Sparse Image Reconstruction via Convex Combination of Deep Networks and Iterative Algorithms
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Solution Overview
Problem
Current image reconstruction methods, particularly those using deep neural networks, face challenges in ensuring convergence and flexibility while maintaining high reconstruction accuracy, especially in sparse image reconstruction tasks.
Innovation Solution
An image processing method that introduces unrestricted network learning parameters based on an iterative soft shrinkage thresholding algorithm, combining it with a differentiable deep neural network using a convex combination to solve linear inverse problems under 1-norm constraints, ensuring convergence and flexibility in network architecture.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional iterative optimization methods are used for image reconstruction, then convergence is guaranteed, but the optimization structure is too rigid and performance is greatly poor compared with deep neural networks
Solution Approach 1:
The patent combines traditional iterative optimization methods with deep neural networks by integrating the iterative soft thresholding algorithm steps into a unified neural network framework. The network learns optimization parameters (step size, threshold) while maintaining the iterative structure, thereby merging the convergence guarantee of traditional methods with the adaptive learning capability of deep networks to achieve both reliability and high performance
Solution Approach 2:
The patent transforms the rigid fixed-parameter iterative optimization into a dynamic system where optimization parameters (step size λ, threshold μ) are learned adaptively by the neural network during training. This allows the optimization process to dynamically adjust parameters based on input data characteristics, improving reconstruction performance while maintaining convergence through the learned parameter updates
2Measurement precision
If deep neural networks are used for image reconstruction, then reconstruction accuracy is improved, but convergence cannot be guaranteed and the structure lacks theoretical foundation
Solution Approach 1:
The patent incorporates feedback mechanisms from the iterative optimization process into the neural network training. The network uses the reconstruction error as feedback to update learned parameters (step size, threshold) in each iteration, ensuring that the optimization process converges while continuously improving reconstruction accuracy through adaptive parameter adjustment based on performance feedback
3Adaptability or versatility
If flexible network parameters are introduced, then model flexibility is improved, but theoretical convergence cannot be demonstrated
Solution Approach 1:
The patent changes the approach to parameter flexibility by having the neural network learn optimization parameters (step size λ, threshold μ) rather than using fixed parameters. This allows the model to adapt to different input characteristics while maintaining theoretical convergence guarantees because the learned parameters follow the iterative optimization framework's convergence conditions, bridging flexibility and theoretical foundation
4Reliability
If traditional iterative algorithms are used, then theoretical foundation is strong, but computational complexity is high and operation speed is slow
Solution Approach 1:
The patent applies preliminary action by pre-training the neural network on training data to learn optimal optimization parameters (step size, threshold) before actual reconstruction. This preliminary learning phase enables the network to perform reconstructions faster during inference, as the learned parameters guide the iterative process more efficiently than traditional fixed-parameter algorithms, reducing the number of iterations needed while maintaining theoretical convergence
Data Source
AI summary
An image processing method for sparse image reconstruction, image denoising, compressed sensing image reconstruction or image restoration, comprising: establishing a general linear optimization inverse problem under the 1-norm constraint of a sparse signal; establishing a differentiable deep network model based on convex combination to solve the problem on the basis of standard or learned iterative soft shrinkage thresholding algorithm; and introducing a deep neural network of arbitrary structure into the solving step to accelerate the solving step and reducing a number of iterations needed to reach a convergence. The present disclosure combines the traditional iterative optimization algorithm with the deep neural network of arbitrary structure to improve the image reconstruction performance and ensure fast convergence to meet the current needs of sparse image reconstruction.