Multi-Material Decomposition Using Total Variation Regularization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Dual-Energy (DE) CT systems face challenges in accurately decomposing more than three materials due to the ill-posed nature of the problem, limiting their applicability in multi-material decomposition tasks.
Innovation Solution
An apparatus and method for multi-material decomposition using dual energy X-ray imagery, which includes an input unit providing Photoelectric and Compton scattering attenuation coefficient images, a processing unit determining volume fractions through an iterative minimization algorithm, and an output unit representing the volume fractions of multiple materials, employing total variation regularization and sparse decomposition mechanisms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If dual energy CT is used for decomposition of more than three materials, then the applicability in multi-material decomposition tasks is improved, but the problem becomes ill-posed and accuracy deteriorates
Solution Approach 1:
The patent transforms the ill-posed decomposition problem into a well-posed optimization problem by changing the mathematical formulation parameters. It introduces regularization terms (total variation and L1 norm) and constraints (non-negativity, volume fractions summing to one) that modify the original system of equations, enabling accurate decomposition of four or more materials while maintaining mathematical stability
Solution Approach 2:
The patent extends the decomposition from traditional two-basis-material decomposition to multi-material decomposition by adding dimensional complexity to the mathematical model. It formulates the problem in terms of volume fractions of multiple materials (four or more) rather than limited to two or three, thereby expanding the solution space to accommodate more material types while maintaining accuracy through regularization
2Device complexity
If traditional DE CT decomposition methods are used, then the system complexity is low, but the number of decomposable materials is limited to three or fewer
Solution Approach 1:
The patent changes the mathematical parameters from a simple linear system to a regularized optimization system with multiple constraints. By introducing total variation regularization, L1 norm sparsity promotion, and volume fraction constraints, the system can handle four or more materials without proportionally increasing hardware complexity, maintaining computational feasibility while expanding material decomposition capability
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
Enables accurate and robust decomposition of four or more materials, improving the quality and explanatory power of quantitative material analysis in medical imaging and beyond.
Implementation Method 1
an X-ray source emits X-ray radiation. The emitted radiation traverses an examination region with a subject or object located within and is detected by a detector array
Implementation Method 2
to solve the photoelectric and Compton contribution that consists of the mass attenuation coefficient of a material
Implementation Method 3
to solve the photoelectric and Compton contribution that consists of the mass attenuation coefficient of a material
Data Source
AI summary
The present invention relates to an apparatus for multi material decomposition of an object. It is described to provide (310) at least one image of an object. The at least one image is derived from at least one spectral X-ray image of the object, and the at least one image comprises a Photoelectric total attenuation coefficient image and a Compton scattering total attenuation coefficient image. A plurality of Photoelectric attenuation coefficients are provided (320) for a plurality of materials, each Photoelectric attenuation coefficient being associated with a corresponding material. A plurality of Compton scattering attenuation coefficients are provided (330) for the plurality of materials, each Compton scattering attenuation coefficient being associated with a corresponding material. A total volume constraint is set (340) at an image location in the at least one image as a function of the sum of individual volumes of the plurality of materials at the image location. Volume fractions of the plurality of materials are determined (350) at the image location according to an overall function comprising: a Photoelectric total attenuation coefficient at the image location taken from the Photoelectric total attenuation coefficient image; a Compton scattering total attenuation coefficient at the image location taken from the Compton scattering total attenuation coefficient image; the plurality of Photoelectric attenuation coefficients for the plurality of materials; the plurality of Compton scattering attenuation coefficients for the plurality of materials; and the total volume constraint. Data representative of the volume fractions of the plurality of materials is output (360).