基于全变差重构算法的数字全息研究

为了消除传统算法对数字全息重构过程中会出现0级像、共轭像干扰的问题,将压缩感知理论与数字全息图再现相结合,提出了基于全变差的两步迭代收缩阈值重构算法（TwIST）,并应用于数字全息图压缩感知全息图重建。 TwIST算法根据重构成分的特点增加正则约束,对相应的形态进行调整,在满足全变差最小的特性的基础上进行重构,提高了重构全息图的质量。结果表明,TwIST算法可以对数字全息图稀疏重建,利用35%的部分全息图数据进行图像重构,重构图像峰值信噪比为36.46dB,且没有0级像和共轭像等干扰。该研究结果对实现计算全息的实时性具有重要的意义。     

A Fast Implementation of a Minimum Variance Estimator for Computerized Tomography Image Reconstruction

Most present day computerized tomography (CT) systems are based on reconstruction algorithms that produce only approximate deterministic solutions of the image reconstruction problem. These algorithms yield reasonable results in cases of low measurement noise and regular measurement geometry, and are considered acceptable because they require far less computation and storage than more powerful algorithms that can yield near optimal results. However, the special geometry of the CT image reconstruction problem can be used to reduce by orders of magnitude the computation required for optimal reconstruction methods, such as the minimum variance estimator. These simplifications can make the minimum variance technique very competitive with well-known approximate techniques such as the algebraic reconstruction technique (ART) and convolution-back projection. The general minimum variance estimator for CT is first presented, and then a fast algorithm is described that uses Fourier transform techniques to implement the estimator for either fan beam or parallel beam geometries. The computational requirements of these estimators are examined and compared to other techniques. To allow further comparison with the commonly used convolution-back projection method, a representation of the fast algorithm is derived which allows its equivalent convolving function to be examined. Several examples are presented.     

代数迭代法在激光反射断层成像目标重构中的应用

为了提高激光反射断层成像目标重构的图像质量,在目前激光反射断层成像普遍采用反投影算法重构图像的基础上,将CT成像中常用的迭代重建算法引入到激光反射断层成像的图像重构过程中。分析了反投影算法中的直接反投影、R-L和S-L滤波反投影以及迭代重建算法在图像重构中的性能特性。进行了仿真和外场实验,结果表明:在直接反投影基础上添加了滤波器的反投影算法在减小误差和抑噪能力上都明显提高;另外相比于反投影算法,代数迭代重建算法表现出更好的重建质量,且具有更强的抑噪性能。     

Iterative Reconstruction?Reprojection: An Algorithm for Limited Data Cardiac-Computed Tomography

Cardiac X-ray computed tomography (CT) has been limited due to scanning times which are considerably longer (1 s) than required to resolve the beating heart (0.1 s). The otherwise attractive convolution-backprojection algorithm is not suited for CT image reconstruction from measurements comprising an incomplete set of projection data. In this paper, an iterative reconstruction-reprojection (IRR) algorithm is proposed for limited projection data CT image reconstruction. At each iteration, the missing views are estimated based on reprojection, which is a software substitute for the scanning process. The standard fan-beam convolution-backprojection algorithm is then used for image reconstruction. The proposed IRR algorithm enables the use of convolution-backprojection in limited angle of view and in limited field of view CT cases. The potential of this method for cardiac CT reconstruction is demonstrated using computer simulated data.     

CT重建中滤波器的设计与实现

CT重建算法主要包括解析法和迭代法,因为解析法重建速度快,所需数据存储空间较小,所以在实际中的应用更为广泛。在商业CT中,几乎毫无例外地采用卷积反投影重建算法,滤波算子是这一算法中一个非常重要的部分。目前CT重建算法的研究热点一方面是改进算法提高图像重建速度,另一研究内容主要集中在预处理滤波器的设计与实现,以便得到边缘清晰、平滑及噪声较少的图像。本文从滤波器的设计定义出发,分析讨论了它的性质,并在此基础上提出来一种新的滤波器。经过实验验证,新的滤波器取得比较理想的结果。     

Suppression of Metal Artifacts in CT Using a Reconstruction Procedure That Combines MAP and Projection Completion

Metal implants such as hip prostheses and dental fillings produce streak and star artifacts in the reconstructed computed tomography (CT) images. Due to these artifacts, the CT image may not be diagnostically usable. A new reconstruction procedure is proposed that reduces the streak artifacts and that might improve the diagnostic value of the CT images. The procedure starts with a maximum a posteriori (MAP) reconstruction using an iterative reconstruction algorithm and a multimodal prior. This produces an artifact-free constrained image. This constrained image is the basis for an image-based projection completion procedure. The algorithm was validated on simulations, phantom and patient data, and compared with other metal artifact reduction algorithms.      

一种基于压缩感知的迭代重建算法

迭代重建算法是一种经典的CT图像重建算法,适合于不完全投影数据的图像重建,其缺点是重建速度慢。为提高图像重建的质量和速度,文中利用压缩感知理论提出了一种改进的基于图像全变差最小的迭代重建算法。该算法在迭代的不同阶段对迭代初始值做不同处理,并在每次迭代结束后采用梯度下降法调整全变差。实验结果表明,该算法不但提高了图像重建质量,同时也加快了迭代图像的收敛速度。     

利用GPU实现单层螺旋CT的三维图像重建

CT数据的获取过程和CT图像的重建过程与图形学的渲染过程极其相似,因此利用图形处理器(GPU)来加速CT重建算法成为了近年来CT研究的热点之一.本文根据单层螺旋CT数据的特点,构造了"平行-扇束"投影模式,实现了基于GPU的单层螺旋CT的三维图像重建算法.数值实验表明,与CPU上的分层重建相比重建速度提高10倍以上.     

Supervised‐learning‐based algorithm for color image compression

A correlation exists between luminance samples and chrominance samples of a color image. It is beneficial to exploit such interchannel redundancy for color image compression. We propose an algorithm that predicts chrominance components Cb and Cr from the luminance component Y. The prediction model is trained by supervised learning with Laplacian‐regularized least squares to minimize the total prediction error. Kernel principal component analysis mapping, which reduces computational complexity, is implemented on the same point set at both the encoder and decoder to ensure that predictions are identical at both the ends without signaling extra location information. In addition, chrominance subsampling and entropy coding for model parameters are adopted to further reduce the bit rate. Finally, luminance information and model parameters are stored for image reconstruction. Experimental results show the performance superiority of the proposed algorithm over its predecessor and JPEG, and even over JPEG‐XR. The compensation version with the chrominance difference of the proposed algorithm performs close to and even better than JPEG2000 in some cases.     

基于TwIST-TV 约束的图像去模糊方法

传统的基于频域和小波域的去模糊算法所得的复原图像总是存在比较明显的边缘振铃及模糊效应,而较为有效的空域迭代优化去模糊算法速度通常比较慢。为了解决上述问题,提出了基于二步迭代阈值收缩（TwIST）与总变分（TV）约束相结合的图像去模糊算法（TwIST-TV）。首先在去模糊目标函数中加入对图像的TV 正则化约束,其次在对图像小波系数的每次二步迭代之前,加入对图像的TV 优化去噪约束,最后迭代获取去模糊图像。实验结果表明:相对于基于频域和小波域的模糊图像恢复算法,TwIST-TV 能有效抑制边缘模糊和振铃效应,复原图像的信噪比（SNR）、峰值信噪比（PSNR）高出1~7 dB,平均结构相似度指标（MSSIM）可高出0.05,相对于空域解卷积算法在保证求解精度相当的情况下具备6 倍以上的速度优势。     

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。     

Reconstruction Algorithm for Fan Beam with a Displaced Center-of-Rotation

A convolutional backprojection algorithm is derived for a fan beam geometry that has its center-of-rotation displaced from the midline of the fan beam. In single photon emission computed tomography (SPECT), where a transaxial converging collimator is used with a rotating gamma camera, it is difficult to precisely align the collimator so that the mechanical center-of-rotation is colinear with the midline of the fan beam. A displacement of the center-of-rotation can also occur in X-ray CT when the X-ray source is mispositioned. Standard reconstruction algorithms which directly filter and backproject the fan beam data without rebinning into parallel beam geometry have been derived for a geometry having its center-of-rotation at the midline of the fan beam. However, in the case of a misalignment of the center-of-rotation, if these conventional reconstruction algorithms are used to reconstruct the fan beam projections, structured artifacts and a loss of resolution will result. We illustrate these artifacts with simulations and demonstrate how the news algorithm corrects for this misalignment. We also show a method to estimate the parameters of the fan beam geometry including the shift in the center-of-rotation.     

Nearly optimal linear transceiver design for amplify‐and‐forward MIMO multiple‐relay systems under MMSE criterion

In this paper, we consider amplify‐and‐forward multiple‐input multiple‐output multiple‐relay systems, where all the nodes have multiple antennas. For enhancing link reliability, we address the problem of designing optimal linear transceiver to minimize the mean squared error (MSE) of symbol estimations subject to the total relay transmit power constraint. This problem is highly complex and has not been solved in the literature. We first simplify this optimization problem to one that takes a singular value vector and a unitary matrix as optimization variables. Then based on the analyses for the simplified problem, we develop an iterative algorithm consisting of one boundary optimization and one unitary matrix constrained optimization. We show analytically that the proposed iterative algorithm always converges, and the MSE is monotonically decreasing from one iteration to the next. Finally, numerical results demonstrate the nearly optimal performance of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

由投影重建图像的对称块迭代算法

由投影重建图像的迭代算法有抑制噪声等优点,但其投影矩阵的计算量大、影响重建速度。该文利用投影线存在的几何对称结构,引入图像重建的对称块迭代算法(简写为SB-IRT),简化了投影矩阵系数的计算,调整了迭代算法的顺序相关性。对于模拟和实测数据进行了图像重建试验,结果表明:与常规算法比较,该文提出的对称块迭代算法重建速度快,重建图像精度高。     

Fast l₁-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime

We present l?-SPIRiT, a simple algorithm for auto calibrating parallel imaging (acPI) and compressed sensing (CS) that permits an efficient implementation with clinically-feasible runtimes. We propose a CS objective function that minimizes cross-channel joint sparsity in the wavelet domain. Our reconstruction minimizes this objective via iterative soft-thresholding, and integrates naturally with iterative self-consistent parallel imaging (SPIRiT). Like many iterative magnetic resonance imaging reconstructions, l?-SPIRiT's image quality comes at a high computational cost. Excessively long runtimes are a barrier to the clinical use of any reconstruction approach, and thus we discuss our approach to efficiently parallelizing l?-SPIRiT and to achieving clinically-feasible runtimes. We present parallelizations of l?-SPIRiT for both multi-GPU systems and multi-core CPUs, and discuss the software optimization and parallelization decisions made in our implementation. The performance of these alternatives depends on the processor architecture, the size of the image matrix, and the number of parallel imaging channels. Fundamentally, achieving fast runtime requires the correct trade-off between cache usage and parallelization overheads. We demonstrate image quality via a case from our clinical experimentation, using a custom 3DFT spoiled gradient echo (SPGR) sequence with up to 8× acceleration via Poisson-disc undersampling in the two phase-encoded directions.     

A moment-based variational approach to tomographic reconstruction

We describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood (ML) estimates of its orthogonal moments. We show how these estimated moments and their (correlated) error statistics can be computed directly, and in a linear fashion from given noisy and possibly sparse projection data. Moreover, thanks to the consistency properties of the Radon transform, this two-step approach (moment estimation followed by image reconstruction) can be viewed as a statistically optimal procedure. Furthermore, by focusing on the important role played by the moments of projection data, we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments. Taking advantage of this connection, our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data. We show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem. We show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back-projection (FBP) algorithm.     

Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry

A new analytical three-dimensional cone beam reconstruction algorithm is presented for truncated spherical detection geometry. The basic idea of the proposed algorithm is the formation of spatially invariant 3D blurred back-projected volumetric image by the use of the weighted backprojection of cone beam projection data and subsequent 3D filtering using an acceptance angle dependent rho filter. The backprojection weighting function is calculated on the basis of each given geometrical condition, i.e. detection geometry or degree of truncation, position of cone beam apex, and backprojection point. The proposed algorithm is derived analytically and is computationally efficient. Performance of the algorithm is evaluated by the reconstruction of 3D volumetric images using simulated data from arbitrarily truncated spherical detector geometries.     

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.     

GPU-Based Iterative Medical CT Image Reconstructions

The algebraic reconstruction technique (ART) is an iterative algorithm for CT (i.e., computed tomography) image reconstruction that delivers better image quality with less radiation dosage than the industry-standard filtered back projection (FBP). However, the high computational cost of ART requires researchers to turn to high-performance computing to accelerate the algorithm. Alas, existing approaches for ART suffer from inefficient design of compressed data structures and computational kernels on GPUs. Thus, this paper presents our CUDA-based CT image reconstruction tool based on the algebraic reconstruction technique (ART) or cuART. It delivers a compression and parallelization solution for ART-based image reconstruction on GPUs. We address the under-performing, but popular, GPU libraries, e.g., cuSPARSE, BRC, and CSR5, on the ART algorithm and propose a symmetry-based CSR format (SCSR) to further compress the CSR data structure and optimize data access for both SpMV and SpMV_T via a column-indices permutation. We also propose sorting-based global-level and sorting-free view-level blocking techniques to optimize the kernel computation by leveraging different sparsity patterns of the system matrix. The end result is that cuART can reduce the memory footprint significantly and enable practical CT datasets to fit into a single GPU. The experimental results on a NVIDIA Tesla K80 GPU illustrate that our approach can achieve up to 6.8x, 7.2x, and 5.4x speedups over counterparts that use cuSPARSE, BRC, and CSR5, respectively.

     

Tomographic reconstruction using an adaptive tetrahedral mesh defined by a point cloud

Medical images in nuclear medicine are commonly represented in three dimensions as a stack of two-dimensional images that are reconstructed from tomographic projections. Although natural and straightforward, this may not be an optimal visual representation for performing various diagnostic tasks. A method for three-dimensional (3-D) tomographic reconstruction is developed using a point cloud image representation. A point cloud is a set of points (nodes) in space, where each node of the point cloud is characterized by its position and intensity. The density of the nodes determines the local resolution allowing for the modeling of different parts of the image with different resolution. The reconstructed volume, which in general could be of any resolution, size, shape, and topology, is represented by a set of nonoverlapping tetrahedra defined by the nodes. The intensity at any point within the volume is defined by linearly interpolating inside a tetrahedron from the values at the four nodes that define the tetrahedron. This approach creates a continuous piecewise linear intensity over the reconstruction domain. The reconstruction provides a distinct multiresolution representation, which is designed to accurately and efficiently represent the 3-D image. The method is applicable to the acquisition of any tomographic geometry, such as parallel-, fan-, and cone-beam; and the reconstruction procedure can also model the physics of the image detection process. An efficient method for evaluating the system projection matrix is presented. The system matrix is used in an iterative algorithm to reconstruct both the intensity and location of the distribution of points in the point cloud. Examples of the reconstruction of projection data generated by computer simulations and projection data experimentally acquired using a Jaszczak cardiac torso phantom are presented. This work creates a framework for voxel-less multiresolution representation of images in nuclear medicine.