The current x-ray source trajectory for C-arm based cone-beam CT is a single arc. Reconstruction
from data acquired with this trajectory yields cone-beam artifacts for regions other than the central slice. In
this work we present the preliminary evaluation of reconstruction from a source trajectory of two concentric arcs
using a flat-panel detector equipped C-arm gantry (GE Healthcare Innova 4100 system, Waukesha, Wisconsin).
The reconstruction method employed is a summation of FDK-type reconstructions from the two individual arcs.
For the angle between arcs studied here, 30°, this method offers a significant reduction in the visibility of cone-beam
artifacts, with the additional advantages of simplicity and ease of implementation due to the fact that it is
a direct extension of the reconstruction method currently implemented on commercial systems. Reconstructed
images from data acquired from the two arc trajectory are compared to those reconstructed from a single arc
trajectory and evaluated in terms of spatial resolution, low contrast resolution, noise, and artifact level.
In this paper, we present shift-invariant filtered backprojection (FBP) cone-beam image reconstruction algorithms
for a cone-beam CT system based on a clinical C-arm gantry. The source trajectory consists of two
concentric arcs which is complete in the sense that the Tuy data sufficiency condition is satisfied. This scanning
geometry is referred to here as a CC geometry (each arc is shaped like the letter "C"). The challenge for image
reconstruction for the CC geometry is that the image volume is not well populated by the familiar doubly
measured (DM) lines. Thus, the well-known DM-line based image reconstruction schemes are not appropriate
for the CC geometry. Our starting point is a general reconstruction formula developed by Pack and Noo which
is not dependent on the existence of DM-lines. For a specific scanning geometry, the filtering lines must be
carefully selected to satisfy the Pack-Noo condition for mathematically exact reconstruction. The new points
in this paper are summarized here. (1) A mathematically exact cone-beam reconstruction algorithm was formulated
for the CC geometry by utilizing the Pack-Noo image reconstruction scheme. One drawback of the
developed exact algorithm is that it does not solve the long-object problem. (2) We developed an approximate
image reconstruction algorithm by deforming the filtering lines so that the long object problem is solved while
the reconstruction accuracy is maintained. (3) In addition to numerical phantom experiments to validate the
developed image reconstruction algorithms, we also validate our algorithms using physical phantom experiments
on a clinical C-arm system.
We present several new families of mathematically exact cone-beam image reconstruction algorithms for a general source trajectory that fulfills Tuy's data sufficiency condition. The basic structure of the new algorithms is to reconstruct images via filtered backprojection (FBP) with a 1-D shift-invariant filter. Specifically, the general weighting function w(x,;t) for redundant data was decomposed into three components w1(x,), w2(x,t), and sgn[·y(t)], viz. w(x,;t)=[w1(x,)w2(x,t)sgn(·y(t))]. Based upon the normalization condition of the weighting function, the first component w1(x,) may be calculated using the second component w2(x,t) Thus, the design of the weighting function was reduced to the selection of the second component w2(x,t). Using this scheme, it has been demonstrated that, for a given scanning configuration, one may develop infinitely many different, exact cone-beam FBP image reconstruction algorithms. To demonstrate how this general procedure may be used to develop FBP image reconstruction algorithms, a two-concentric-circle scanning configuration is discussed in detail. Numerical simulations have been conducted to validate several of the derived image reconstruction algorithms. Several possible scan strategies are presented, and the possibility of performing multiple reconstructions with different scan configurations to reduce image noise is described. Noise properties also have been numerically studied for the implemented image reconstruction algorithms, then compared with two other shift-invariant FBP reconstruction algorithms.
We present a cone-beam image reconstruction algorithm for helical CT scanning with a tilted gantry and N-PI data acquisition. When the gantry is tilted, the effective source trajectory in the patient's reference frame lies on an elliptical cylinder, rather than on a circular cylinder as in the standard helical scanning mode. The aim of this work is to provide a means of reconstructing an image object directly from cone-beam projection data without transforming the image object into a virtual object and without rebinning projection data acquired for a real object into the projection data of the virtual object. This task has been accomplished by the application of an exact reconstruction algorithm, which utilizes an important geometrical property of the elliptical helical trajectory: the existence of generalized N-PI lines for a given image point. Based on this property, a mathematically exact image reconstruction scheme via filtering the backprojection image of differentiated projection data (FBPD) is applied to solve the reconstruction problem. Due to the gantry tilt, the required detector size is different from that of the standard helical trajectory (nontilted). A systematic analysis of the required detector size is presented. For an N-PI data acquisition scheme, an image may be reconstructed using data from an N-PI window, an (N?2)-PI window, and so on. Although the images reconstructed using an N-PI (N>1) window are noisier than the images reconstructed from a 1-PI window, a weighted-average scheme over reconstructed images is presented to generate a final image with significantly lower noise variance than that in the 1-PI data acquisition scheme. The image reconstruction algorithm was numerically validated using a mathematical phantom.
A novel exact fan-beam image reconstruction formula is presented and validated using both mathematical phantom data and clinical data. This algorithm takes the form of the standard ramp filtered backprojection (FBP) algorithm plus local compensation terms. An equal weighting scheme is utilized in this algorithm in order to properly account for redundantly measured projection data. The algorithm has the desirable property of maintaining a mathematically exact result for: the full scan mode (2π), the short scan mode (π+ full fan angle), and the super-short scan mode (less than (π + full fan angle)). Another desirable feature of this algorithm is that it is derivative-free. The derivative-free nature of this algorithm distinguishes it from other exact fan-beam FBP algorithms.
Conventionally, the FDK algorithm is used to reconstruct images from cone-beam projections in many imaging systems. One advantage of this algorithm is its shift-invariant feature in the filtering process. In this paper, a new cone-beam reconstruction algorithm is derived for a single arc source trajectory. Examples of the arc trajectory include the full circular scan mode, a short-scan mode and a super-short-scan mode depending upon the angular range of the scanning path. Since the single arc does not satisfy Tuy's data sufficiency condition, there is no mathematically exact algorithm. However, one advantage of this reconstruction is that the shift-invariance property has been preserved despite the lack of a mathematically complete data set. The new algorithm includes backprojections from three adjacent segments of the arc defined by T1(vector x), T2(vector x) and T3(vector x). Each backprojection step consists of a weighted
combination of 1D Hilbert filtering of the modified cone-beam data along horizontal and non-horizontal directions. The non-horizontal filtering is a new feature of this FBP algorithm. For the full circle scanning path, this algorithm reduces to the conventional FDK algorithm plus a term involving a first order derivative filter. Numerical simulations have been performed to validate the algorithm.