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

VSEngineering 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

Engineering Contradiction:
Improvereconstruction reliabilityVSAvoidtrajectory adaptability
Core Design Contradiction:
ReliabilityVSAdaptability or versatility

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.

Inventive Principle:
Principle #35Parameter changes

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.

Inventive Principle:
Principle #15Dynamics

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

Engineering Contradiction:
Improvetrajectory adaptabilityVSAvoidreconstruction precision
Core Design Contradiction:
Adaptability or versatilityVSManufacturing precision

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.

Inventive Principle:
Principle #10Preliminary action

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.

Inventive Principle:
Principle #24Intermediary (Mediator)

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

Engineering Contradiction:
Improvedetector array complexityVSAvoid3D imaging capability
Core Design Contradiction:
Device complexityVSAdaptability or versatility

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.

Inventive Principle:
Principle #17Another dimension (Dimensionality change)

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

Methodology Applied
Scientific EffectX-ray emission: X-Ray

Implementation Method 2

Each detector produces an electrical signal that is a measurement of the attenuation of the X-ray beam by the object

Methodology Applied
Scientific EffectX-ray attenuation: Absorption (EM radiation)

Data Source

PatentEP2317477B1Reconstruction of 3D image datasets from X-ray cone-beam data
Publication Date: 2013.03.27 SIEMENS AG
  • EP2317477B1 patent drawingFigure 1
  • EP2317477B1 patent drawingFigure 2~3
  • EP2317477B1 patent drawingFigure 4~6

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.