Focused Blind Deconvolution for Unique Response Function Recovery
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Solution Overview
Problem
Existing blind deconvolution techniques face significant non-uniqueness issues, making it difficult to accurately recover response functions and source signals due to multiple possible estimated response functions that, when convolved, result in the recorded signal.
Innovation Solution
The implementation of focused blind deconvolution methods using constraints that maximize the whiteness and front-loading of response functions, allowing for the recovery of system response functions without prior assumptions about the source signal or system physics, through a two-step optimization process involving focused blind interferometric deconvolution and phase retrieval.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional blind deconvolution techniques are used, then the method can process measured signals, but the response function estimation is non-unique and inaccurate
Solution Approach 1:
The patent applies parameter changes by transforming the deconvolution problem into the frequency domain using spectral analysis. By working with spectra instead of time-domain signals directly, the method converts the non-unique time-domain deconvolution into a unique frequency-domain solution, resolving the ambiguity in response function estimation while maintaining measurement precision.
Solution Approach 2:
The patent substitutes the mechanical signal processing approach with a mathematical spectral analysis approach. Instead of using traditional time-domain deconvolution algorithms that suffer from non-uniqueness, the invention uses spectral factorization and cross-spectral density methods to obtain unique and accurate response function estimates.
2Loss of information
If multiple possible estimated response functions are considered, then the recorded signal can be reproduced, but the actual system response cannot be uniquely identified
Solution Approach 1:
The patent employs feedback mechanisms through iterative spectral factorization processes. The method continuously refines the response function estimate by comparing predicted and actual spectral characteristics, using the differences to adjust and improve the estimation until convergence is achieved, thereby recovering the actual response function information that would otherwise be lost.
Solution Approach 2:
The patent applies preliminary action by pre-processing the measured signals to compute spectral estimates and cross-spectral densities before performing the actual deconvolution. This preliminary spectral analysis prepares the data in a transformed domain where the response function can be uniquely identified, preventing information loss before it occurs.
3Device complexity
If conventional deconvolution methods are used without constraints, then the processing is simpler, but the results are ambiguous and imprecise
Solution Approach 1:
The patent segments the deconvolution process into distinct sequential steps: spectral estimation, spectral factorization, and inverse transformation. By dividing the complex deconvolution problem into these manageable segments, the method achieves precise response function recovery while keeping each individual step computationally simple and well-defined.
Data Source
AI summary
Systems and methods for performing focused blind deconvolution of signals received by a plurality of sensors are disclosed. In some embodiments, this may include determining a cross-correlation of first and second signals, obtaining a cross-correlation of a first response function and a second response function based on the cross-correlation of the first and second signals and subject to a first constraint that the first and second response functions are maximally white, and obtaining the first and second response functions based on the cross-correlation of the first and second response functions and subject to a second constraint that the first and second response functions are maximally front-loaded.