Complex-valued Neural Network for MR Fingerprinting Phase Preservation
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Solution Overview
Problem
Current neural networks for medical imaging, particularly in magnetic resonance (MR) applications, often ignore the complex phase information, leading to distortion and inefficiency in processing complex-valued signals, which are crucial for applications like MR fingerprinting and flow imaging.
Innovation Solution
A complex-valued neural network with learnable parameters in the complex domain, such as the Cardioid or kernel activation functions, is trained to maintain and exploit the phase information, allowing for better representation and processing of complex-valued data, including real and imaginary components or magnitude and phase dimensions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If real-valued neural networks are used for MR imaging, then the system is simpler to implement, but phase information is lost leading to reduced accuracy
Solution Approach 1:
The patent transitions from real-valued to complex-valued neural networks, adding an imaginary dimension to the network operations. This allows the network to process both magnitude and phase information simultaneously through complex arithmetic operations, resolving the contradiction by sacrificing some implementation simplicity for significant gains in phase information preservation and measurement precision.
Solution Approach 2:
The patent changes the fundamental parameter domain from real numbers to complex numbers. By defining activation functions, weight updates, and mathematical operations in the complex domain, the network can naturally preserve phase information while maintaining learnable parameters, thus improving measurement precision without excessive complexity increase.
2Ease of operation
If complex values are split into separate real and imaginary channels with real-valued non-linearities, then the network is easier to implement, but phase information is distorted
Solution Approach 1:
Instead of treating real and imaginary parts as separate independent channels, the patent operates in the complex domain where these components are intrinsically linked through complex arithmetic. Complex activation functions and operations preserve the phase relationship between real and imaginary parts, preventing information loss while maintaining reasonable implementation complexity through established complex mathematics.
Solution Approach 2:
The patent merges the treatment of real and imaginary components by using complex-valued activation functions that operate on the combined complex input. This unified approach preserves the phase information that would be lost if real and imaginary parts were processed separately with real-valued non-linearities.
3Loss of information
If complex-valued activation functions are used, then phase information is preserved, but the network complexity increases
Solution Approach 1:
The patent changes the parameter domain to complex numbers, allowing activation functions to preserve phase information naturally. While this increases theoretical complexity, practical implementation benefits from the well-established framework of complex arithmetic and can be efficiently computed using standard libraries and hardware support for complex operations.
Data Source
AI summary
For machine training and application of a trained complex-valued machine learning model, an activation function of the machine learning model, such as a neural network, includes a learnable parameter that is complex or defined in a complex domain with two dimensions, such as real and imaginary or magnitude and phase dimensions. The complex learnable parameter is trained for any of various applications, such as MR fingerprinting, other medical imaging, or non-medical uses.