Variational Auto-Encoder Image Reconstruction for Ill-Conditioned Inversion
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Solution Overview
Problem
Image reconstruction in electromagnetic data imaging is challenged by non-linear ill-conditioned problems due to a large number of pixels exceeding data points, requiring priori knowledge that is difficult to mathematically constrain, leading to computationally intensive and inflexible inversion processes.
Innovation Solution
Utilizing a variational auto-encoder deep neural network to minimize an actually measured data inversion objective function, reducing the number of unknowns by encoding and decoding latent space parameters to obtain a reconstructed image.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a large number of pixels are used to decompose the inversion domain, then the image reconstruction precision is improved, but the computational complexity increases and the problem becomes non-linear ill-conditioned
Solution Approach 1:
The patent extracts the essential features of the image by encoding pixel data into a compressed latent space representation. Instead of directly inverting all pixel values, the method extracts key characteristics into a lower-dimensional latent space, reducing the number of unknowns while preserving the essential information needed for accurate reconstruction.
Solution Approach 2:
The patent changes the parameter space by transforming the original pixel domain into a latent space domain. By optimizing the objective function in the latent space rather than the pixel space, the method reduces computational complexity while maintaining reconstruction precision. The latent space parameters serve as intermediate variables that are more efficient to optimize.
2Reliability
If traditional inversion methods are used with priori knowledge, then the reconstruction can be achieved, but the method is inflexible and difficult to mathematically constrain
Solution Approach 1:
The patent introduces a dynamic and flexible deep learning framework that can adapt to different imaging scenarios. The variational auto-encoder and objective function optimization provide a versatile approach that can incorporate various types of priori knowledge through the loss function design, making the method adaptable to different applications while maintaining mathematical rigor.
Solution Approach 2:
The patent replaces traditional mechanical inversion methods with a data-driven deep learning approach. By using neural networks to learn the mapping from measurements to images and employing gradient-based optimization, the method achieves both flexibility in handling different priori knowledge and mathematical constrainability through the differentiable objective function.
3Manufacturing precision
If the number of pixels is much larger than the quantity of data, then the image detail resolution is improved, but the inversion problem becomes ill-conditioned and requires reasonable reconstruction relying on priori knowledge
Solution Approach 1:
The patent introduces a new dimension by adding the latent space as an intermediate representation layer between measurements and final images. This additional dimensional space allows the method to bridge the gap between limited data and high-resolution images by learning meaningful representations that capture essential features without requiring as many direct pixel measurements.
Solution Approach 2:
The patent performs preliminary action by pre-training the variational auto-encoder on large datasets to learn effective latent space representations before applying it to the specific inversion problem. This preliminary learning phase enables the model to capture general image features and priors, which then stabilize the subsequent inversion process even with limited measurement data.
Data Source
AI summary
The present disclosure belongs to the technical field of image reconstruction, and relates to an image reconstruction method and apparatus, and an electronic device and a storage medium. In the present disclosure, an actually measured data inversion objective function is minimized by means of a variational auto-encoder deep neural network, so as to obtain a target latent space parameter of the actually measured data inversion objective function, and the target latent space parameter is then decoded by using the variational auto-encoder deep neural network, so as to obtain a reconstructed image. The image reconstruction method comprises: acquiring actually measured data of a target; constructing, according to the actually measured data, an actually measured data inversion objective function which takes a latent space parameter of a variational auto-encoder deep neural network as an unknown number; minimizing the actually measured data inversion objective function by using the variational auto-encoder deep neural network, so as to obtain a target latent space parameter; and decoding the target latent space parameter by using the variational auto-encoder deep neural network, so as to obtain a target reconstructed image.