3D Image Reconstruction from Variable-Radius Cone-Beam Data
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Solution Overview
Problem
Current methods for reconstructing three-dimensional image datasets from cone-beam projections are limited by the need for circular or convex trajectories, which restrict the use of non-circular and variable-radius trajectories in X-ray imaging systems, particularly those with telescopic arms, where the X-ray source moves along a planar polygon-based path.
Innovation Solution
A novel reconstruction algorithm that allows for exact or approximate three-dimensional image reconstruction from cone-beam data acquired along a variable-radius, planar source trajectory, which can be non-convex and described by a series of points in space, using a combination of differentiation, filtering, redundancy weighting, and backprojection steps, enabling the use of non-circular and complex geometries.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If circular or convex trajectories are used for X-ray source movement, then reliable 3D image reconstruction is achieved, but the adaptability to non-circular and variable-radius trajectories is limited
Solution Approach 1:
The patent changes the fundamental parameters of the reconstruction algorithm to accommodate variable-radius trajectories. It introduces a new geometric model that parameterizes the source trajectory using polynomial functions, allowing the radius to vary as a function of the angular position. This enables the system to handle non-circular trajectories while maintaining reconstruction reliability through mathematically rigorous transformations of the projection data.
Solution Approach 2:
The patent makes the trajectory dynamic by allowing the source-to-rotation-axis distance to vary continuously during the scan. Instead of fixing the radius as a constant, the system dynamically adjusts the radial parameter based on the actual trajectory, enabling adaptation to elliptical, polygonal, and other non-circular paths while maintaining accurate 3D reconstruction.
2Adaptability or versatility
If non-circular and variable-radius trajectories are used, then the adaptability of imaging systems is improved, but the manufacturing precision of reconstruction algorithms deteriorates
Solution Approach 1:
The patent performs preliminary actions by pre-characterizing the actual source trajectory before reconstruction. It measures or estimates the variable radius as a function of angular position, fits this data to a polynomial model, and uses this pre-computed geometric information to guide the reconstruction process. This preliminary characterization ensures that the subsequent reconstruction maintains high precision despite the non-circular trajectory.
Solution Approach 2:
The patent introduces an intermediary geometric model that acts as a bridge between the actual variable-radius trajectory and the reconstruction algorithm. This intermediate representation, based on polynomial parameterization of the source position, transforms the complex non-circular trajectory into a form that can be processed by modified backprojection or iterative reconstruction algorithms, preserving precision while enabling adaptability.
3Device complexity
If conventional fan-beam geometry with one-dimensional detector array is used, then the device complexity is reduced, but the ability to acquire cone-beam projections for 3D reconstruction is limited
Solution Approach 1:
The patent transitions from the conventional two-dimensional fan-beam geometry to three-dimensional cone-beam geometry by introducing a second spatial dimension to the detector array. Instead of a one-dimensional array detecting fan-shaped beams, the system uses a two-dimensional array to capture cone-shaped beams, enabling true 3D volume reconstruction from projections acquired during the variable-radius trajectory scan.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The algorithm effectively recovers the shape of the field-of-view and provides accurate 3D image reconstruction for a wide range of geometries, including those with significant variations in source-detector distance and non-circular scan radii, enabling the use of X-ray systems with telescopic arms for medical and industrial imaging.
Implementation Method 1
an X-ray source emitting X-rays in a cone-shaped beam (generally called cone beam) and a detector comprising a two-dimensional (2D) array of detector elements for acquiring one projection image
Implementation Method 2
Each detector produces an electrical signal that is a measurement of the attenuation of the X-ray beam by the object
Data Source
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AI summary
The invention is directed to a method for producing a 3D image dataset of an object (20) with an imaging system (1) having an X-ray source (4) for emitting photon rays in a cone beam and a detector (10) comprising a two-dimensional array of detector elements adapted for receiving photons emitted by the X-ray source, the method comprising: acquiring (100) a series of two-dimensional arrays of cone beam data from the detector (10) while the source (4) moves along a substantially planar trajectory (40) around the object to be imaged, the trajectory being described by a series of source points serially numbered by a counter parameter; and reconstructing a 3D image from the cone beam data by performing the following steps: A) differentiating the cone beam data with respect to the counter parameter (λ) of the source trajectory at fixed ray direction (α) to produce a derivative of the cone beam data; B) filtering the derivative with a Hilbert-like filter to produce filtered cone beam data; C) either before step A), or after step B) multiplying the acquired cone beam data or the filtered cone beam data, respectively, with a redundancy weighting function; and D) back-projecting the cone beam data to compute a 3D image dataset. The invention is also directed to an imaging system (1) and a computer program product.