X-射线工业CT射束硬化校正中噪声的抑制

X-射线工业CT中,传统的线性化(ConventionalLinearization,CL)校正法去除射束硬化影响时,会放大投影的噪声,进而降低CT图像的信噪比(SNR)。为克服该点不足,提出了一种改进的线性化(ImprovedLinearization,IL)校正法。该方法基于投影噪声的特点,设计了一种自适应滤波器;利用该滤波器从原始投影数据中提取其噪声,求得由噪声引起的校正误差;根据该误差对校正结果进行修正以抑制投影噪声的放大。通过不同管电压和被检材质,对IL校正法进行了验证。实验结果表明,IL校正法能去除射束硬化的影响,并能有效地抑制校正过程中投影噪声的放大。与CL校正法相比,IL校正的CT图像SNR提高了约6倍。     

Wavelet‐based denoising and its impact on analytical SPECT reconstruction with nonuniform attenuation compensation

In single photon emission computed tomography (SPECT), the nonstationary Poisson noise in projection data (sinogram) is a major cause of compromising the quality of reconstructed images. To improve the quality, we must suppress the Poisson noise in the sinogram before or during image reconstruction. However, the conventional space or frequency domain denoising methods will likely remove some information that is very important for accurate image reconstruction, especially for analytical SPECT reconstruction with compensation for nonuniform attenuation. As a time‐frequency analysis tool, wavelet transform has been widely used in the signal and image processing fields and demonstrated its powerful functions in the application of denoising. In this article, we studied the denoising abilities of wavelet‐based denoising method and the impact of the denoising on analytical SPECT reconstruction with nonuniform attenuation. Six popular wavelet‐based denoising methods were tested. The reconstruction results showed that the Revised BivaShrink method with complex wavelet is better than others in analytical SPECT reconstruction with nonuniform attenuation compensation. Meanwhile, we found that the effect of the Anscombe transform for denoising is not significant on the wavelet‐based denoising methods, and the wavelet‐based de‐noise methods can obtain good denoising result even if we do not use Anscombe transform. The wavelet‐based denoising methods are the good choice for analytical SPECT reconstruction with compensation for nonuniform attenuation. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 36–43, 2013     

Similarities and differences in radiation therapy optimization and tomographic reconstruction

Modern photon radiotherapy optimization methods require the use of a number of nonuniform dose distributions incident on the tumor. From this point of view, radiotherapy optimization has strong similarities with the reconstruction problem in tomographic imaging. In general, the image reconstruction problem is simpler because in the absence of noise and with sufficiently many projections and exact solution always exists. However, it is in general impossible by external beam irradiation to produce an arbitrary desired dose distribution in the patient. This is primarily because the order of events from physical collection of projection data to reconstruction theory is reversed in therapy optimization, starting with the theory and ending with physical irradiation, where negative dose delivery is impossible. Despite this fundamental problem, many approximate image reconstruction methods work quite well for therapy optimization even though strict optimization requires radiobiological models and the finest external beam radiation tool available: the pencil beam.     

Sparse‐view statistical iterative head CT image reconstruction via joint regularization

It is a significant challenge to accurately reconstruct medical computed tomography (CT) images with important details and features. Reconstructed images always suffer from noise and artifact pollution because the acquired projection data may be insufficient or undersampled. In reality, some “isolated noise points” (similar to impulse noise) always exist in low‐dose CT projection measurements. Statistical iterative reconstruction (SIR) methods have shown greater potential to significantly reduce quantum noise but still maintain the image quality of reconstructions than the conventional filtered back‐projection (FBP) reconstruction algorithm. Although the typical total variation‐based SIR algorithms can obtain reconstructed images of relatively good quality, noticeable patchy artifacts are still unavoidable. To address such problems as impulse‐noise pollution and patchy‐artifact pollution, this work, for the first time, proposes a joint regularization constrained SIR algorithm for sparse‐view CT image reconstruction, named “SIR‐JR” for simplicity. The new joint regularization consists of two components: total generalized variation, which could process images with many directional features and yield high‐order smoothness, and the neighborhood median prior, which is a powerful filtering tool for impulse noise. Subsequently, a new alternating iterative algorithm is utilized to solve the objective function. Experiments on different head phantoms show that the obtained reconstruction images are of superior quality and that the presented method is feasible and effective.     

A study of errors due to reconstruction filters in computed tomography

In the summation convolution backprojection method of image reconstruction in computed tomography, the final image accuracy depends on the convolution filter used. Filters are designed to attenuate high spatial frequencies when noisy projection data are used. This paper explores the differences between the images reconstructed using a range of filters, and compares the results with the case of the ramp filter that provides the “best” image for ideal, noise-free, projection data. It is shown that systematic errors between these images and the best image exist, and that these errors are related to the second differential of the reconstruction filter with respect to spatial frequency. This error determination may be used to correct computed tomography images that have been reconstructed using inappropriate filters, and this theory is tested using noise-free projection data from two computer simulated images. It is shown that the corrected images are far closer to the original images.     

A Study of Errors due to Reconstruction Filters in Computed Tomography

Abstract

In the summation convolution backprojection method of image reconstruction in computed tomography, the final image accuracy depends on the convolution filter used. Filters are designed to attenuate high spatial frequencies when noisy projection data are used. This paper explores the differences between the images reconstructed using a range of filters, and compares the results with the case of the ramp filter that provides the “best” image for ideal, noise-free, projection data. It is shown that systematic errors between these images and the best image exist, and that these errors are related to the second differential of the reconstruction filter with respect to spatial frequency. This error determination may be used to correct computed tomography images that have been reconstructed using inappropriate filters, and this theory is tested using noise-free projection data from two computer simulated images. It is shown that the corrected images are far closer to the original images.     

超声反射CT在水下物体成像中的应用

本文重点介绍了沿平面扫描成像，提出了修正扫描起始点位置以及换能器孔径影响的一种方法，得到较好的实验结果。     

The integrated acceleration of the Chambolle-Pock algorithm applied to constrained TV minimization in CT image reconstruction

Background and Objective: The constrained, total variation (TV) minimization algorithm has been applied in computed tomography (CT) for more than 10 years to reconstruct images accurately from sparse-view projections. Chambolle-Pock (CP) algorithm framework has been used to derive the algorithm instance for the constrained TV minimization programme. However, the ordinary CP (OCP) algorithm has slower convergence rate and each iteration is also time-consuming. Thus, we investigate the acceleration approaches for achieving fast convergence and high-speed reconstruction. Methods: To achieve fast convergence rate, we propose a new algorithm parameters setting approach for OCP. To achieve high-speed reconstruction in each iteration, we use graphics processing unit (GPU) to speed-up the two time-consuming operations, projection and backprojection. Results: We evaluate and validate our acceleration approaches via two-dimensional (2D) reconstructions of a low-resolution Shepp–Logan phantom from noise-free data and a high-resolution Shepp–Logan phantom from noise-free and noisy data. For the three-specific imaging cases considered here, the convergence process are speeded up for 89, 9 and 81 times, and the reconstruction in each iteration maybe speeded up for 120, 340 and 340 times, respectively. Totally, the whole reconstructions for the three cases are speeded up for about 10,000, 3060 and 27,540 times, respectively. Conclusions: The OCP algorithm maybe tremendously accelerated by use of the improved algorithm parameters setting and use of GPU. The integrated acceleration techniques make the OCP algorithm more practical in the CT reconstruction area.     

An adaptive dynamic combined energy minimization model for few‐view computed tomography reconstruction

Recently, the potential harm of electromagnetic radiation used in computed tomography (CT) scanning has been paid much attention to. This makes the few‐view CT reconstruction become an important issue in medical imaging. In this article, an adaptive dynamic combined energy minimization model is proposed for few‐view CT reconstruction based on the compress sensing theory. The L2 energy of the image gradient and the total variation (TV) energy are combined, and the working regions of them are separated adaptively with a dynamic threshold. With the proposed model, the TV model's disadvantageous tendency of uniformly penalize the image gradient irrespective of the underlying image structures is overcome. Numerical experiments of the proposed model are performed with various insufficient data problems in fan‐beam CT and suggest that both the reconstruction speed and quality of the results are generally improved. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 44–52, 2013.     

投影幅数和采样间隔对 CT 重建能力的影响

目的 探讨投影幅数和采样间隔对CT重建能力的影响程度，为图像重建时选择参数提供依据。方法 通过计算机仿真测定参数值不同时CT重建图像的能力。结果 CT的图像重建能力与投影幅数和采样间隔的大小密切相关。结论 通过增大抽影幅数或减小采样间隔可以提高CT的图像重建能力。     

一种通用CT图像硬化校正算法研究

为消除射束硬化对工业CT(Computed Tomography)重建质量的影响．从多色系统参数校正算法推导出发,将多色投影数据通过多项式运算转化为单色投影数据,同时利用数字图像趋势项产生及消除的基本原理,结合小波滤波方法,提出了一种与被照射工件的材料和结构无关,而且能够适用于整个工业射线能量使用范围的综合校正方法,并给出了获得多色系统参数的实验方法．用该方法对受硬化影响的模拟图像及实际图像进行硬化校正,结果表明改方法不需要准确的先验知识且校正效果良好,具有通用性．     

Super resolution in CT

The general framework of super resolution in computed tomography (CT) system is introduced. Two data acquisition ways before or after the reconstruction respectively are described. Three models including the sinogram model, the in‐plane model and the z‐axis model, are addressed to adapt super resolution to CT system. The improved iterative back projection algorithm is used in this work. Experimental results based on simulated data, GE performance phantom scanned by GE LightSpeed VCT system, one patient volunteer scanned by TOSHIBA Aquilion system, and a special experimental apparatus demonstrate that super resolution is effective to improve the resolution of CT images. The sinogram model is suitable for future CT system; the in‐plane model is restricted to some special clinical diagnoses; and the z‐axis model is practicable for current general clinical CT images. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 92–101, 2015     

彩色伪随机编码闪光投影系统的建模及其标定

为实现仅用一幅图象在真正的三维欧氏空间重构三维场景,尤其是动态的三维场景,系统需要对彩色伪随机编码闪光投影系统进行建模和预标定。当系统参数改变后,利用伪随机编码图案的几何约束,不需重新标定,可实现自适应重构三维场景。通过对投影仪像质的的无畸变性分析,用线性模型对投影仪成像过程进行建模,并提出一种高精度的投影系统直接标定方法,通过测出靶标上各投影编码特征点在空间的三维齐次坐标,求出内外参数实现了对投影仪的预标定。标定精度达到0.1单元格,欧氏重构结果较为理想。     

Filling the Radon domain in computed tomography by local convex combination

Radon data interpolation is a necessary procedure in computed tomography (CT), especially for reconstruction from divergent beam scanning. In a polar-grid representation, the Radon data of a fanbeam projection are populated on an arc, rather on a radial line. Collectively, the Radon data generated from a fanbeam CT system are unevenly populated: The population becomes sparser as the polar distance increases. In CT reconstruction, the Fourier central slice theorem requires a radial scanline full of Radon data. Therefore the vacant entries of a scanline must be filled by interpolation. In addition, interpolation is also required in polar-to-Cartesian conversion. In this paper we propose a practical interpolation technique for filling the vacant entries by local convex combination. It is a linear interpolant that generates a value for a grid point from the available data lying in its neighborhood, by a weighted average, with the weights corresponding to the inverse distances. In fact, the linear convex combination serves as a general flat-smoothing operation in filling a vacancy. Specifically, this technique realizes a variety of linear interpolations, including nearest-neighbor replication, two-point collinear, three-point triangulation, and four-point quadrilateral, and local extrapolation, in a unified framework. Algorithms and a simulation demonstration are provided.     

Tomographic reconstruction of three-dimensional refractive index fields by use of a regularized phase-tracking technique and a polynomial approximation method

We present a complete data-processing procedure for quantitative reconstruction of three-dimensional (3D) refractive index fields from limited multidirectional interferometric data. The proposed procedure includes two parts: (1) extraction of the projection data from limited multidirectional interferograms by a regularized phase-tracking technique and wavefront fitting and (2) reconstruction of the 3D refractive index fields by a modified polynomial approximation method. It has been shown that the procedure gives a satisfactory solution to the reconstruction issue in interferometric tomography, from the initial projection data extraction to the final image reconstruction. Computer simulation and experimental results are both presented.     

Impact of measurement precision and noise on superresolution image reconstruction

The performance of uniform and nonuniform detector arrays for application to the PANOPTES (processing arrays of Nyquist-limited observations to produce a thin electro-optic sensor) flat camera design is analyzed for measurement noise environments including quantization noise and Gaussian and Poisson processes. Image data acquired from a commercial camera with 8 bit and 14 bit output options are analyzed, and estimated noise levels are computed. Noise variances estimated from the measurement values are used in the optimal linear estimators for superresolution image reconstruction.     

Bayesian reconstruction for SPECT: Validation with monte carlo simulation,experimental phantom,and real patient data

A method for Bayesian image reconstruction from projections is applied to Monte Carlo simulation, experimental phantom, and real patient data from a SPECT acquisition system. This statistical image reconstruction method has three distinct aspects: (1) it uses a priori information about image density distribution of a multinomial process; (2) it considers a spatial correlation of nearby image elements; and (3) it incorporates the Poisson nature of photon detection fluctuation. The Monte Carlo simulation data are generated by computer codes for selected mathematical phantoms containing hot and cold rods. The experimental phantom data are acquired with a Triad SPECT system using radioactive phantoms containing hot and cold rods. The real patient data are obtained from a patient brain scan using the Triad SPECT system. A parallel beam geometry is used. The data are acquired from 120 projection angles uniformly distributed from 0 to 360 degrees. At each projection angle, a 128 X 128 projection image is measured. This 128 X 128 projection samples are equally spaced along the axis of detector rotation and perpendicular to the axis, respectively. Each image slice is reconstructed using a 128 X 128 pixel array. Comparisons between this Bayesian method and maximum likelihood method and filtered backprojection method are give. An improvement in noise suppression is demonstrated using the Bayesian method while image resolution is preserved.     

Bootstrap method for nonlinear filtering of EM-ML reconstructions of PET images

Reconstructions of positron emission tomography images are obtained with the iterative expectation maximization (EM) algorithm. The EM algorithm is halted according to a cross-validation procedure. For the cases studied, this method yields a reconstruction with high variability about its expected value. The variability of the reconstruction about its expected value is reduced by computing its bootstrap expectation. Based on the reconstruction computed from the observed projection data, synthetic projection data sets are simulated. Reconstructions of the synthetic projection data sets are averaged to yield the bootstrap expectation. This bootstrap procedure is a nonlinear filtering method. The procedure is automatic; no smoothing kernel or bandwidth parameter need be specified. For simulated data, the bootstrap method yielded somewhat sharper reconstructions than did an optimized linear approach. The method is applied to real data from a fluorodeoxiglucose study of the human brain. Near the boundaries, the resampling procedure yielded a sharper reconstruction. © 1996 John Wiley & Sons, Inc.     

Non-interferometric methods of phase estimation for application in optical tomography

Abstract

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.