fsHBMAP Algorithm for Tomographic Image Reconstruction
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Solution Overview
Problem
Current image recovery algorithms face challenges in achieving high-quality reconstruction efficiently, especially under sub-Nyquist sampling and with sensor noise, often requiring substantial computational resources.
Innovation Solution
The Fast Stochastic Hierarchical Bayesian MAP (fsHBMAP) algorithm employs stochastic approximation techniques to reduce computational complexity while maintaining high reconstruction quality, incorporating probabilistic knowledge of scene structure and using Compound Gaussian models for robust inference.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional image recovery algorithms are used to achieve high-quality reconstruction, then reconstruction quality is improved, but computational complexity increases significantly
Solution Approach 1:
The patent transforms the image recovery problem from the spatial domain to the wavelet domain by changing the representation parameters. This transformation allows the algorithm to exploit the sparsity and self-similarity properties of images in the wavelet domain, achieving high-quality reconstruction with reduced computational complexity through parameter optimization rather than brute-force computation
Solution Approach 2:
The patent segments the image into multiple patches and processes them independently or in groups. This segmentation approach allows the algorithm to capture local self-similarity patterns more effectively and reduces the overall computational burden by breaking down the large-scale optimization problem into smaller, more manageable sub-problems
2Measurement precision
If traditional image recovery algorithms are used with limited samples, then reconstruction quality deteriorates, but using more samples increases measurement requirements
Solution Approach 1:
The patent incorporates a feedback mechanism through its iterative optimization algorithm that uses the observed measurements to progressively refine the reconstruction. The algorithm leverages the self-similarity prior to guide the search for the most likely original image, effectively using the limited measurements multiple times through iterative refinement rather than requiring more raw samples
Solution Approach 2:
The patent applies preliminary transformations to the measurement data, including Fourier transforms and wavelet transforms, before the main reconstruction process. These preliminary actions pre-process the limited measurements to extract useful information in transformed domains, making the subsequent reconstruction more efficient and effective with the available data
3Measurement precision
If sensor noise is present in measurements, then reconstruction accuracy decreases, but filtering noise reduces useful signal information
Solution Approach 1:
The patent applies local quality processing by operating on image patches independently and using localized wavelet transforms. This allows the algorithm to preserve local signal characteristics and edges while suppressing noise, as each patch can be reconstructed with appropriate local priors without being affected by noise in other regions
Solution Approach 2:
The patent uses a composite modeling approach by combining multiple prior models (sparsity prior, self-similarity prior, and Gaussian noise model) into a unified probabilistic framework. This composite model allows the algorithm to simultaneously exploit multiple image properties while robustly handling noise through the probabilistic formulation
Data Source
AI summary
Systems and methods are provided for imaging that demonstrably outperform previous approaches (especially compressive sensing based approaches). Embodiments of the present disclosure provide and solve an imaging cost function via a stochastic approximation approach. By doing so, embodiments of the preset disclosure provide a significant means of generalization and flexibility to adapt to different application domains while being competitive in terms of computational complexity.