FFT-Based Neural Network for Low-Complexity Medical Image Reconstruction
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Solution Overview
Problem
Current medical imaging technologies face challenges in efficiently transforming scan data from the measurement domain to the image domain, particularly with high-resolution or 3D imaging, due to the computational expense and suboptimal quality of iterative reconstruction methods, and the limitations of fully connected networks in learning tomographic reconstruction operators.
Innovation Solution
A neural network architecture based on the Cooley-Tukey fast Fourier transform (FFT) is used to learn optimal reconstruction operators, maintaining O(n log n) complexity, which includes a convolutional splitting layer, parallel recursive deep networks, and a convolutional butterfly layer, enabling efficient transformation and reconstruction in medical imaging systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative reconstruction methods are used to transform scan data to image domain, then image quality can be improved by modeling noise and artifacts, but computational expense and reconstruction time increase significantly
Solution Approach 1:
The patent replaces the traditional iterative mechanical reconstruction process with a neural network-based system. The neural network learns the reconstruction mapping from training data and performs direct transformation without iterative loops, substituting the step-by-step mechanical iterative process with a learned direct mapping that achieves similar quality much faster.
Solution Approach 2:
The neural network is trained in advance on large datasets of scan data and corresponding ground truth images. This preliminary training phase allows the network to learn optimal reconstruction patterns beforehand, so that during actual use, reconstruction can be performed rapidly without needing to perform the complex modeling and iterative optimization in real-time.
2Measurement precision
If fully connected networks are used to learn tomographic reconstruction operators, then optimal operators can be learned, but storage and computation complexities become quadratic in the number of pixels, precluding use for high-resolution or 3D imaging
Solution Approach 1:
The patent segments the image reconstruction problem by processing it in the Fourier domain rather than directly in the spatial pixel domain. The neural network operates on frequency components separately, and the inverse Fourier transform reconstructs the final image. This segmentation avoids the quadratic complexity of fully connected networks by working with transformed data that has more favorable computational properties.
Solution Approach 2:
The patent substitutes the traditional fully connected neural network architecture with a hybrid approach that combines Fourier transform operations with a simplified neural network. The Fourier transform component handles the bulk of the transformation with linear complexity, while a smaller neural network component learns only the residual or correction terms, dramatically reducing overall complexity from quadratic to near-linear.
Data Source
AI summary
For low-complexity to learned reconstruction and/or learned Fourier transform-based operators for reconstruction, a neural network is used for the transform operators. The network architecture is modeled on the Cooley-Tukey fast Fourier transform (FFT) approach. By splitting input data before recursive calls in the network architecture, the network may be trained to perform the transform with similar complexity as FFT. The learned operators may be used in a trained network for reconstruction, such as with a learned iterative framework and image regularizer.