A constrained, total-variation minimization algorithm for low-intensity x-ray CT

Purpose: The authors developed an iterative image-reconstruction algorithm for application to low-intensity computed tomography projection data, which is based on constrained, total-variation (TV) minimization. The algorithm design focuses on recovering structure on length scales comparable to a detector bin width.Methods: Recovering the resolution on the scale of a detector bin requires that pixel size be much smaller than the bin width. The resulting image array contains many more pixels than data, and this undersampling is overcome with a combination of Fourier upsampling of each projection and the use of constrained, TV minimization, as suggested by compressive sensing. The presented pseudocode for solving constrained, TV minimization is designed to yield an accurate solution to this optimization problem within 100 iterations.Results: The proposed image-reconstruction algorithm is applied to a low-intensity scan of a rabbit with a thin wire to test the resolution. The proposed algorithm is compared to filtered backprojection (FBP).Conclusions: The algorithm may have some advantage over FBP in that the resulting noise level is lowered at equivalent contrast levels of the wire.     

Simultaneous misalignment correction for approximate circular cone-beam computed tomography

Currently, CT scanning is often performed using flat detectors which are mounted on C-arm units or dedicated gantries as in radiation therapy or micro CT. For perspective cone-beam backprojection of the Feldkamp type (FDK) the geometry of an approximately circular scan trajectory has to be available for reconstruction. If the system or the scan geometry is afflicted with geometrical instabilities, referred to as misalignment, a non-perfect approximate circular scan is the case. Reconstructing a misaligned scan without knowledge of the true trajectory results in severe artefacts in the CT images. Unlike current methods which use a pre-scan calibration of the geometry for defined scan protocols and calibration phantoms, we propose a real-time iterative restoration of reconstruction geometry by means of entropy minimization. Entropy minimization is performed combining a simplex algorithm for multi-parameter optimization and iterative graphics card (GPU)-based FDK-reconstructions. Images reconstructed with the misaligned geometry were used as an input for the entropy minimization algorithm. A simplex algorithm changes the geometrical parameters of the source and detector with respect to the reduction of entropy. In order to reduce the size of the high-dimensional space required for minimization, the trajectory was described by only eight fix points. A virtual trajectory is generated for each iteration using a least-mean-squares algorithm to calculate an approximately circular path including these points. Entropy was minimal for the ideal dataset, whereas strong misalignment resulted in a higher entropy value. For the datasets used in this study, the simplex algorithm required 64-200 iterations to achieve an entropy value equivalent to the ideal dataset, depending on the grade of misalignment using random initialization conditions. The use of the GPU reduced the time per iteration as compared to a quad core CPU-based backprojection by a factor of 10 resulting in a total of 15-20 ms per iteration, and thus providing an online geometry restoration after a total computation time of approximately 1-3 s, depending on the number of iterations. The proposed method provides accurate geometry restoration for approximately circular scans and eliminates the need for an elaborate off-line calibration for each scan. If a priori information about the trajectory is used to initialize the simplex algorithm, it is expected that the entropy minimization will converge significantly faster.     

General surface reconstruction for cone-beam multislice spiral computed tomography

A new family of cone-beam reconstruction algorithm, the General Surface Reconstruction (GSR), is proposed and formulated in this paper for multislice spiral computed tomography (CT) reconstructions. It provides a general framework to allow the reconstruction of planar or nonplanar surfaces on a set of rebinned short-scan parallel beam projection data. An iterative surface formation method is proposed as an example to show the possibility to form nonplanar reconstruction surfaces to minimize the adverse effect between the collected cone-beam projection data and the reconstruction surfaces. The improvement in accuracy of the nonplanar surfaces over planar surfaces in the two-dimensional approximate cone-beam reconstructions is mathematically proved and demonstrated using numerical simulations. The proposed GSR algorithm is evaluated by the computer simulation of cone-beam spiral scanning geometry and various mathematical phantoms. The results demonstrate that the GSR algorithm generates much better image quality compared to conventional multislice reconstruction algorithms. For a table speed up to 100 mm per rotation, GSR demonstrates good image quality for both the low-contrast ball phantom and thorax phantom. All other performance parameters are comparable to the single-slice 180 degrees LI (linear interpolation) algorithm, which is considered the "gold standard." GSR also achieves high computing efficiency and good temporal resolution, making it an attractive alternative for the reconstruction of next generation multislice spiral CT data.     

Prior image constrained scatter correction in cone-beam computed tomography image-guided radiation therapy

X-ray scatter is a significant problem in cone-beam computed tomography when thicker objects and larger cone angles are used, as scattered radiation can lead to reduced contrast and CT number inaccuracy. Advances have been made in x-ray computed tomography (CT) by incorporating a high quality prior image into the image reconstruction process. In this paper, we extend this idea to correct scatter-induced shading artifacts in cone-beam CT image-guided radiation therapy. Specifically, this paper presents a new scatter correction algorithm which uses a prior image with low scatter artifacts to reduce shading artifacts in cone-beam CT images acquired under conditions of high scatter. The proposed correction algorithm begins with an empirical hypothesis that the target image can be written as a weighted summation of a series of basis images that are generated by raising the raw cone-beam projection data to different powers, and then, reconstructing using the standard filtered backprojection algorithm. The weight for each basis image is calculated by minimizing the difference between the target image and the prior image. The performance of the scatter correction algorithm is qualitatively and quantitatively evaluated through phantom studies using a Varian 2100 EX System with an on-board imager. Results show that the proposed scatter correction algorithm using a prior image with low scatter artifacts can substantially mitigate scatter-induced shading artifacts in both full-fan and half-fan modes.     

PI-line-based image reconstruction in helical cone-beam computed tomography with a variable pitch

Current applications of helical cone-beam computed tomography (CT) involve primarily a constant pitch where the translating speed of the table and the rotation speed of the source-detector remain constant. However, situations do exist where it may be more desirable to use a helical scan with a variable translating speed of the table, leading a variable pitch. One of such applications could arise in helical cone-beam CT fluoroscopy for the determination of vascular structures through real-time imaging of contrast bolus arrival. Most of the existing reconstruction algorithms have been developed only for helical cone-beam CT with constant pitch, including the backprojection-filtration (BPF) and filtered-backprojection (FBP) algorithms that we proposed previously. It is possible to generalize some of these algorithms to reconstruct images exactly for helical cone-beam CT with a variable pitch. In this work, we generalize our BPF and FBP algorithms to reconstruct images directly from data acquired in helical cone-beam CT with a variable pitch. We have also performed a preliminary numerical study to demonstrate and verify the generalization of the two algorithms. The results of the study confirm that our generalized BPF and FBP algorithms can yield exact reconstruction in helical cone-beam CT with a variable pitch. It should be pointed out that our generalized BPF algorithm is the only algorithm that is capable of reconstructing exactly region-of-interest image from data containing transverse truncations.     

An approximate reconstruction method for helical cone-beam differential phase-contrast computed tomography images

Differential phase-contrast computed tomography (DPC-CT) is a novel x-ray inspection method. Currently, DPC-CT reconstruction problems are solved by using parallel-beam, fan-beam and cone-beam algorithms. The above algorithms cannot show the internal structures of rod-shaped objects well enough for only reconstructing a few slices. The helical cone-beam algorithms have significant advantages for rod-shaped objects over other algorithms. Along with our numerical evaluation and verification, we report a PI-line-based approximate algorithm for helical cone-beam DPC-CT, which can be applied to reconstruct the refractive index decrement distribution of the samples directly from phase-contrast projection images. Simulations using a 3D Shepp-Logan phantom are carried out to verify the proposed algorithm. Reconstruction results show that the proposed algorithm can provide higher quality performance compared with the existing interpolation-based reconstruction algorithm.     

Region-of-interest image reconstruction in circular cone-beam microCT

Cone-beam microcomputed tomography (microCT) is one of the most popular choices for small animal imaging which is becoming an important tool for studying animal models with transplanted diseases. Region-of-interest (ROI) imaging techniques in CT, which can reconstruct an ROI image from the projection data set of the ROI, can be used not only for reducing imaging-radiation exposure to the subject and scatters to the detector but also for potentially increasing spatial resolution of the reconstructed images. Increasing spatial resolution in microCT images can facilitate improved accuracy in many assessment tasks. A method proposed previously for increasing CT image spatial resolution entails the exploitation of the geometric magnification in cone-beam CT. Due to finite detector size, however, this method can lead to data truncation for a large geometric magnification. The Feldkamp-Davis-Kress (FDK) algorithm yields images with artifacts when truncated data are used, whereas the recently developed backprojection filtration (BPF) algorithm is capable of reconstructing ROI images without truncation artifacts from truncated cone-beam data. We apply the BPF algorithm to reconstructing ROI images from truncated data of three different objects acquired by our circular cone-beam microCT system. Reconstructed images by use of the FDK and BPF algorithms from both truncated and nontruncated cone-beam data are compared. The results of the experimental studies demonstrate that, from certain truncated data, the BPF algorithm can reconstruct ROI images with quality comparable to that reconstructed from nontruncated data. In contrast, the FDK algorithm yields ROI images with truncation artifacts. Therefore, an implication of the studies is that, when truncated data are acquired with a configuration of a large geometric magnification, the BPF algorithm can be used for effective enhancement of the spatial resolution of a ROI image.     

Isotope computed tomography using cone-beam geometry: a comparison of two reconstruction algorithms

A CT scanner has been constructed specifically to determine the three-dimensional distribution of bone mineral in the medullary cavities of the radius, ulna and femur. A source of x-rays (153Gd) and a multiwire proportional counter (MWPC) are mounted at opposite ends of a diameter of an annular mounting. The limb is placed on the axis of rotation of the annulus and a series of two-dimensional transmission projections are obtained at equal angular spacings over 360 degrees. The distribution of bone mineral is reconstructed from the projections either by the method of maximum entropy (ME) or by convolution and back projection (CBP). These two methods have been evaluated by reconstructing a single slice of a phantom, representing the forearm, from projections simulated by computer. With a clinically acceptable exposure time, the mean medullary densities of the ulna and radius were determined with systematic errors of less than 3.5% (ME) and 11% (CBP), although for the latter method of reconstruction the systematic error was reduced to less than 2% by increasing the number of views. The mean medullary densities of the ulna and radius were determined with precisions better than 2.5% (ME) and 3.5% (CBP).     

Image reconstruction for fan-beam differential phase contrast computed tomography

Recently, x-ray differential phase contrast computed tomography (DPC-CT) has been experimentally implemented using a conventional tube combined with gratings. Images were reconstructed using a parallel-beam reconstruction formula. However, parallel-beam reconstruction formulae are not applicable when the parallel-beam approximation fails. In this paper, we present a new image reconstruction formula for fan-beam DPC-CT. There are several novel features of the new image reconstruction formula: (i) when the scanning angular range of data acquisition is larger than pi + gamma(m) (gamma(m) is the full fan angle), the entire field of view can be exactly reconstructed; (ii) when the scanning angular range is smaller than pi + gamma(m), a local region of interest (ROI) can be exactly reconstructed; (iii) it enables an exact reconstruction for a local ROI when the projection data are truncated at some view angles; (iv) it enlarges the imaging field of view when the detector is asymmetrically placed. In this last case, the data are truncated from every view angle. Numerical simulations have been conducted to validate the new reconstruction formula.     

Streaking artifacts reduction in four-dimensional cone-beam computed tomography

Cone-beam computed tomography (CBCT) using an "on-board" x-ray imaging device integrated into a radiation therapy system has recently been made available for patient positioning, target localization, and adaptive treatment planning. One of the challenges for gantry mounted image-guided radiation therapy (IGRT) systems is the slow acquisition of projections for cone-beam CT (CBCT), which makes them sensitive to any patient motion during the scans. Aiming at motion artifact reduction, four-dimensional CBCT (4D CBCT) techniques have been introduced, where a surrogate for the target's motion profile is utilized to sort the cone-beam data by respiratory phase. However, due to the limited gantry rotation speed and limited readout speed of the on-board imager, fewer than 100 projections are available for the image reconstruction at each respiratory phase. Thus, severe undersampling streaking artifacts plague 4D CBCT images. In this paper, the authors propose a simple scheme to significantly reduce the streaking artifacts. In this method, a prior image is first reconstructed using all available projections without gating, in which static structures are well reconstructed while moving objects are blurred. The undersampling streaking artifacts from static structures are estimated from this prior image volume and then can be removed from the phase images using gated reconstruction. The proposed method was validated using numerical simulations, experimental phantom data, and patient data. The fidelity of stationary and moving objects is maintained, while large gains in streak artifact reduction are observed. Using this technique one can reconstruct 4D CBCT datasets using no more projections than are acquired in a 60 s scan. At the same time, a temporal gating window as narrow as 100 ms was utilized. Compared to the conventional 4D CBCT reconstruction, streaking artifacts were reduced by 60% to 70%.     

An error-reduction-based algorithm for cone-beam computed tomography

Image reconstruction from cone-beam projections collected along a single circular source trajectory is commonly done using the Feldkamp algorithm, which performs well only with a small cone angle. In this report, we propose an error-reduction-based algorithm to increase the cone angle by several folds to achieve satisfactory image quality at the same radiation dose. In our scheme, we first reconstruct the object using the Feldkamp algorithm. Then, we synthesize cone-beam projection data from the reconstructed volume in the same geometry, and reconstruct the volume again from the synthesized projections. Finally, these two reconstruction results are combined to reduce the reconstruction error and produce a superior image volume. The merit of this algorithm is demonstrated in numerical simulation.     

Image reconstruction algorithm for single-photon-emission computed tomography with uniform attenuation

A new method is presented for obtaining an analytical solution to the image-reconstruction problem in single-photon-emission computed tomography. The rigorous solution is introduced by applying an analytical continuation process to the two-dimensional Fourier transform of the image, which is derived from the one-dimensional Fourier transforms of projection functions. The calculations can be carried out in a short computation time without involving unstable procedures. Numerical simulations were made to demonstrate the effectiveness of the proposed method.     

3D cone-beam CT reconstruction for circular trajectories

3D reconstruction from 2D projections obtained along a single circular source trajectory is most commonly done using an algorithm due to Feldkamp, Davis and Kress. In this paper we propose an alternative approach based on a cone-beam to parallel-beam rebinning step, a corresponding rebinning step into a rectangular virtual detector plane and a filtered backprojection. This approach yields an improved image quality reflected by a decreased low-intensity drop which is well known for 3D reconstruction from projection data obtained along circular trajectories. At the same time the computational complexity is lower than in Feldkamp's original approach. Based on this idea, a hybrid 3D cone-beam reconstruction method is formulated that enlarges the reconstruction volume in its dimension along the rotation axis of the cone-beam CT system. This enlargement is achieved by applying different reconstruction conditions for each voxel. An optimal ratio between the reconstructible and irradiated volume of the scanned object is achieved.     

A novel image-domain-based cone-beam computed tomography enhancement algorithm

Kilo-voltage (kV) cone-beam computed tomography (CBCT) plays an important role in image-guided radiotherapy. However, due to a large cone-beam angle, scatter effects significantly degrade the CBCT image quality and limit its clinical application. The goal of this study is to develop an image enhancement algorithm to reduce the low-frequency CBCT image artifacts, which are also called the bias field. The proposed algorithm is based on the hypothesis that image intensities of different types of materials in CBCT images are approximately globally uniform (in other words, a piecewise property). A maximum a posteriori probability framework was developed to estimate the bias field contribution from a given CBCT image. The performance of the proposed CBCT image enhancement method was tested using phantoms and clinical CBCT images. Compared to the original CBCT images, the corrected images using the proposed method achieved a more uniform intensity distribution within each tissue type and significantly reduced cupping and shading artifacts. In a head and a pelvic case, the proposed method reduced the Hounsfield unit (HU) errors within the region of interest from 300 HU to less than 60 HU. In a chest case, the HU errors were reduced from 460 HU to less than 110 HU. The proposed CBCT image enhancement algorithm demonstrated a promising result by the reduction of the scatter-induced low-frequency image artifacts commonly encountered in kV CBCT imaging.     

Four-dimensional cone-beam computed tomography using an on-board imager

On-board cone-beam computed tomography (CBCT) has recently become available to provide volumetric information of a patient in the treatment position, and holds promises for improved target localization and irradiation dose verification. The design of currently available on-board CBCT, however, is far from optimal. Its quality is adversely influenced by many factors, such as scatter, beam hardening, and intra-scanning organ motion. In this work we quantitatively study the influence of organ motion on CBCT imaging and investigate a strategy to acquire high quality phase-resolved [four-dimensional (4D)] CBCT images based on phase binning of the CBCT projection data. An efficient and robust method for binning CBCT data according to the patient's respiratory phase derived in the projection space was developed. The phase-binned projections were reconstructed using the conventional Feldkamp algorithm to yield 4D CBCT images. Both phantom and patient studies were carried out to validate the technique and to optimize the 4D CBCT data acquisition protocol. Several factors that are important to the clinical implementation of the technique, such as the image quality, scanning time, number of projections, and radiation dose, were analyzed for various scanning schemes. The general references drawn from this study are: (i) reliable phase binning of CBCT projections is accomplishable with the aid of external or internal marker and simple analysis of its trace in the projection space, and (ii) artifact-free 4D CBCT images can be obtained without increasing the patient radiation dose as compared to the current 3D CBCT scan.     

Dose reduction for kilovotage cone-beam computed tomography in radiation therapy

Kilovotage cone-beam computed tomography (kV-CBCT) has shown potentials to improve the accuracy of a patient setup in radiotherapy. However, daily and repeated use of CBCT will deliver high extra radiation doses to patients. One way to reduce the patient dose is to lower mAs when acquiring projection data. This, however, degrades the quality of low mAs CBCT images dramatically due to excessive noises. In this work, we aim to improve the CBCT image quality from low mAs scans. Based on the measured noise properties of the sinogram, a penalized weighted least-squares (PWLS) objective function was constructed, and the ideal sinogram was then estimated by minimizing the PWLS objection function. To preserve edge information in the projection data, an anisotropic penalty term was designed using the intensity difference between neighboring pixels. The effectiveness of the presented algorithm was demonstrated by two experimental phantom studies. Noise in the reconstructed CBCT image acquired with a low mAs protocol was greatly suppressed after the proposed sinogram domain image processing, without noticeable sacrifice of the spatial resolution.     

Compensators for dose and scatter management in cone-beam computed tomography

The ability of compensators (e.g., bow-tie filters) designed for kV cone-beam computed tomography (CT) to reduce both scatter reaching the detector and dose to the patient is investigated. Scattered x rays reaching the detector are widely recognized as one of the most significant challenges to cone-beam CT imaging performance. With cone-beam CT gaining popularity as a method of guiding treatments in radiation therapy, any methods that have the potential to reduce the dose to patients and/or improve image quality should be investigated. Simple compensators with a design that could realistically be implemented on a cone-beam CT imaging system have been constructed to determine the magnitude of reduction of scatter and/or dose for various cone-beam CT imaging conditions. Depending on the situation, the compensators were shown to reduce x-ray scatter at the detector and dose to the patient by more than a factor of 2. Further optimization of the compensators is a possibility to achieve greater reductions in both scatter and dose.