Schrödinger Operator Image Reconstruction Denoising
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Solution Overview
Problem
Current image reconstruction and denoising methods are inefficient in effectively decomposing and analyzing signals, particularly in noisy environments, and lack the ability to preserve image details and edges.
Innovation Solution
The method employs semi-classical signal analysis (SCSA) using squared eigenfunctions associated with the discrete spectrum of a semi-classical Schrödinger operator, decomposing signals into localized functions and reducing the semi-classical parameter to improve image reconstruction and denoising, particularly by optimizing the λ and γ parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard decomposition methods (Fourier transform, Wavelet, total variations) are used for image reconstruction, then the reconstruction can be achieved, but the performance is insufficient in preserving image details and edges, particularly in noisy environments
Solution Approach 1:
The patent applies parameter changes by introducing the semi-classical parameter h and optimizing λ and γ parameters in the Schrödinger operator framework. By adjusting these parameters, the method adapts to different noise levels and image characteristics, achieving superior reconstruction accuracy and noise resistance compared to fixed-parameter methods like Fourier transform or Wavelet
Solution Approach 2:
The patent replaces traditional mechanical decomposition methods (Fourier transform, Wavelet analysis) with a quantum-inspired Schrödinger operator approach. This substitution introduces squared eigenfunctions as basis functions, which provide better localization properties and adaptability to image features, resulting in improved edge preservation and noise filtering
2Manufacturing precision
If the semi-classical parameter h is reduced to improve image reconstruction quality, then image details and edges are better preserved, but the computational complexity increases
Solution Approach 1:
The patent applies partial action by selectively using only the most significant squared eigenfunctions for reconstruction rather than computing all possible eigenfunctions. This approach maintains high image quality while reducing computational burden, as the method focuses on the essential components needed for accurate reconstruction
Solution Approach 2:
The patent performs preliminary computation of the Schrödinger operator and its eigenfunctions before the actual reconstruction process. By pre-computing the basis functions and organizing them efficiently, the method reduces the computational complexity during the reconstruction phase, making the overall process more manageable
Data Source
AI summary
A method and system can analyze, reconstruct, and/or denoise an image. The method and system can include interpreting a signal as a potential of a Schrödinger operator, decomposing the signal into squared eigenfunctions, reducing a design parameter of the Schrödinger operator, analyzing discrete spectra of the Schrödinger operator and combining the analysis of the discrete spectra to construct the image.