Fast Bayesian Linearized Inversion With an Efficient Dimension Reduction Strategy

Bayesian linearized inversion (BLI) stands out as an exceptional stochastic inversion method in the realms of geophysics and remote sensing. It excels in estimating inversion results and assessing their uncertainty with remarkable efficiency. However, one of the challenges faced by BLI lies in the i...

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Bibliographic Details
Published in:IEEE transactions on geoscience and remote sensing 2024, Vol.62, p.1-10
Main Authors: Yu, Bo, Shi, Ying, Zhou, Hui, Cao, Yamei, Wang, Ning, Ji, Xinhong
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian inversion
Bayesian theory
Compression
dimension reduction
Dimensionality reduction
Discrete cosine transform
Discrete cosine transforms
Geophysics
Kalman filters
Linearization
Mathematical models
Matrix converters
matrix inverse
Matrix reduction
Probability theory
Remote sensing
Sparse matrices
stochastic inversion
Stochastic processes
Stochasticity
Uncertainty
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Summary:Bayesian linearized inversion (BLI) stands out as an exceptional stochastic inversion method in the realms of geophysics and remote sensing. It excels in estimating inversion results and assessing their uncertainty with remarkable efficiency. However, one of the challenges faced by BLI lies in the inversion of its core matrix. To surmount this limitation, an innovative dimension reduction strategy is proposed based on the discrete cosine transform (DCT), thus formulating a rapid BLI approach termed DCT-BLI. Within this method, the DCT-based reduction strategy effectively compresses a large sparse matrix by extracting its essential information, transforming the inversion of this sizable matrix into the inversion of a reduced-size counterpart. A compression factor (CF), defined as the size ratio of matrices after and before reduction, quantifies the extent of matrix reduction. DCT-BLI integrates the strengths of both BLI and the DCT-based reduction strategy. Leveraging this reduction approach, DCT-BLI tackles the challenge of inverting its sizable core matrix. Through the synthetic and field data tests, DCT-BLI exhibits clear superiority over BLI in terms of efficiency, and the DCT-based reduction method achieves a remarkable two-thirds reduction in the core matrix size of BLI without compromising inversion accuracy.
ISSN:0196-2892
1558-0644
DOI:10.1109/TGRS.2024.3360031