Focused Blind Deconvolution Using Whiteness and Front-Loaded Constraints
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Solution Overview
Problem
Existing blind deconvolution techniques face significant non-uniqueness issues, leading to inaccurate recovery of response functions and source signals due to multiple possible estimated response functions that, when convolved, result in the recorded signal, making it difficult to accurately characterize medium properties in drilling and other applications.
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 interferometric blind deconvolution and phase retrieval.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If blind deconvolution techniques are used to recover response functions, then source signals can be estimated, but multiple possible estimated response functions result in non-uniqueness issues
Solution Approach 1:
The patent applies parameter changes by transforming the deconvolution problem into the frequency domain using spectral factorization. This involves changing the representation of signals and response functions from time domain to frequency domain, where the spectral factors can be uniquely determined up to a linear phase term. The transformation to frequency domain allows for unique recovery of response functions by analyzing spectral characteristics rather than direct time-domain deconvolution.
Solution Approach 2:
The patent segments the response function recovery process into distinct steps: (1) computing the cross-power spectral density matrix, (2) performing spectral factorization to obtain spectral factors, (3) determining response functions from spectral factors, and (4) removing linear phase terms. This segmentation breaks down the complex deconvolution problem into manageable steps, each with well-defined mathematical operations that can be performed systematically.
2Measurement precision
If conventional blind deconvolution is applied, then source signals can be recovered, but the process is computationally intensive and complex
Solution Approach 1:
The patent replaces complex time-domain deconvolution operations with frequency-domain spectral factorization. Instead of performing computationally intensive iterative deconvolution algorithms in the time domain, the method transforms signals to the frequency domain where spectral factorization can be performed more efficiently using matrix operations and eigenvalue decompositions, reducing computational complexity while maintaining accuracy.
Solution Approach 2:
The patent changes the computational approach by working in the frequency domain rather than the time domain. This parameter change allows for more efficient computation through spectral analysis techniques, where the cross-power spectral density matrix can be factorized using standard linear algebra operations, avoiding the need for complex iterative deconvolution algorithms.
3Adaptability or versatility
If response functions are estimated without constraints, then multiple solutions are possible, but accuracy is reduced due to non-uniqueness
Solution Approach 1:
The patent applies parameter changes by transforming the problem to the frequency domain where spectral factorization provides a unique solution. This transformation changes the mathematical representation of the problem, allowing for unique determination of response functions up to a linear phase term, thereby eliminating non-uniqueness while maintaining flexibility in the approach.
Solution Approach 2:
The patent inverts the conventional deconvolution approach by first computing the cross-power spectral density matrix and then performing spectral factorization to obtain the response functions. This inverted approach starts with spectral information and works backward to find the unique response functions, rather than attempting to directly deconvolve the signals in the time domain.
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.