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1. Superresolution Reconstruction of Severely Undersampled Point-spread Functions Using Point-source Stacking and Deconvolution

   https://doi.org/https://doi.org/10.3847/1538-4365/abcaa5  

   Symons, Teresa; Zemcov, Michael; Bock, James; Cheng, Yung-Ting; Crill, Brendan; Hirata, Christopher; Venuto, Stephanie (February 2021, The Astrophysical journal)

   null (Ed.)

   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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2. A compressed data approach for image-domain least-squares migration

   Ram Tuvi, Zeyu Zhao (September 2021, Geophysics)

   Jeffrey Shragge (Ed.)

   We consider the problem of image-domain least-squares migration (LSM) based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, in which beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with nonnegligible amplitudes need to be used to image the subsurface. In addition, due to the beams’ spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix — an essential ingredient for LSM. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data 

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3. A compressed data approach for image-domain least-squares migration

   Ram Tuvi, Zeyu Zhao (September 2022, Geophysics)

   Jeffrey Shragge (Ed.)

   We consider the problem of image-domain least-squares migration (LSM) based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, in which beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with nonnegligible amplitudes need to be used to image the subsurface. In addition, due to the beams’ spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix — an essential ingredient for LSM. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data. 

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4. A compressed data approach for image-domain least-squares migration

   Ram Tuvi, Zeyu Zhao (September 2022, Geophysics)

   Jeffrey Shragge (Ed.)

   We consider the problem of image-domain least-squares migration (LSM) based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, in which beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with nonnegligible amplitudes need to be used to image the subsurface. In addition, due to the beams’ spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix — an essential ingredient for LSM. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data. 

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5. Edge-Informed Estimation of Gaussian Point Spread Functions in Convolutional Blurring Models

   https://doi.org/10.1109/CISA60639.2024.10576511  

   Hume, Jacob; McDonald, Daniel; Newman, Allan; Liveoak, Donald; Hristova, Yulia; Viswanathan, Aditya (May 2024, IEEE)

   The underlying physics of imaging processes and associated instrumentation limitations mean that blurring artifacts are unavoidable in many applications such as astronomy, microscopy, radar and medical imaging. In several such imaging modalities, convolutional models are used to describe the blurring process; the observed image or function is a convolution of the true underlying image and a point spread function (PSF) which characterizes the blurring artifact. In this work, we propose and analyze a technique - based on convolutional edge detectors and Gaussian curve fitting - to approximate unknown Gaussian PSFs when the underlying true function is piecewise-smooth. For certain simple families of such functions, we show that this approximation is exponentially accurate. We also provide preliminary two dimensional extensions of this technique. These findings - confirmed by numerical simulations - demonstrate the feasibility of recovering accurate approximations to the blurring function, which serves as an important prerequisite to solving deblurring problems. 

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