Methods and apparatus for back-projection and forward-projection
First Claim
1. In reconstruction imaging in which a volume is reconstructed from a series of measured projection images, each generated by projection of a radiation source positioned at a respective focus through the volume to a detector at which the respective measured projection image is acquired (“
- detector plane”
), an improved method of back-projecting a two-dimensional (2D) representation (“
first 2D representation”
) to a generate three-dimensional (3D) representation, where the first 2D representation is in the detector plane, the improvement comprising for each of one or more slices of the 3D representation parallel to the detector plane and for each distinct focus at which a said measured projection images is generated, performing the steps of;
i) warping the first 2D representation to generate a second 2D representation, the warping step including applying to the first 2D representation a selected linear mapping, where that selected linear mapping would map, in order to match dimensions of the respective slice within the 3D representation, a region defined by projection, at the respective focus, of corners of that slice onto the detector plane, ii) incrementing values of each of one or more voxels of the respective slice by an amount that is a function of a value of a correspondingly indexed pixel of the second 2D representation.
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Abstract
The invention provides improvements in reconstructive imaging of the type in which a volume is reconstructed from a series of measured projection images (or other two-dimensional representations) generated by projection of a point x-ray source (or other radiation source), positioned at a distinct focus, through the volume to a plane at which the respective projection image is acquired (“detector plane”). In one aspect, the improvements are with respect to back-projecting a two-dimensional representation lying in the detector plane (representing, for example, a difference between an originally-acquired measured projection image and a subsequently-generated estimate thereof) to generate three-dimensional representation (which can be used, for example, to update an estimate of the volume). According to this aspect, for each of one or more slices of the 3D representation parallel to the projection plane and for each distinct focus at which a projection is generated, the following steps are performed in connection with the back-projection: (i) warping the first 2D representation to generate a second 2D representation by applying to the first 2D representation a selected linear mapping, where that selected linear mapping would map, in order to match dimensions of the respective slice within the 3D representation, a region defined by projection, at the respective focus, of comers of that slice onto the detector plane, and (ii) incrementing values of each of one or more voxels of the respective slice by an amount that is a function of a value of a correspondingly indexed pixel of the second 2D representation. A related aspect provides improvements with respect to forward-projecting, as well as in iterative (and non-iterative) methodologies that incorporate both back-projection and forward-projection.
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Citations
24 Claims
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1. In reconstruction imaging in which a volume is reconstructed from a series of measured projection images, each generated by projection of a radiation source positioned at a respective focus through the volume to a detector at which the respective measured projection image is acquired (“
- detector plane”
), an improved method of back-projecting a two-dimensional (2D) representation (“
first 2D representation”
) to a generate three-dimensional (3D) representation, where the first 2D representation is in the detector plane, the improvement comprisingfor each of one or more slices of the 3D representation parallel to the detector plane and for each distinct focus at which a said measured projection images is generated, performing the steps of;
i) warping the first 2D representation to generate a second 2D representation, the warping step including applying to the first 2D representation a selected linear mapping, where that selected linear mapping would map, in order to match dimensions of the respective slice within the 3D representation, a region defined by projection, at the respective focus, of corners of that slice onto the detector plane, ii) incrementing values of each of one or more voxels of the respective slice by an amount that is a function of a value of a correspondingly indexed pixel of the second 2D representation. - View Dependent Claims (2, 3, 4, 5, 6)
- detector plane”
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7. In reconstruction imaging in which a volume is reconstructed from one or more projection images, each generated by projection of a radiation source positioned at a respective focus through the volume to a plane at which the respective projection image is acquired (“
- detector plane”
), an improved method of forward-projecting a three-dimensional (3D) representation (“
first 3D representation”
) to generate a two-dimensional (2D) representation, where the 2D representation is in the detector plane, the improvement comprisingfor each distinct focus at which a said projection image is generated and for each of one or more slices in the first 3D representation parallel to the detector plane, performing the steps of i) warping the respective slice of the first 3D representation to generate a respective slice of second 3D representation, the warping step including applying to the respective slice of the 3D representation a selected linear mapping, where that selected linear mapping would map a region defined by projection of corners of the respective projection image onto the respective slice for the respective focus to match dimensions of the projection image in the detector plane, ii) incrementing values of each of one or more pixels of the 2D representation by an amount that is a function of a value of a correspondingly indexed pixel of the respective slice of the second 3D representation. - View Dependent Claims (8, 9, 10, 11)
- detector plane”
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12. In a method of medical imaging in which a volume is reconstructed from a series of projection images, each generated by projection of a radiation source positioned at a respective focus through the volume to a detector plane at which the respective projection is acquired (“
- detector plane”
), the improvement comprising the steps of;
A. for each focus, forward-projecting a three-dimensional (3D) representation (“
first 3D representation”
that is an estimate of the volume) to generate a two-dimensional (2D) representation (“
first 2D representation”
) that is an estimate of the projection acquired with the source positioned at that respective focus,the forward-projecting step including warping one or more slices of the first 3D representation to generate corresponding slices of a second 3D representation by mapping voxels of the respective slice of the first 3D representation to voxels of the corresponding slice of the second 3D representation as if rays from the source, when positioned at the respective focus, projected through the volume at a substantially constant angle normal to the detector plane of the respective projection, where the 2D representation is in the detector plane and where the slices of the first and second 3D representation are parallel to the detector plane, B. for each of the selected focus, back-projecting a 2D representation (“
second 2D representation”
) that is a function of the first 2D representation and a respective projection to generate a third 3D representation,the back-projecting step including warping the second 2D representation to generate a third 2D representation by mapping pixels of the second 2D representation to pixels of the third 2D representation as if rays from the source, when positioned at the respective focus, projected through the volume at a substantially constant angle normal to the detector plane of the respective projection, where the second and third 2D representations are in the detector plane. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24)
- detector plane”
Specification