Method and system of fluorescence molecular tomography based on wavelet and Schur decomposition
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The existing methods for fluorescence molecular tomography reconstruction face significant challenges in speed due to the large-scale matrix calculations involved in solving direct matrix equations, which hinder the improvement of reconstruction speed and efficiency.
Innovation Solution
A reconstruction method and system utilizing wavelet transform and Schur decomposition to transform and solve the linear matrix equation, reducing the number of conditions through Schur complement decomposition, thereby facilitating faster and more accurate reconstruction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If direct solution method is used for large-scale matrix equations in fluorescence molecular tomography reconstruction, then reconstruction accuracy can be maintained, but reconstruction speed deteriorates significantly
Solution Approach 1:
The patent applies wavelet transform to decompose the large-scale matrix equation into multiple resolution levels, segmenting the problem into coarse and fine components. This allows iterative refinement from coarse to fine scales, maintaining accuracy while reducing computational burden at each level.
Solution Approach 2:
The patent transforms the original matrix equation into a different dimensional representation using wavelet basis functions. By changing the representation dimension from spatial domain to wavelet coefficient domain, the computational complexity is reduced while preserving the essential information needed for accurate reconstruction.
2Manufacturing precision
If direct solution method is used for matrix equations, then reconstruction quality can be maintained, but calculation amount increases
Solution Approach 1:
The patent extracts and separates the dominant low-frequency components from the high-frequency details using wavelet transform. By solving the coarse approximation first and then adding detailed corrections iteratively, the method reduces the total calculation amount while maintaining reconstruction quality.
Solution Approach 2:
The patent performs preliminary wavelet decomposition and coarse-scale solution before refining with detailed components. This preliminary action at coarse resolution reduces the overall computational burden by pre-establishing the dominant features, reducing the quantity of subsequent calculations needed.
3Loss of information
If direct solution method is used for large-scale matrix equations, then complete information can be processed, but reconstruction time increases
Solution Approach 1:
The patent implements a dynamic iterative refinement process where the solution evolves from coarse to fine scales. At each iteration level, information completeness is progressively enhanced while controlling reconstruction time through adaptive stopping criteria and multi-resolution processing.
Solution Approach 2:
The patent uses nested wavelet decomposition levels where coarse-scale solutions are embedded within fine-scale refinements. This nesting structure allows progressive information completion from inner (coarse) to outer (fine) layers, managing reconstruction time through hierarchical processing.
Data Source
AI summary
The present invention discloses a reconstruction method and system of fluorescence molecular tomography based on wavelet and Schur decomposition, the method including the steps of: transforming the inverse problem of fluorescence molecular tomography into a linear matrix equation; solving the linear matrix equation and updating reconstruction parameters iteratively using the obtained solution to obtain a final reconstruction result; in which, in the process of solution of the linear matrix equation, wavelet transform is performed on the linear matrix equation to obtain an overview matrix equation, Schur decomposition is performed on the overview matrix equation to obtain a subsystem with a reduced number of conditions, and the linear matrix equation is calculated using the solution of the subsystem. The present invention reduces the amount of calculation in the process of reconstruction, speedups the process of reconstruction, improves the imaging efficiency and further improves the imaging quality.