Tomographic Reconstruction via Convex Optimization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing tomographic reconstruction methods face challenges in producing high-quality images from incomplete measured frequency samples, particularly when the object or its Fourier transform is not sparse, leading to inefficiencies in image acquisition and potential artifacts like ringing due to diffraction limitations.
Innovation Solution
A computer-implemented method for tomographic reconstruction that employs a convex optimization model maximizing sparsity of image variations using a priori attributes, with a weighting factor, and an iterative process involving homotopic and quadratic relaxation parameters to generate image data, allowing for piece-wise constant images without penalizing large discontinuities, and incorporating efficient algorithms for real-time imaging.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional tomographic reconstruction methods are used with incomplete frequency samples, then image reconstruction can be performed, but image quality deteriorates due to diffraction limitations and ringing artifacts
Solution Approach 1:
The patent transforms the reconstruction problem by changing the parameter space from direct Fourier inversion to a homotopic optimization approach. By introducing a homotopic parameter that continuously deforms the reconstruction from a relaxed state to the final solution, the method achieves superresolution beyond traditional diffraction limits while working with incomplete frequency samples.
Solution Approach 2:
The patent introduces an intermediary optimization framework that mediates between the incomplete frequency data and the final image reconstruction. The homotopic optimization process acts as an intermediary mechanism that gradually builds the image solution, avoiding the direct inversion problems that cause ringing artifacts and allowing recovery of high-frequency information that would otherwise be lost.
2Measurement precision
If more frequency samples are acquired to improve image quality, then measurement precision increases, but acquisition time increases
Solution Approach 1:
The patent applies partial action by acquiring only a subset of the full frequency spectrum - specifically, incomplete frequency samples without needing to cover the entire k-space. The homotopic optimization method recovers the missing information through mathematical transformation, achieving high-quality reconstruction with less data acquisition than traditional methods would require.
Solution Approach 2:
By changing the reconstruction parameter space to include homotopic deformation and total variation minimization, the system can achieve high-resolution images from accelerated (reduced sampling) data. This parameter transformation allows the reconstruction algorithm to infer missing high-frequency information without requiring prolonged data acquisition.
3Measurement precision
If complete frequency sampling is performed to avoid artifacts, then image quality improves, but the amount of data to be processed increases
Solution Approach 1:
The patent extracts only the essential frequency information needed for reconstruction by using incomplete sampling strategies. Rather than processing the complete frequency spectrum, the method identifies and utilizes the critical sampling points, then recovers the full image through homotopic optimization, thereby reducing the quantity of data that must be acquired and processed while maintaining image quality.
Solution Approach 2:
The method performs partial sampling of the frequency domain - acquiring fewer samples than the full Nyquist requirement - and relies on the homotopic optimization process to compensate for the missing data. This partial action approach reduces data volume while the mathematical framework ensures complete image reconstruction without traditional artifacts.
4Productivity
If conventional reconstruction algorithms are used with undersampled data, then processing speed is maintained, but image quality deteriorates due to ringing artifacts
Solution Approach 1:
The patent replaces the conventional direct Fourier inversion mechanism with a homotopic optimization system. Instead of using the traditional mechanical approach of direct inverse transformation that produces ringing artifacts from undersampled data, the system employs a continuous deformation optimization process that gradually reconstructs the image, eliminating artifacts while maintaining computational efficiency through iterative refinement.
Solution Approach 2:
The homotopic optimization framework serves as an intermediary processing layer between the undersampled data and the final image. This intermediary process transforms the reconstruction approach from direct inversion to gradual optimization, resolving the conflict between processing speed and image quality by finding the optimal path through parameter space that avoids artifact generation.
Data Source
Figure 1
Figure 2
Figure 3~4
AI summary
Systems and methods for tomographic reconstruction of an image include systems and methods for producing images from k-space data. A k-space data set of an imaged object is acquired using know k-space data acquisition systems and methods. A portion of the k-space data set is sampled so as to collect some portion of the k-space data. An image is then reconstructed from the collected portion of the k-space data set according to a convex optimization model.