Simplified Spherical Harmonics Algorithm for DOT Image Reconstruction
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Solution Overview
Problem
Diffuse optical tomography (DOT) imaging for diagnosing conditions like rheumatoid arthritis faces significant challenges due to lengthy computation times and high computational resource requirements, primarily attributed to the complexity of algorithms used in image reconstruction, particularly with the equation of radiative transfer (ERT) models.
Innovation Solution
The implementation of a combined partial differential equation (PDE)-constrained and simplified spherical harmonics (SPN) algorithm for image reconstruction in DOT, which serves as a forward model in a PDE-constrained reduced space sequential quadratic programming (rSQP) optimization method, reducing computational resources and time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the equation of radiative transfer (ERT) algorithm is used for image reconstruction, then measurement precision is improved, but computation time and device complexity increase significantly
Solution Approach 1:
The patent uses simplified spherical harmonics (SPN) equations as an approximate copy of the more accurate but computationally intensive ERT model. The SPN equations replicate the essential physics of light propagation in tissue while using a simplified mathematical formulation that can be solved much faster, achieving a balance between accuracy and computational efficiency.
Solution Approach 2:
The patent changes the mathematical parameters and formulation of the light propagation model by transitioning from the ERT equation to the SPN equation system. This parameter change involves reformulating the radiative transfer equation in terms of spherical harmonics expansions, which fundamentally alters the computational complexity while maintaining physical accuracy for the intended application.
2Measurement precision
If the equation of radiative transfer (ERT) algorithm is used for image reconstruction, then measurement precision is improved, but computational resources (RAM) required increase significantly
Solution Approach 1:
The patent creates a simplified computational model (SPN equations) that copies the essential functional behavior of the ERT model without requiring the same computational resources. The SPN formulation uses fewer mathematical operations and smaller data structures, reducing RAM requirements while maintaining sufficient accuracy for clinical diagnosis.
Solution Approach 2:
The patent applies partial action by using a truncated spherical harmonics expansion (e.g., up to order 3 or 5) rather than the complete ERT solution. This partial approximation captures the most important physical effects for tissue imaging while omitting higher-order terms that would require proportionally more computational resources.
3Loss of time
If simplified spherical harmonics (SPN) algorithm is used for image reconstruction, then computation time is reduced, but measurement precision may deteriorate
Solution Approach 1:
The patent optimizes the SPN formulation by carefully selecting the expansion order and implementing specialized algorithms (such as the rSQP optimization method with PDE constraints) that enhance the accuracy of the simplified model. These parameter optimizations allow the SPN approach to achieve diagnostic accuracy comparable to ERT while maintaining significant computational speedup.
Solution Approach 2:
The patent incorporates feedback mechanisms through the PDE-constrained optimization framework, where the SPN model predictions are continuously compared with measured data and used to iteratively refine the reconstruction. This feedback loop compensates for the simplifications in the SPN equations, improving the final measurement precision.
Data Source
AI summary
Systems, methods, and devices for image reconstruction using combined PDE-constrained and simplified spherical harmonics (SPN) algorithm are presented herein. SPN equations can be used as the forward model in diffuse optical tomography (DOT) and employed in a PDE-constrained reduced space sequential quadratic programming (rSQP) optimization method to reconstruct spatially distributed optical properties, such as absorption, scattering, fat, oxygenated hemoglobin, de-oxygenated hemoglobin, fluorescent concentration, quantum yield, etc. The SPN algorithm with the PDE-constrained rSQP optimization method allows for DOT imaging that uses significantly less computational resources (e.g., time and random-access memory (RAM)) than methods employing the equation of radiative transfer (ERT). The techniques disclosed herein allow for more expeditious image processing as well as the potential for clinical diagnosis using DOT imaging. Diagnosis can be performed by a computer-aided diagnosis (CAD) system, which can provide clinically relevant analysis and interaction shortly after patient imaging.