Geometric misalignment correction method for chest tomosynthesis reconstruction

Abstract

A method and system to correct for alignment errors between assumed and actual geometric parameters of an acquisition geometry during image reconstruction in a chest tomosynthesis application includes receiving at least 2 raw projection images acquired on at least 2 different positions in a known acquisition geometry, determining an actual geometric parameter value by determining the minimum of a redundant planes cost function which is calculated for a varying range of the geometric parameter values, and which is determined by: a) at least one plane which intersects an X-ray source trajectory with at least two points, b) an intersection between the planes and a detector surface for which points the source positions are determined, and c) for which the parameters determining the intersection (, , l) are used for the construction of the cost function, applying the calculated actual geometric parameter value of the acquisition geometry for the image reconstruction of the plurality of images, characterized in that, a weighting function is applied to the plurality of acquired images prior to calculating the cost function.

Claims

1. A method to correct for alignment errors between assumed and actual geometric parameters of an acquisition geometry during image reconstruction in a tomosynthesis application, the method comprising the steps of: receiving at least two projection images acquired at least two different positions in a known acquisition geometry; applying a weighting function to the at least two projection images; after applying the weighting function, determining a minimum of a redundant planes cost function for the at least two projection images, which is calculated for a varying range of geometric parameter values, and which is determined by: a) planes each of which intersects an X-ray source trajectory at at least two points; b) intersection points between the planes and a detector surface for which source positions are determined; and c) for which parameters determining the intersection points are used for construction of the redundant planes cost function; calculating an actual geometric parameter value based on the determined minimum of the redundant planes cost function; and applying the calculated actual geometric parameter value of the acquisition geometry for the image reconstruction of the at least two projection images.

2. The method according to claim 1, wherein the calculated actual geometric parameter of the acquisition geometry is an angle between an actual orientation of an image detector relative to one of the planes that intersects with the at least two points defining the X-ray source trajectory in an imaging modality.

3. The method according to claim 1, wherein the weighting function is a Gaussian function, and weights of pixel values, or redundant cost function values, are increased from 0 to 1 according to a Gaussian distribution in which 3=L.sub.1 and 3=R.sub.1, and L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

4. The method according to claim 1, wherein the weighting function is a sigmoid function, and weights of pixel values, or respectively redundant cost function values, are increased from 0 to 1 according to a sigmoid distribution between 0 and L.sub.1 and between R.sub.1 and 0, in which L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

5. The method according to claim 1, wherein the weighting function is a linear function, and weights of pixel values, or respectively redundant cost function values, are increased from 0 to 1 according to a linear distribution between 0 and L.sub.1, and between R.sub.1 and 0, in which L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

6. A medical imaging apparatus for a tomosynthesis application, the medical imaging apparatus comprising: an image detector that acquires at least two projection images from an imaged object at two different positions in an acquisition geometry; a first data processor that calculates alignment errors between assumed and actual geometric parameters of the acquisition geometry, the first data processor configured for: applying a weighting function to the at least two projection images; after applying the weighting function to the at least two projection images, calculating a minimum of a redundant planes cost function, which is determined by: a) planes each of which intersects an X-ray source trajectory at at least two points; b) intersection points between the planes and a detector surface for which source positions are determined; and c) for which parameters determining the intersection points are used for construction of the redundant planes cost function; and calculating the actual geometric parameters based on the calculated minimum of the redundant planes cost function; and a second data processor that calculates parameters of the acquisition geometry for an image reconstruction of a plurality of images.

7. The medical imaging apparatus according to claim 6, further comprising: an X-ray source that exposes the imaged object with X-rays and moves along a predetermined trajectory including a first position and a second position; and an X-ray detector that faces the X-ray source and detects X-rays emitted from the X-ray source and transmitted through the object.

8. The medical imaging apparatus according to claim 7, wherein the calculated parameters of the acquisition geometry includes an angle between an actual orientation of an image detector relative to one of the planes that intersects with the at least two points defining the X-ray source trajectory.

9. The medical imaging apparatus according to claim 7, wherein the weighting function is a Gaussian function, and weights of pixel values, or respectively redundant cost function values, are increased from 0 to 1 according to a Gaussian distribution in which 3=L.sub.1 and 3=R.sub.1, and L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

10. The medical imaging apparatus according to claim 7, wherein the weighting function is a sigmoid function, and weights of pixel values, or respectively redundant cost function values, are increased from 0 to 1 according to a sigmoid distribution between 0 and L.sub.1 and between R.sub.1 and 0, and L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

11. The medical imaging apparatus according to claim 7, wherein the weighting function is a linear function, and weights of pixel values, or respectively redundant cost function values, are increased from 0 to 1 according to a linear distribution between 0 and L.sub.1 and between R.sub.1 and 0, and L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

12. The medical imaging apparatus according to claim 6, wherein the calculated parameters of the acquisition geometry includes an angle between an actual orientation of an image detector relative to one of the planes that intersects with the points defining the X-ray source trajectory.

13. The medical imaging apparatus according to claim 6, wherein the weighting function is a Gaussian function, and weights of pixel values, or respectively redundant cost function values, are increased from 0 to 1 according to a Gaussian distribution in which 3=L.sub.1 and 3=R.sub.1, and L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

14. The medical imaging apparatus according to claim 6, wherein the weighting function is a sigmoid function, and weights of pixel values, or respectively redundant cost function values, are increased from 0 to 1 according to a sigmoid distribution between 0 and L.sub.1 and between R.sub.1 and 0, and L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

15. The medical imaging apparatus according to claim 6, wherein the weighting function is a linear function, and weights of pixel values, or respectively redundant cost function values, are increased from 0 to 1 according to a linear distribution between 0 and L.sub.1 and between R.sub.1 and 0, and L.sub.1 and R.sub.1 are relative widths of an applied truncation filter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates the geometric setup of a chest tomosynthesis acquisition in one embodiment of the invention. N X-ray images are acquired on a stationary flat panel with an X-ray tube that moves on a straight line S. The angle represents the orientation of the digital image detector relative to the X-ray source path. Most chest tomosynthesis systems are designed so that =0.

(2) FIG. 2 shows the shapes of different proposed weighting functions which may be applied to the projection image prior to or after calculating the redundant cost planes function C.sub.RP.

(3) FIG. 3 shows the shape of cost function C.sub.RP for estimated digital image detector angle without truncation filtering applied first. The cost function is calculated for a simulated chest tomosynthesis exam using the XCAT phantom.

(4) FIG. 4 shows the shape of different cost functions calculated for the same simulated chest tomosynthesis exam. Vertical Gaussian truncation filters where used with varying values of w=L.sub.1=L.sub.2.

(5) FIG. 5 shows the shape of different cost functions calculated for the same simulated chest tomosynthesis exam. Horizontal Gaussian truncation filters where used with varying values of w=L.sub.1=L.sub.2.

(6) FIG. 6 shows the shape of different cost functions calculated for the same simulated chest tomosynthesis exam. Gaussian truncation filters where used in both horizontal and vertical direction. The calculated results for the disclosed experimental setup show that the cost function reaches a minimum around an angle correction of about 13 in case that filters with w<0.01 are chosen. The correct result (around 10) prominently appears as the minima of the different cost functions calculated with values w>0.05.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(7) In the following detailed description, reference is made in sufficient detail to the above referenced drawings, allowing those skilled in the art to practice the embodiments explained below.

(8) Embodiments of the present invention provide a system and a method for acquiring and reconstructing a chest tomosynthesis projection image data set. The method disclosed by this invention is based on the original method of Debbeler (already referred to above), and is a modification of this method to improve the robustness against truncation.

(9) A schematic representation of chest tomosynthesis is illustrated in FIG. 1. Projections are acquired of a patient f with a stationary detector . The N subsequent positions of the X-ray source are indicated as s(.sub.i). In one embodiment of the invention, the X-ray source moves on a linear path S. In other embodiments of this invention, the source might move on a circular path over a limited angle.

(10) The detailed description given here will further focus on the first embodiment in which the source moves on a linear path. The coordinate frame attached to the detector has axes (U, V, W).

(11) The epipolar redundancy criterion describes the following relationship between two projection images. For two source points s(.sub.n) and s(.sub.n), multiple planes can be drawn that intersect both points and the detector along an intersection which can be parameterized by an angle and a distance l from the detector center (u.sub.0, v.sub.0). For noiseless acquisitions and without truncation, it can be proven that
g.sub.3(.sub.n,,l)=g.sub.3(.sub.n,,l)(1)
with g.sub.3 defined as:

(12) $\begin{array}{cc}{g}_3\left({}_n,,l\right)=\frac{}{l}{g}_2\left({}_n,,l\right)& \left(2\right)\\ \mathrm{where}& \\ g_2\left({}_n,,l\right)={}_{-}^{}{g}_1\left({}_n,l\cos -t\sin ,l\sin +t\cos \right)dt& \left(3\right)\\ \mathrm{and}& \\ g_1\left({}_n,u,v\right)=\frac{1}{.Math.w.Math.t\left({}_n,u,v\right).Math.}p\left({}_n,u,v\right)& \left(4\right)\end{array}$

(13) with p the projection data, w the normal of the detector and t(n,u,v) the direction of the ray arriving in detector pixel (u, v) of the n.sup.th projection. Based on this, a redundant cost planes function C.sub.RP can be derived which reaches a minimum if the geometric parameters (and hence and l) are correctly estimated:

(14) $C_{\mathrm{RP}}=\sqrt{\underset{n=0}{\overset{N-1}{.Math.}}\underset{=-/2}{\overset{/2}{.Math.}}\underset{l=-L_{\max }}{\overset{L_{\max }}{.Math.}}{\left(g_3\left({}_n,,l\right)-g_3\left({}_{n^{}},,l\right)\right)}^2}$

(15) Although that other geometric parameters may be optimized to achieve a minimum in the cost planes function C.sub.RP, a first embodiment of this invention optimizes the detector orientation , relative to the linear motion path of the X-ray tube.

(16) More specifically in chest tomosynthesis, substantial truncation of the object is present in the projections both in the horizontal and vertical direction. In the case of even very small angle deviations p it can be expected that the largest inconsistencies between the projections are found at the top and bottom regions of the projections, as certain parts of the patient will not be imaged in this case, depending on the acquisition angle of the tube. Intuitively, the horizontal truncation would cause fewer inconsistencies. While in the prior art it has been attempted to optimize the efficiency of the cost function calculation by applying a weighting function to reduce the weight in the cost function of pixels that were suspected to contain information that was not present in all projections (see A. Grulich, Tobias and Holub, Wolfgang and Hassler, Ulf and Aichert, Andr and Maier, Geometric Adjustment of X-ray Tomosynthesis, in Fully Three-Dimensional Image Reconstr. Radiol. Nucl. Med., Newport, 2015, pp. 468-471.), the invention described in this application proposes a different approach.

(17) The equation above (3) is very sensitive for pixels near the upright (horizontal) image edges, even if an object would have been imaged that fitted perfectly on the detector without horizontal truncation. A small deviation from 0 in would cause a large part of the image pixels in the image border to fall off the intersection with the plane , causing a large discontinuity in g.sub.3 and thus making the entire cost function C.sub.RP unstable.

(18) Therefore, in order to reduce the impact of pixels near the edge of the projections on the cost function and in a specific embodiment of this invention, a specific weighting function is applied. In the regions of relative width L.sub.1 and R.sub.1, weights are increased from 0 to 1 according to a Gaussian distribution with L.sub.1=3 and respectively R.sub.1=3. See FIG. 2.

(19) In another embodiment, the same filter is also disclosed to compensate for vertical truncation.

(20) In yet other embodiments, different shapes of weighting curves are proposed, such as linear, rectangular or sigmoid shaped sighting curves (such as depicted in FIG. 2).

(21) The above has been confirmed by a simulated chest tomosynthesis exam experiment using the XCAT phantom as the imaged object. A set of 11 simulated projections was generated using a mathematical (computer) toolkit with a source-image distance of 120 cm and linear tube motion path of 20 cm. Detector size was set to 360420 pixels of 1 mm size. The detector was placed at a relative rotation of 10 with the motion path of the X-ray tube. Experiments were performed to estimate this simulated detector rotation, through the calculation of the said redundant cost planes functions.

(22) The maximum achievable accuracy of the estimation of the detector rotation is related to the detector size; the maximum accuracy is defined as the angle increment for which a rays passes through a neighbouring pixel at the edge of the image: =tan.sup.1( 1/210)=0.27.

(23) FIG. 3 clearly shows that the estimation of the orientation angle, based on the uncorrected raw projection images results in the estimation of =12.7 as the correct angle. As can be seen in FIG. 3, the cost function C.sub.RP achieved a minimum value at 12.7 which is however well above the true angle of 10.

(24) FIGS. 4 and 5 show similar calculations of the detector rotation, but here the different cost function curves are calculated based on the same set of projection images, but where respectively vertical and horizontal Gaussian truncation filters with varying values of w=L.sub.1=L.sub.2 where applied before the reconstruction. Surprisingly, when the applied filter widths are w>0.10, the minimum of C.sub.RP moves towards 10. When w is further increased beyond 0.40, the calculations show that the value of no longer is estimated correctly, which is not a surprise since the amount of useable image data is dramatically reduced and potentially no longer representative. Combining both horizontal and vertical filters (FIG. 6) more or less produces the same results, confirming the need for horizontal filtering despite the mainly vertical truncation inconsistencies.

(25) In another embodiment, the same weighting functions are applied, but as opposed to the previous embodiment, to the calculated cost functions themselves (without applying the weighting functions to the projection images). This method is supported by the fact that the calculation of the weighting functions out of the different projection images is a mathematically linear operation.