Multi-Channel Image Restoration via Frequency Domain Diagonalization
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Solution Overview
Problem
Current multi-channel image restoration techniques are inefficient as they process channels independently, ignoring inter-channel degradations, and rely on time and resource-intensive iterative methods involving large matrix inversions.
Innovation Solution
The method processes all channels simultaneously, addressing both intra-channel and inter-channel degradations by transforming the restoration into smaller frequency domain operations, avoiding large matrix inversions, and allowing for spatial adaptation and efficient processing of window-boundary data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If multi-channel image restoration processes each color channel independently, then the processing is simpler and faster, but it ignores inter-channel degradations and correlations resulting in inferior restoration quality
Solution Approach 1:
The patent merges all color channels into a single multi-channel image vector g and formulates a unified restoration equation that processes all channels simultaneously. This combining approach captures inter-channel correlations and degradations while maintaining computational efficiency through the derived closed-form solution, resolving the contradiction between processing speed and restoration accuracy.
Solution Approach 2:
The patent transforms the restoration problem from spatial domain to frequency domain by applying Fourier transforms. This parameter transformation allows the use of efficient frequency-domain convolution and matrix operations, achieving both fast processing and accurate restoration by exploiting the diagonal structure of the degradation operator in the frequency domain.
2Measurement precision
If multi-channel image restoration uses joint processing of all channels, then restoration accuracy improves by capturing inter-channel correlations, but computational complexity increases due to large matrix inversions
Solution Approach 1:
The patent changes the domain parameter from spatial to frequency domain, where the degradation operator becomes diagonal. This transformation reduces the computational complexity from inverting a large non-diagonal matrix to inverting smaller diagonal matrices in the frequency domain, achieving both accurate joint processing and computational efficiency.
Solution Approach 2:
The patent replaces the computationally intensive iterative spatial-domain matrix inversion with an efficient closed-form frequency-domain solution. By substituting the mechanical iterative process with a direct frequency-domain calculation, the method achieves accurate multi-channel restoration without the burden of large matrix inversions.
3Measurement precision
If multi-channel image restoration uses joint processing of all channels, then restoration accuracy improves by capturing inter-channel correlations, but processing time increases due to iterative or recursive methods
Solution Approach 1:
The patent inverts the conventional approach by deriving a closed-form solution instead of using iterative methods. By inverting the degradation operator directly in the frequency domain and applying it to the multi-channel image vector, the method achieves accurate restoration in a single computational pass, eliminating the time-consuming iterative loops while maintaining joint channel processing.
Data Source
AI summary
An imager and method for operating the imager. The imager comprises a pixel array for producing an image signal and an image processor configured to restore images degraded by inter-channel degradations and intra-channel degradations in all channels of the image simultaneously by diagonalizing an image degradation matrix and componentizing the diagonalized image degradation matrix and multi-channel image.