method was also applied to the FIR (filtered iterative reconstruction) algorithm, and the images were found to be better than those obtained by the convolution backprojection method.     

Gap filling strategies for 3-D-FBP reconstructions of High-Resolution Research Tomograph scans

The High-Resolution Research Tomograph (HRRT) is a dedicated human brain positron emission tomography scanner. Currently available iterative reconstruction algorithms show bias due to nonnegativity constraints. Consequently, implementation of 3-D filtered backprojection (3-D-FBP) is of interest. To apply 3-D-FBP all missing data including those due to gaps between detector heads need to be estimated. The aim of this study was to evaluate various gap filling strategies for 3-D-FBP reconstructions of HRRT data, such as linear and bilinear interpolation or constraint Fourier space gap filling (confosp). Furthermore, missing planes were estimated using segment 0 image data only (noniterative) or by using reconstructed images based on all previous segments (iterative method). Use of bilinear interpolation showed worst correspondence between reconstructed and true activity concentration, especially for small structures. Moreover, phantom data indicated that use of linear interpolation resulted in artifacts in planes located near the edge of the field-of-view. Use of confosp did not show these artifacts. Iterative estimations of the missing planes for $vert {hbox {segments}}vert > 0$ improved image quality at the cost of more computation time. Therefore, use of confosp for filling sinogram gaps with both iterative and noniterative estimation of missing planes are recommended for quantitative 3-D-FBP of HRRT studies.      

X-ray CT metal artifact reduction using wavelets: an application for imaging total hip prostheses

Traditional computed tomography (CT) reconstructions of total joint prostheses are limited by metal artifacts from corrupted projection data. Published metal artifact reduction methods are based on the assumption that severe attenuation of X-rays by prostheses renders corresponding portions of projection data unavailable, hence the "missing" data are either avoided (in iterative reconstruction) or interpolated (in filtered backprojection with data completion; typically, with filling data "gaps" via linear functions). In this paper, we propose a wavelet-based multiresolution analysis method for metal artifact reduction, in which information is extracted from corrupted projection data. The wavelet method improves image quality by a successive interpolation in the wavelet domain. Theoretical analysis and experimental results demonstrate that the metal artifacts due to both photon starving and beam hardening can be effectively suppressed using our method. As compared to the filtered backprojection after linear interpolation, the wavelet-based reconstruction is significantly more accurate for depiction of anatomical structures, especially in the immediate neighborhood of the prostheses. This superior imaging precision is highly advantageous in geometric modeling for fitting hip prostheses.     

Emission Spectral Tomography Reconstruction Based on Maximum Entropy Interpolation

To improve the performance of optical computed tomography (OpCT) reconstruction in the case of limited projection views, maximum entropy (ME) algorithms were proposed and can achieve better results than traditional ones. However, in the discrete iterative process of ME, the variables of the iterative function are continuous. Hence, interpolation methods ought to be used to improve the precision of the iterative function values. Here, a sinc function interpolation approach was adopted in ME algorithm (SINCME) and its reconstruction results for OpCT with limited views were studied using four typical phantoms. Compared results with ME without interpolation, traditional medical CT back-projection algorithm (BP), and iterative algorithm algebraic reconstruction technique (ART) showed that the SINCME algorithm achieved the best reconstruction results. In an experiment of emission spectral tomography reconstruction, SINCME was also adopted to calculate the three-dimensional distribution of physical parameters of a candle flame. The studies of both algorithm and experiment demonstrated that SINCME met the demand of limited-view OpCT reconstruction.     

Comparison of list-mode and DIRECT approaches for time-of-flight PET reconstruction

Early clinical results with time-of-flight (TOF) positron emission tomography (PET) systems have demonstrated the advantages of TOF information in PET reconstruction. Reconstruction approaches in TOF-PET systems include list-mode and binned iterative algorithms as well as confidence-weighted analytic methods. List-mode iterative TOF reconstruction retains the resolutions of the data in the spatial and temporal domains without any binning approximations but is computationally intensive. We have developed an approach [DIRECT (direct image reconstruction for TOF)] to speed up TOF-PET reconstruction that takes advantage of the reduced angular sampling requirement of TOF data by grouping list-mode data into a small number of azimuthal views and co-polar tilts and depositing the grouped events into histo-images, arrays with the sampling and geometry of the final image. All physical effects are included in the system model and deposited in the same histo-image structure. Using histo-images allows efficient computation during reconstruction without ray-tracing or interpolation operations. The DIRECT approach was compared with 3-D list-mode TOF ordered subsets expectation maximization (OSEM) reconstruction for phantom and patient data taken on the University of Pennsylvania research LaBr (3) TOF-PET scanner. The total processing and reconstruction time for these studies with DIRECT without attention to code optimization is approximately 25%-30% that of list-mode TOF-OSEM to achieve comparable image quality. Furthermore, the reconstruction time for DIRECT is independent of the number of events and/or sizes of the spatial and TOF kernels, while the time for list-mode TOF-OSEM increases with more events or larger kernels. The DIRECT approach is able to reproduce the image quality of list-mode iterative TOF reconstruction both qualitatively and quantitatively in measured data with a reduced time.     

基于功率谱AR模型的3D激光虚拟图像重建研究

当前常用的无样本图像重建方法具有分辨率低的弊端,有样本图像重建方法得到的3D激光虚拟图像重建结果有很大误差。为此,提出一种基于功率谱AR模型的3D激光虚拟图像重建方法。建立功率谱AR模型,将Burg技术和自相关法结合在一起,得到合理的AR模型参数。在存在平移、旋转参数的情况下,在功率谱AR模型基础上对图像进行配准处理,先完成旋转步长,然后进行平移估计与步长,以提高旋转配准精度与平移配准精度。将3D激光虚拟图像信息看作希尔伯特空间的元素,依据配准结果,在重建的3D激光虚拟图像重建视觉效果达到要求或连续若干次迭代结果改变情况区域稳定的情况下,结束迭代,实现3D激光虚拟图像重建。经验证,所提方法重建精度最低为97%,重建误差最低为2%,而且重建花费时间较短,证明了本文方法在图像重建方面的优越性,可应用于图像重建的相关工作中。     

基于角谱插值的数字全息在任意斜面的重建方法

为了在任意非平行斜面上重建数字全息像,提出了一种基于角谱旋转变换和插值的数字处理方法,用角谱衍射理论进行了分析,给出了正反旋转两种数字插值方法,基于旋转变换信息量不变的原则分析了倾斜面上的抽样间隔取值范围,其大小取决于斜面带宽和全息图空间带宽积大小。实现了在71°倾斜物面上的全息重建,消除了倾斜造成的局部离焦现象,同时验证了算法在斜面上抽样间隔取值范围。     

条纹管激光成像雷达目标三维重构快速算法

实现目标实时动态追踪与识别是条纹管激光成像雷达中亟待解决的问题,针对条纹管激光成像雷达峰值探测三维重构算法运算时间长的问题,提出一种抽样插值目标三维重构算法,以一定的抽样率对条纹图像等间隔抽样并插值运算,再进行峰值特征提取运算。当抽样率为4%时,对于探测距离为706 m的目标,抽样双线性插值重构法的运算速度比原重构法提高了2.3倍,三维重构矩阵的相关系数约为0.99;抽样最近邻插值重构法的运算速度比原重构法提高了3.5倍,三维重构矩阵的相关系数约为0.98。实验结果表明所提算法可以提高目标三维重构速度,并且目标条纹图像帧幅数越多,目标三维重构速度改善效果越好。     

基于小波域滤波的迭代硬阈值压缩感知重构

图像压缩感知迭代重构算法主要采用迭代阈值法解决信号的重构问题,但是迭代阈值法仅仅利用变换系数进行阈值处理,并未考虑系数的邻域统计特性,导致重构性能不高。提出一种基于小波域滤波的迭代硬阈值迭代算法,利用小波域系数的邻域统计特性修订迭代硬阈值重构算法的代价函数,进行两步迭代收缩,并在迭代中用小波域滤波除去其中的重构噪声。实验结果表明,在相同的观测数据下,相比已有的经典算法,新算法的重构图像质量较高,并且可以获得快速的重构速度。     

三维B超医学图像插值重构研究

本文讨论了图像插值在超声图像三维重建中的应用,着重于在进行可视化之前如何利用合适的插值算法把三维规则不均匀数据场转换为三维规则均匀数据场,提出有偏距离加权同心插值,并从峰值信噪比、归一化互相关系数和运算速度等几个方面与线性插值,三次插值以及高斯插值等三种较典型的插值算法进行了比较。     

A generalized interpolative vector quantization method for jointlyoptimal quantization, interpolation, and binarization of textimages

This paper presents an approach for the effective combination of interpolation with binarization of gray level text images to reconstruct a high resolution binary image from a lower resolution gray level one. We study two nonlinear interpolative techniques for text image interpolation. These nonlinear interpolation methods map quantized low dimensional 2x2 image blocks to higher dimensional 4x4 (possibly binary) blocks using a table lookup operation. The first method performs interpolation of text images using context-based, nonlinear, interpolative, vector quantization (NLIVQ). This system has a simple training procedure and has performance (for gray-level high resolution images) that is comparable to our more sophisticated generalized interpolative VQ (GIVQ) approach, which is the second method. In it, we jointly optimize the quantizer and interpolator to find matched codebooks for the low and high resolution images. Then, to obtain the binary codebook that incorporates binarization with interpolation, we introduce a binary constrained optimization method using GIVQ. In order to incorporate the nearest neighbor constraint on the quantizer while minimizing the distortion in the interpolated image, a deterministic-annealing-based optimization technique is applied. With a few interpolation examples, we demonstrate the superior performance of this method over the NLIVQ method (especially for binary outputs) and other standard techniques e.g., bilinear interpolation and pixel replication.     

Enhanced resolution in Sar/ISAR imaging using iterative sidelobe apodization.

Resolution enhancement techniques in radar imaging have attracted considerable interest in recent years. In this work, we develop an iterative sidelobe apodization technique and investigate its applications to synthetic aperture radar (SAR) and inverse SAR (ISAR) image processing. A modified noninteger Nyquist spatially variant apodization (SVA) formulation is proposed, which is applicable to direct iterative image sidelobe apodization without using computationally intensive upsampling interpolation. A refined iterative sidelobe apodization procedure is then developed for image-resolution enhancement. Examples using this technique demonstrate enhanced image resolution in various applications, including airborne SAR imaging, image processing for three-dimensional interferometric ISAR imaging, and foliage-penetration ultrawideband SAR image processing.     

A general class of preconditioners for statistical iterativereconstruction of emission computed tomography

A major drawback of statistical iterative image reconstruction for emission computed tomography is its high computational cost. The ill-posed nature of tomography leads to slow convergence for standard gradient-based iterative approaches such as the steepest descent or the conjugate gradient algorithm. Here, new theory and methods for a class of preconditioners are developed for accelerating the convergence rate of iterative reconstruction. To demonstrate the potential of this class of preconditioners, a preconditioned conjugate gradient (PCG) iterative algorithm for weighted least squares reconstruction (WLS) was formulated for emission tomography. Using simulated positron emission tomography (PET) data of the Hoffman brain phantom, it was shown that the convergence rate of the PCG can reduce the number of iterations of the standard conjugate gradient algorithm by a factor of 2-8 times depending on the convergence criterion