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Abstract By fitting observed data with predicted seismograms, least‐squares migration (LSM) computes a generalized inverse for a subsurface reflectivity model, which can improve image resolution and reduce artifacts caused by incomplete acquisition. However, the large computational cost of LSM required for simulations and migrations limits its wide applications for large‐scale imaging problems. Using point‐spread function (PSF) deconvolution, we present an efficient and stable high‐resolution imaging method. The PSFs are first computed on a coarse grid using local ray‐based Gaussian beam Born modeling and migration. Then, we interpolate the PSFs onto a fine‐image grid and apply a high‐dimensional Gaussian function to attenuate artifacts far away from the PSF centers. With 2D/3D partition of unity, we decompose the traditional adjoint migration results into local images with the same window size as the PSFs. Then, these local images are deconvolved by the PSFs in the wavenumber domain to reduce the effects of the band‐limited source function and compensate for irregular subsurface illumination. The final assembled image is obtained by applying the inverse of the partitions for the deconvolved local images. Numerical examples for both synthetic and field data demonstrate that the proposed PSF deconvolution can significantly improve image resolution and amplitudes for deep structures, while not being sensitive to velocity errors as the data‐domain LSM.
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Superresolution Reconstruction of Severely Undersampled Point-spread Functions Using Point-source Stacking and Deconvolution
Point-spread function (PSF) estimation in spatially undersampled images is challenging because large pixels average fine-scale spatial information. This is problematic when fine-resolution details are necessary, as in optimal photometry where knowledge of the illumination pattern beyond the native spatial resolution of the image may be required. Here, we introduce a method of PSF reconstruction where point sources are artificially sampled beyond the native resolution of an image and combined together via stacking to return a finely sampled estimate of the PSF. This estimate is then deconvolved from the pixel-gridding function to return a superresolution kernel that can be used for optimally weighted photometry. We benchmark against the <1% photometric error requirement of the upcoming SPHEREx mission to assess performance in a concrete example. We find that standard methods like Richardson–Lucy deconvolution are not sufficient to achieve this stringent requirement. We investigate a more advanced method with significant heritage in image analysis called iterative back-projection (IBP) and demonstrate it using idealized Gaussian cases and simulated SPHEREx images. In testing this method on real images recorded by the LORRI instrument on New Horizons, we are able to identify systematic pointing drift. Our IBP-derived PSF kernels allow photometric accuracy significantly better than the requirement in individual SPHEREx exposures. This PSF reconstruction method is broadly applicable to a variety of problems and combines computationally simple techniques in a way that is robust to complicating factors such as severe undersampling, spatially complex PSFs, noise, crowded fields, or limited source numbers.
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- Award ID(s):
- 1659740
- PAR ID:
- 10227753
- Date Published:
- Journal Name:
- The Astrophysical journal
- Volume:
- 252
- Issue:
- 2
- ISSN:
- 1538-4365
- Page Range / eLocation ID:
- 24
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/https://doi.org/10.3847/1538-4365/abcaa5
