English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We propose a sparse regularization model for inversion of incomplete Fouriertransforms and apply it to seismic wavefield modeling. The objective functionof the proposed model employs the Moreau envelope of the $\ell_0$ norm under atight framelet system as a regularization to promote sparsity. This model leadsto a non-smooth, non-convex optimization problem for which traditionaliteration schemes are inefficient or even divergent. By exploiting specialstructures of the $\ell_0$ norm, we identify a local minimizer of the proposednon-convex optimization problem with a global minimizer of a convexoptimization problem, which provides us insights for the development ofefficient and convergence guaranteed algorithms to solve it. We characterizethe solution of the regularization model in terms of a fixed-point of a mapdefined by the proximity operator of the $\ell_0$ norm and develop afixed-point iteration algorithm to solve it. By connecting the map with an$\alpha$-averaged nonexpansive operator, we prove that the sequence generatedby the proposed fixed-point proximity algorithm converges to a local minimizerof the proposed model. Our numerical examples confirm that the proposed modeloutperforms significantly the existing model based on the $\ell_1$-norm. Theseismic wavefield modeling in the frequency domain requires solving a series ofthe Helmholtz equation with large wave numbers, which is a computationallyintensive task. Applying the proposed sparse regularization model to theseismic wavefield modeling requires data of only a few low frequencies,avoiding solving the Helmholtz equation with large wave numbers. Numericalresults show that the proposed method performs better than the existing methodbased on the $\ell_1$ norm in terms of the SNR values and visual quality of therestored synthetic seismograms.

Inverting Incomplete Fourier Transforms by a Sparse Regularization Model and Applications in Seismic Wavefield Modeling