Reconstruction algorithm for polychromatic CT imaging: application to beam hardening correction

This paper presents a new reconstruction algorithm for both single- and dual-energy computed tomography (CT) imaging. By incorporating the polychromatic characteristics of the X-ray beam into the reconstruction process, the algorithm is capable of eliminating beam hardening artifacts. The single energy version of the algorithm assumes that each voxel in the scan field can be expressed as a mixture of two known substances, for example, a mixture of trabecular bone and marrow, or a mixture of fat and flesh. These assumptions are easily satisfied in a quantitative computed tomography (QCT) setting. The authors have compared their algorithm to three commonly used single-energy correction techniques. Experimental results show that their algorithm is much more robust and accurate. The authors have also shown that QCT measurements obtained using their algorithm are five times more accurate than that from current QCT systems (using calibration). The dual-energy mode does not require any prior knowledge of the object in the scan field, and can be used to estimate the attenuation coefficient function of unknown materials. The authors have tested the dual-energy setup to obtain an accurate estimate for the attenuation coefficient function of K₂ HPO₄ solution     

Volume rendering in the presence of partial volume effects

In tomographic imagery, partial volume effects (PVEs) cause several artifacts in volume renditions. In X-ray computed tomography (CT), for example, soft-tissue-like pseudo structures appear in bone-to-air and bone-to-fat interfaces. Further, skin, which is identical to soft tissue in terms of CT number, obscures the rendition of the latter. The purpose of this paper is to demonstrate these phenomena and to provide effective solutions that yield significantly improved renditions. We introduce two methods that detect and classify voxels with PVE in X-ray CT. Further, a method is described to automatically peel skin so that PVE-resolved renditions of bone and soft tissue reveal considerably more detail. In the first method to address PVE, called the fraction measure (FM) method, the fraction of each tissue material in each voxel v is estimated by taking into account the intensities of the voxels neighboring v. The second method, called uncertainty principle (UP) method, is based on the following postulate (Saha and Udupa, 2001): In any acquired image, voxels with the highest uncertainty occur in the vicinity of object boundaries. The removal of skin is achieved by means of mathematical morphology. Volume renditions have been created before and after applying the methods for several patient CT datasets. A mathematical phantom experiment involving different levels of PVE has been conducted by adding different degrees of noise and blurring. A quantitative evaluation is done utilizing the mathematical phantom and clinical CT data wherein an operator carefully masked out voxels with PVE in the segmented images. All results have demonstrated the enhanced quality of display of bone and soft tissue after applying the proposed methods. The quantitative evaluations indicate that more than 98% of the voxels with PVE are removed by the two methods and the second method performs slightly better than the first. Further, skin peeling vividly reveals fine details in the soft tissue structures.     

Super-resolution registration using tissue-classified distance fields

We present a method for registering the position and orientation of bones across multiple computed-tomography (CT) volumes of the same subject. The method is subvoxel accurate, can operate on multiple bones within a set of volumes, and registers bones that have features commensurate in size to the voxel dimension. First, a geometric object model is extracted from a reference volume image. We use then unsupervised tissue classification to generate from each volume to be registered a super-resolution distance field--a scalar field that specifies, at each point, the signed distance from the point to a material boundary. The distance fields and the geometric bone model are finally used to register an object through the sequence of CT images. In the case of multiobject structures, we infer a motion-directed hierarchy from the distance-field information that allows us to register objects that are not within each other's capture region. We describe a validation framework and evaluate the new technique in contrast with grey-value registration. Results on human wrist data show average accuracy improvements of 74% over grey-value registration. The method is of interest to any intrasubject, same-modality registration applications where subvoxel accuracy is desired.     

Reproducibility of global and local reconstruction of three-dimensional micro-computed tomography of iliac crest biopsies

Variation in computed tomography (CT) image grayscale and spatial geometry due to specimen orientation, magnification, voxel size, differences in X-ray photon energy and limited field-of-view during the scan, were evaluated in repeated micro-CT scans of iliac crest biopsies and test phantoms. Using the micro-CT scanner on beamline X2B at the Brookhaven National Laboratory's National Synchrotron Light Source, 3-D micro-CT images were generated. They consisted of up to 1024 X 2400², 4-mum cubic voxels, each with 16-bit gray-scale. We also reconstructed the images at 16-, 32-, and 48-mum voxel resolution. Scan data were reconstructed from the complete profiles using filtered back-projection and from truncated profiles using profile-extension and with a Local reconstruction algorithm. Three biopsies and one bonelike test phantom were each rescanned at three different times at annual intervals. For the full-data-set reconstructions, the reproducibility of the estimates of mineral content of bone at mean bone opacity value, was plusmn28.8 mg/cm³ , i.e., 2.56%, in a 4-mum cubic voxel at the 95% confidence level. The reproducibility decreased with increased voxel size. The interscan difference in imaged bone volume ranged from 0.86 plusmn 0.64% at 4-mum voxel resolution, and 2.64 plusmn 2.48% at 48 mum.     

Computerized tomography with X-ray, emission, and ultrasound sources

This paper reviews the major developments that have taken place during the last three years in imaging with computed tomography (CT) using X-ray, emission, and ultrasound sources. Space limitations have resulted in some selection of topics by the author. There are four major sections dealing with algorithms, X-ray CT, emission CT, and ultrosound CT. Since most of the currently used algorithms are of filtered-backprojection type, we have concentrated on these in the section on algorithms (with emphasis on their implementation aspects). In X-ray CT an important question raised during the last few years has concerned the parameter measured by a CT scanner, given the fact that the X-rays used in CT scanners are polychromatic and the fact that tissue attenuation coefficients are energy dependent. Answers to this question are reviewed in the section on X-ray CT where we have also discussed the artifacts caused by the polychromaticity of the X-ray photons. Methods for the removal of these artifacts have also been reviewed. In emission CT the biggest development of the last three years is the great interest in positron tomography, although space constraints have dictated an essentially introductory treatment and not all aspects of the single photon and positron tomography have been surveyed. Finally, we have reviewed recent developments in ultrasound CT. We have pointed out that because of the sensitivity of this technique to refraction, it is currently limited to soft tissue structures, with ultrasonic detection of tumors in the female breast a significant application.     

一种基于多小波变换的医学图像融合方法

本文讨论了医学图像CT与NMR的融合问题。由于骨骼组织仅能在CT中清晰显示,而软组织仅能在NMR中清晰显示,所以CT与NMR图像各自都不能同时清晰显示骨骼组织和软组织。在分析了CT与NMR图像成像机理的基础上,提出了一种基于多小波变换的融合方法。它可将CT与NMR图像进行有效的综合。所获得的融合图像,可同时清晰地显示骨组织和软组织信息。     

A projector/backprojector with slice-to-slice blurring forefficient three-dimensional scatter modeling

Scatter correction is an important factor in single photon emission computed tomography (SPECT). Many scatter correction techniques, such as multiple-window subtraction and intrinsic modeling with iterative algorithms, have been under study for many years. Previously, we developed an efficient slice-to-slice blurring technique to model attenuation and system geometric response in a projector/backprojector pair, which was used in an ML-EM algorithm to reconstruct SPECT data. This paper proposes a projector/backprojector that models the three-dimensional (3-D) first-order scatter in SPECT, also using an efficient slice-to-slice blurring technique. The scatter response is estimated from a known nonuniform attenuation distribution map. It is assumed that the probability of detection of a first-order scattered photon from a photon that is emitted in a given source voxel and scattered in a given scatter voxel is proportional to the attenuation coefficient value at that voxel. Monte Carlo simulations of point sources and an MCAT torso phantom were used to verify the accuracy of the proposed projector/backprojector model. An experimental Jaszczak torso/cardiac phantom SPECT study was also performed. For a 64 x 64 x 64 image volume, it took 8.7 s to perform each iteration per slice on a Sun ULTRA Enterprise 3000 (167 MHz, 1 Gbyte RAM) computer, when modeling 3-D scatter, attenuation, and system geometric response functions. The main advantage of the proposed method is its easy implementation and the possibility of performing reconstruction in clinically acceptable time.     

Monotonic penalized-likelihood image reconstruction for X-ray fluorescence computed tomography

In this paper, we derive a monotonic penalized-likelihood algorithm for image reconstruction in X-ray fluorescence computed tomography (XFCT) when the attenuation maps at the energies of the fluorescence X-rays are unknown. In XFCT, a sample is irradiated with pencil beams of monochromatic synchrotron radiation that stimulate the emission of fluorescence X-rays from atoms of elements whose K- or L-edges lie below the energy of the stimulating beam. Scanning and rotating the object through the beam allows for acquisition of a tomographic dataset that can be used to reconstruct images of the distribution of the elements in question. XFCT is a stimulated emission tomography modality, and it is thus necessary to correct for attenuation of the incident and fluorescence photons. The attenuation map is, however, generally known only at the stimulating beam energy and not at the energies of the various fluorescence X-rays of interest. We have developed a penalized-likelihood image reconstruction strategy for this problem. The approach alternates between updating the distribution of a given element and updating the attenuation map for that element's fluorescence X-rays. The approach is guaranteed to increase the penalized likelihood at each iteration. Because the joint objective function is not necessarily concave, the approach may drive the solution to a local maximum. To encourage the algorithm to seek out a reasonable local maximum, we include in the objective function a prior that encourages a relationship, based on physical considerations, between the fluorescence attenuation map and the distribution of the element being reconstructed.     

Alternating minimization algorithms for transmission tomography

A family of alternating minimization algorithms for finding maximum-likelihood estimates of attenuation functions in transmission X-ray tomography is described. The model from which the algorithms are derived includes polyenergetic photon spectra, background events, and nonideal point spread functions. The maximum-likelihood image reconstruction problem is reformulated as a double minimization of the I-divergence. A novel application of the convex decomposition lemma results in an alternating minimization algorithm that monotonically decreases the objective function. Each step of the minimization is in closed form. The family of algorithms includes variations that use ordered subset techniques for increasing the speed of convergence. Simulations demonstrate the ability to correct the cupping artifact due to beam hardening and the ability to reduce streaking artifacts that arise from beam hardening and background events.     

Multi‐“Color” Delineation of Bone Microdamages Using Ligand‐Directed Sub‐5 nm Hafnia Nanodots and Photon Counting CT Imaging

The early detection of bone microdamages is crucial to make informed decisions about the therapy and taking precautionary treatments to avoid catastrophic fractures. Conventional computed tomography (CT) imaging faces obstacles in detecting bone microdamages due to the strong self‐attenuation of photons from bone and poor spatial resolution. Recent advances in CT technology as well as novel imaging probes can address this problem effectively. Herein, the bone microdamage imaging is demonstrated using ligand‐directed nanoparticles in conjunction with photon counting spectral CT. For the first time, Gram‐scale synthesis of hafnia (HfO₂) nanoparticles is reported with surface modification by a chelator moiety. The feasibility of delineating these nanoparticles from bone and soft tissue of muscle is demonstrated with photon counting spectral CT equipped with advanced detector technology. The ex vivo and in vivo studies point to the accumulation of hafnia nanoparticles at microdamage site featuring distinct spectral signal. Due to their small sub‐5 nm size, hafnia nanoparticles are excreted through reticuloendothelial system organs without noticeable aggregation while not triggering any adverse side effects based on histological and liver enzyme function assessments. These preclinical studies highlight the potential of HfO₂‐based nanoparticle contrast agents for skeletal system diseases due to their well‐placed K‐edge binding energy.     

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted /spl lscr//sup 1/ and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.     

Shading 3D-Images from CT Using Gray-Level Gradients

For the 3D-reconstruction of organ surfaces from tomograms, a shading method based on the partial volume effect is presented. In contrast to methods based on the depth and/or the angle of the voxel surface, here the gray-level gradient along the surface is used for shading. It is shown, that at least for bone and soft tissue surfaces, the results are superior to conventional shading. This is due to the high dynamic range of the gray levels within a small spatial neighborhood.     

Volume registration using needle paths and point landmarks for evaluation of interventional MRI treatments

We created a method for three-dimensional (3-D) registration of medical images (e.g., magnetic resonance imaging (MRI) or computed tomography) to images of physical tissue sections or to other medical images and evaluated its accuracy. Our method proved valuable for evaluation of animal model experiments on interventional-MRI guided thermal ablation and on a new localized drug delivery system. The method computes an optimum set of rigid body registration parameters by minimization of the Euclidean distances between automatically chosen correspondence points, along manually selected fiducial needle paths, and optional point landmarks, using the iterative closest point algorithm. For numerically simulated experiments, using two needle paths over a range of needle orientations, mean voxel displacement errors depended mostly on needle localization error when the angle between needles was at least 20 degrees. For parameters typical of our in vivo experiments, the mean voxel displacement error was < 0.35 mm. In addition, we determined that the distance objective function was a useful diagnostic for predicting registration quality. To evaluate the registration quality of physical specimens, we computed the misregistration for a needle not considered during the optimization procedure. We registered an ex vivo sheep brain MR volume with another MR volume and tissue section photographs, using various combinations of needle and point landmarks. Mean registration error was always < or = 0.54 mm for MR-to-MR registrations and < or = 0.52 mm for MR to tissue section registrations. We also applied the method to correlate MR volumes of radio-frequency induced thermal ablation lesions with actual tissue destruction. In this case, in vivo rabbit thigh volumes were registered to photographs of ex vivo tissue sections using two needle paths. Mean registration errors were between 0.7 and 1.36 mm over all rabbits, the largest error less than two MR voxel widths. We conclude that our method provides sufficient spatial correspondence to facilitate comparison of 3-D image data with data from gross pathology tissue sections and histology.     

Enhancing digital cephalic radiography with mixture models and local gamma correction

We present a new algorithm, called the soft-tissue filter, that can make both soft and bone tissue clearly visible in digital cephalic radiographies under a wide range of exposures. It uses a mixture model made up of two Gaussian distributions and one inverted lognormal distribution to analyze the image histogram. The image is clustered in three parts: background, soft tissue, and bone using this model. Improvement in the visibility of both structures is achieved through a local transformation based on gamma correction, stretching, and saturation, which is applied using different parameters for bone and soft-tissue pixels. A processing time of 1 s for 5 Mpixel images allows the filter to operate in real time. Although the default value of the filter parameters is adequate for most images, real-time operation allows adjustment to recover under- and overexposed images or to obtain the best quality subjectively. The filter was extensively clinically tested: quantitative and qualitative results are reported here.     

Penalized weighted least-squares image reconstruction for dual energy X-ray transmission tomography

We present a dual-energy (DE) transmission computed tomography (CT) reconstruction method. It is statistically motivated and features nonnegativity constraints in the density domain. A penalized weighted least squares (PWLS) objective function has been chosen to handle the non-Poisson noise added by amorphous silicon (aSi:H) detectors. A Gauss-Seidel algorithm has been used to minimize the objective function. The behavior of the method in terms of bias/standard deviation tradeoff has been compared to that of a DE method that is based on filtered back projection (FBP). The advantages of the DE PWLS method are largest for high noise and/or low flux cases. Qualitative results suggest this as well. Also, the reconstructed images of an object with opaque regions are presented. Possible applications of the method are: attenuation correction for positron emission tomography (PET) images, various quantitative computed tomography (QCT) methods such as bone mineral densitometry (BMD), and the removal of metal streak artifacts.     

Developments with maximum likelihood X-ray computed tomography

An approach to the maximum-likelihood estimation of attenuation coefficients in transmission tomography is presented as an extension of earlier theoretical work by K. Lange and R. Carson (J. Comput. Assist. Tomography, vol.8, p.306-16, 1984). The reconstruction algorithm is based on the expectation-maximization (EM) algorithm. Several simplifying approximations are introduced which make the maximization step of the algorithm available. Computer simulations are presented using noise-free and Poisson randomized projections. The images obtained with the EM-type method are compared to those reconstructed with the EM method of Lange and Carson and with filtered backprojection. Preliminary results show that there are potential advantages in using the maximum likelihood approaches in situations where a high-contrast object, such as bone, is embedded in low-contrast soft tissue.     

A novel local thresholding algorithm for trabecular bone volume fraction mapping in the limited spatial resolution regime of in vivo MRI

Recent advances in micro-magnetic resonance imaging have shown the possibility of in vivo assessment of trabecular bone architecture. However, the small feature size and relatively low signal-to-noise ratio (SNR) achievable in vivo cause the intensity histogram to be unimodal. The critical first step in the processing of these images is the extraction of bone volume fraction for each voxel. Here, we propose a local threshold algorithm (LTA) that determines the marrow intensity value in the neighborhood of each voxel based on nearest-neighbor statistics. Using the local marrow intensities we threshold the image and scale the intensities of voxels partially occupied by bone to produce a marrow volume fraction map of the trabecular bone region. We show that structural parameters derived with the LTA are highly correlated with those obtained with the previously published histogram deconvolution algorithm (HDA) and that the LTA is robust to image noise corruption. The LTA is found to correctly identify trabeculae with a significantly higher reliability than HDA. Finally, we demonstrate that the LTA is superior in preserving connectivity by showing for 75 in vivo images that the genus of the trabecular bone surface is always higher than when processed with the HDA.     

一种三维数据场多表面显示方法

本文提出了一种基于体绘制的三维数据场多表面显示方法.首先,采用灰度梯度加权提取出三维数据场中不同物质间的边界,根据显示的需要只对这些边界上的体元赋予相应的阻光度并进行光亮度合成计算,因而可大大减少计算量,提高显示的速度;将边界上的体元作为不同物质的混合体,采用与方向有关的三线性插值来计算视线方向与体素内等值面的交点,根据交点的法向量进行光照效应计算以提高显示图像的质量;最后用投影成像法显示最终的图像.本文对医学CT图像做了相关的实验,取得了较好的效果.     

A novel approach to extract colon lumen from CT images for virtual colonoscopy

An automatic method has been developed for segmentation of abdominal computed tomography (CT) images for virtual colonoscopy obtained after a bowel preparation of a low-residue diet with ingested contrast solutions to enhance the image intensities of residual colonic materials. Removal of the enhanced materials was performed electronically by a computer algorithm. The method is a multistage approach that employs a modified self-adaptive on-line vector quantization technique for a low-level image classification and utilizes a region-growing strategy for a high-level feature extraction. The low-level classification labels each voxel based on statistical analysis of its three-dimensional intensity vectors consisting of nearby voxels. The high-level processing extracts the labeled stool, fluid and air voxels within the colon, and eliminates bone and lung voxels which have similar image intensities as the enhanced materials and air, but are physically separated from the colon. This method was evaluated by volunteer studies based on both objective and subjective criteria. The validation demonstrated that the method has a high reproducibility and repeatability and a small error due to partial volume effect. As a result of this electronic colon cleansing, routine physical bowel cleansing prior to virtual colonoscopy may not be necessary.     

肌肉组织超声传输衰减特性的研究

探讨超声对肌肉组织超声传输特性。采用脉冲反射法,对肌肉组织沿纤维不同方向传播速度及其衰减规律进行研究。结果表明,对于肌肉组织,超声在顺纤维方向传播时,声速较大;在横纤维方向传播时,声衰减系数较大;水分含量多少对肌肉组织声速影响不大,而对衰减系数影响较大,其变化是影响组织声衰减的主要因素。这表明肌肉组织超声传输衰减特性具有随纤维方向结构变化特征,对研究生物软组织声学特性及其临床应用具有参考价值。