Double-Exposure Image Recovery via Toeplitz Matrix Inversion
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Solution Overview
Problem
Conventional shearographic imaging systems require additional conventional spotting imagers for double-exposure image processing, leading to increased size, weight, power consumption, and processing complexity, as well as difficulty in undoing double-exposure effects in unrelated images.
Innovation Solution
The method involves aligning the shift direction of double-exposure images along a coordinate axis, expressing the double-exposure operator as a Toeplitz matrix, and recovering single-exposure images through regularized pseudo-inversion or singular value decomposition, followed by modified Landweber iteration to improve the estimated images, reducing the need for additional imagers and processing complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional spotting imagers are paired with shearographic imagers for double-exposure image processing, then single-exposure images can be obtained, but system size, weight, power consumption, and processing complexity increase
Solution Approach 1:
The patent extracts and removes the conventional spotting imager from the shearographic imaging system, eliminating the need for separate single-exposure imaging devices while maintaining the ability to obtain single-exposure images through computational methods applied to the double-exposure shearogram data
Solution Approach 2:
The patent replaces the mechanical/optical system of conventional spotting imagers with a computational algorithm that processes double-exposure shearogram data to recover single-exposure images, substituting physical hardware with mathematical processing
2Loss of information
If conventional spotting imagers are used for double-exposure image processing, then context information is provided, but additional processing required to co-register the spotting functions with shearography systems
Solution Approach 1:
The patent merges the functions of the spotting imager and shearographic imager into a single integrated system, where both single-exposure context information and shearographic measurement data are obtained through one device, eliminating the need for separate co-registration processing between two different imagers
3Loss of information
If double exposures are constructed from unrelated images, then additional information is captured, but undoing the double exposure is extremely difficult or impossible
Solution Approach 1:
The patent introduces the shear vector as an intermediary mathematical parameter that encodes the relationship between the two exposures in the double-exposure shearogram. This intermediary structure allows the recovery algorithm to use the known shear displacement to separate and reconstruct the individual single-exposure images from the combined data
Solution Approach 2:
The patent applies preliminary computational processing steps including aligning the shift direction along a coordinate axis, separating the shift in the coordinate system, and expressing the double-exposure operator as a Toeplitz matrix before performing the actual image recovery, preparing the data in advance to make the inversion feasible
Data Source
AI summary
Systems and methods for double-exposure image processing utilizing inversion techniques are provided. The systems and methods of the present disclosure recover single-exposure images from double-exposure images and strain images from double-exposure images.