Fan-beam Projection Data Research Articles

A dual-domain deep learning-based reconstruction method for fully 3D sparse data helical CT

Helical CT has been widely used in clinical diagnosis. In this work, we focus on a new prototype of helical CT, equipped with sparsely spaced multidetector and multi-slit collimator (MSC) in the axis direction. This type of system can not only lower radiation dose, and suppress scattering by MSC, but also cuts down the manufacturing cost of the detector. The major problem to overcome with such a system, however, is that of insufficient data for reconstruction. Hence, we propose a deep learning-based function optimization method for this ill-posed inverse problem. By incorporating a Radon inverse operator, and disentangling each slice, we significantly simplify the complexity of our network for 3D reconstruction. The network is composed of three subnetworks. Firstly, a convolutional neural network (CNN) in the projection domain is constructed to estimate missing projection data, and to convert helical projection data to 2D fan-beam projection data. This is follwed by the deployment of an analytical linear operator to transfer the data from the projection domain to the image domain. Finally, an additional CNN in the image domain is added for further image refinement. These three steps work collectively, and can be trained end to end. The overall network is trained on a simulated CT dataset based on eight patients from the American Association of Physicists in Medicine (AAPM) Low Dose CT Grand Challenge. We evaluate the trained network on both simulated datasets and clinical datasets. Extensive experimental studies have yielded very encouraging results, based on both visual examination and quantitative evaluation. These results demonstrate the effectiveness of our method and its potential for clinical usage. The proposed method provides us with a new solution for a fully 3D ill-posed problem.

Weighted expectation maximization reconstruction algorithms with application to gated megavoltage tomography

We propose and investigate weighted expectation maximization (EM) algorithms for image reconstruction in x-ray tomography. The development of the algorithms is motivated by the respiratory-gated megavoltage tomography problem, in which the acquired asymmetric cone-beam projections are limited in number and unevenly sampled over view angle. In these cases, images reconstructed by use of the conventional EM algorithm can contain ring- and streak-like artefacts that are attributable to a combination of data inconsistencies and truncation of the projection data. By use of computer-simulated and clinical gated fan-beam megavoltage projection data, we demonstrate that the proposed weighted EM algorithms effectively mitigate such image artefacts.

MO-D-I-611-03: A New Fan-Beam Data Consistency Condition to Estimate Erroneous Or Missing Projection Data

Purpose: During diagnostic x-ray CT imaging procedures or image guided radiotherapy, some projection data may be missing due to malfunctioning detectors or limited field of view (LFOV) which is not big enough to cover the entire object. We present and validate a novel fan-beam data consistency condition (FDCC) to estimate missed or erroneous data due to the conditions given above. Method and Materials: A local Fourier transform of fan-beam projection data is introduced and the relationship with the Fourier transform of image function is established. Using the property of causality, a new FDCC is derived. The new FDCC provides an explicit estimation of any given missing projection data by filtering all other available fan-beam projections. This algorithm can be used to reduce the severity of artifacts when there are erroneous projection values present in the measured sinogram. The reconstructed image quality is significantly improved after correction compared to the image quality achieved by directly reconstructing with corrupted projection data. Results: Numerical simulations have been conducted using this FDCC in the case that some detectors are out of order and constantly report a zero value. Two images of Shepp-Logan phantom are reconstructed using the standard filtered backprojection (FBP) reconstruction algorithm. One image is reconstructed with the original corrupted projection data and the other one is reconstructed with the projection data corrected by FDCC. Details in the phantom not visible in the original reconstruction are recovered and ring artifacts are significantly reduced using this algorithm. Conclusion: This new FDCC was validated and has been proven to be a very powerful tool in correcting ring artifacts caused by corrupted projection data. Although the simulation was conducted for the malfunctioning detector case, this algorithm can be similarly applied to the LFOV case.

Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector

In this paper, we present a new algorithm designed for a specific data truncation problem in fan-beam CT. We consider a scanning configuration in which the fan-beam projection data are acquired from an asymmetrically positioned half-sized detector. Namely, the asymmetric detector only covers one half of the scanning field of view. Thus, the acquired fan-beam projection data are truncated at every view angle. If an explicit data rebinning process is not invoked, this data acquisition configuration will reek havoc on many known fan-beam image reconstruction schemes including the standard filtered backprojection (FBP) algorithm and the super-short-scan FBP reconstruction algorithms. However, we demonstrate that a recently developed fan-beam image reconstruction algorithm which reconstructs an image via filtering a backprojection image of differentiated projection data (FBPD) survives the above fan-beam data truncation problem. Namely, we may exactly reconstruct the whole image object using the truncated data acquired in a full scan mode (2π angular range). We may also exactly reconstruct a small region of interest (ROI) using the truncated projection data acquired in a short-scan mode (less than 2π angular range). The most important characteristic of the proposed reconstruction scheme is that an explicit data rebinning process is not introduced. Numerical simulations were conducted to validate the new reconstruction algorithm.

On few-view tomographic reconstruction with megavoltage photon beams.

Currently portal imaging devices are used to obtain information on patient localization during radiation therapy treatments. Such obtained information is two dimensional in nature, limited to the plane of the captured image. It has been proposed that megavoltage computed tomography images be reconstructed to overcome this limitation. This study explores the feasibility of reconstructing tomographic images from fan-beam projection data acquired with a commercial portal imaging device on a standard radiotherapy linear accelerator. Several CT reconstruction algorithms are examined as to their performance and suitability for applications in radiation therapy verification. The results show that it is possible, using some of the iterative reconstruction techniques, to obtain an image useful for patient localization from only several (< or =10) projection views.

Backprojection filtering for variable orbit fan-beam tomography

Backprojection filtering algorithms are presented for three variable orbit fan-beam geometries. Expressions for the fan-beam projection and backprojection operators are given for a flat detector fan-beam geometry with fixed focal length, with variable focal length, and with fixed focal length and off-center focusing. Backprojection operators are derived for each geometry using transformation of coordinates to transform from a parallel geometry backprojector to a fan-beam backprojector for the appropriate geometry. The backprojection operator includes a factor which is a function of the coordinates of the projection ray and the coordinates of the pixel in the backprojected image. The backprojection filtering algorithm first backprojects the variable orbit fan-beam projection data using the appropriately derived backprojector to obtain a 1/r blurring of the original image, then takes the two-dimensional (2D) Fast Fourier Transform (FFT) of the backprojected image, then multiples the transformed image by the 2D ramp filter function, and finally takes the inverse 2D FFT to obtain the reconstructed image. Computer simulations verify that backprojectors with appropriate weighting give artifact free reconstructions of simulated line integral projections. Also, it is shown that it is not necessary to assume a projection model of line integrals, but the projector and backprojector can be defined to model the physics of the imaging detection process. A backprojector for variable orbit fan-beam tomography with fixed focal length is derived which includes an additional factor which is a function of the flux density along the flat detector. It is shown that the impulse response for the composite of the projection and backprojection operations is equal to 1/r.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Videographic tomography. II. Reconstruction with fan-beam projection data

For pt.I see ibid., vol.9, p.366-75 (1990). Presents approaches for the realization of fast electro-optical reconstruction systems for fan-beam projection data. Two of the proposed systems were implemented. Requiring only 30 ms for the reconstruction of one image, the systems are two orders of magnitude faster than the special-purpose hardware in commercial CT reconstruction systems. The speed of the reconstruction systems would allow real-time interactive CT imaging.

On the possibility of direct Fourier reconstruction from divergent-beam projections

A great number of tomographic systems, especially those equipped with fast data acquisition techniques, scan the objects investigated by divergent (fan) X-ray beams. Fan-beam projection data require special reconstruction techniques to be implemented. Among reconstruction techniques from parallel projection data, the direct Fourier method (DFM) proved to be one of the most promising ones, especially for high-speed image reconstruction in the high-end 3-D and dynamic tomographic systems. The goal of this work is to answer the topical question: how would direct use of the DFM influence the quality of image reconstruction from the fan-beam data? The formula describing the error caused by such an approximation is derived. The conclusions deduced from the formula are confirmed by computer simulations. The boundary values of data acquisition geometry parameters have been estimated for the case of using the DFM without recalculating the fan-beam data.

The reconstruction of fan-beam data by filtering the back-projection

Expressions for the fan-beam projection and back-projection operators are given along with an evaluation of the impulse response for the composite of the projection and back-projection operations. The fan-beam geometries for both curved and flat detectors have back-projection operators such that the impulse response for the composite of the projection and back-projection operations is equal to 1/| r − r 0| if the data are taken over 360°, and thus two-dimensional Fourier filter techniques can be used to reconstruct transverse sections from fan-beam projection data. It is shown that the impulse response for the composite of the projection and back-projection operators for fan-beam geometry is not spatially invariant if the data are taken over 180° as is true for parallel-beam projection data. The convolution algorithm is approximately four times faster and requires 40% less memory than the filter of the back-projection algorithm. However, the filter of the back-projection algorithm has the advantage of easily implementing different frequency space filters which lends itself to easily changing the noise propagation vs resolution properties of the convolution kernel.