Strong Gravitational Lens Modeling With Spatially Variant Point-Spread Functions

Rogers, Adam; Fiege, Jason D.

doi:10.1088/0004-637x/743/1/68

Cited by 3 publications

(3 citation statements)

References 28 publications

(52 reference statements)

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“…The order in which convolution and weighting are applied is essential: weighting first, then convolution. The converse order is used in Nagy and O'Leary (1998) and in many other subsequent works: Calvetti et al (2000); Nagy et al (2004); Preza and Conchello (2004); Bardsley et al (2006); Ng et al (2007); Rogers and Fiege (2011). The resulting operator is however not equivalent to H, as illustrated in Table 2 and further discussed in section 3.…”

Section: Piecewise Constant Psfsmentioning

confidence: 99%

Fast Approximations of Shift-Variant Blur

et al. 2015

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International audienceImage deblurring is essential in high resolution imaging, e.g., astronomy, microscopy or computational photography. Shift-invariant blur is fully characterized by a single point-spread-function (PSF). Blurring is then modeled by a convolution, leading to efficient algorithms for blur simulation and removal that rely on fast Fourier transforms. However, in many different contexts, blur cannot be considered constant throughout the field-of-view, and thus necessitates to model variations of the PSF with the location. These models must achieve a trade-off between the accuracy that can be reached with their flexibility, and their computational efficiency. Several fast approximations of blur have been proposed in the literature. We give a unified presentation of these methods in the light of matrix decompositions of the blurring operator. We establish the connection between different computational tricks that can be found in the litterature and the physical sense of corresponding approximations in terms of equivalent PSFs, physically-based approximations being preferable. We derive an improved approximation that preserves the same desirable low complexity as other fast algorithms while reaching a minimal approximation error. Comparison of theoretical properties and empirical performances of each blur approximation suggests that the proposed general model is preferable for approximation and inversion of a known shift-variant blur

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Section: Piecewise Constant Psfsmentioning

confidence: 99%

Fast Approximations of Shift-Variant Blur

et al. 2015

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“…Here we use a product-convolution scheme. Convolution interpolation schemes have been used in image restoration and deblurring [29,47,55] in photography [56], astronomy [1,31,52], and microscopy [51], as well as in wireless communication signal processing [40], ultrasound imaging [48], systems biology [33], and Hessian approximation in seismic inversion [58]. 3 Aside from the application, convolution interpolation schemes differ based on how they construct the functions ω k and ψ k .…”

Section: Convolution Interpolationmentioning

confidence: 99%

Scalable Matrix-Free Adaptive Product-Convolution Approximation for Locally Translation-Invariant Operators

Alger¹,

Rao²,

Myers³

et al. 2019

SIAM J. Sci. Comput.

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We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operators that are locally translation-invariant, even if these operators are high-rank or full-rank. Such operators arise in Schur complement methods for solving partial differential equations (PDEs), as Hessians in PDE-constrained optimization and inverse problems, as integral operators, as covariance operators, and as Dirichlet-to-Neumann maps. Constructing the approximation requires computing the impulse responses of the operator to point sources centered on nodes in an adaptively refined grid of sample points. A randomized a-posteriori error estimator drives the adaptivity. Once constructed, the approximation can be efficiently applied to vectors using the fast Fourier transform. The approximation can be efficiently converted to hierarchical matrix (H-matrix) format, then inverted or factorized using scalable H-matrix arithmetic. The quality of the approximation degrades gracefully as fewer sample points are used, allowing cheap lower quality approximations to be used as preconditioners. This yields an automated method to construct preconditioners for locally translationinvariant Schur complements. We directly address issues related to boundaries and prove that our scheme eliminates boundary artifacts. We test the scheme on a spatially varying blurring kernel, on the non-local component of an interface Schur complement for the Poisson operator, and on the data misfit Hessian for an advection dominated advection-diffusion inverse problem. Numerical results show that the scheme outperforms existing methods.

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“…Our lens models use the same ACS PSF that was used for the lens galaxy subtraction. Although it is known that the ACS PSF is position dependent (Bandara et al 2009), we simplify our treatment by assuming a constant PSF over the region of interest, though we have previously developed methods to include spatially variant PSFs in the gravitational lens problem (Rogers & Fiege 2011b). We output the sigma image from the GALFIT code (Peng et al 2010) that corresponds with the region of interest to estimate the errors on the image plane.…”

Section: Boltonmentioning

confidence: 99%

Global Optimization Methods for Gravitational Lens Systems With Regularized Sources

Rogers¹,

Fiege²

2012

ApJ

Self Cite

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Several approaches exist to model gravitational lens systems. In this study, we apply global optimization methods to find the optimal set of lens parameters using a genetic algorithm. We treat the full optimization procedure as a two-step process: an analytical description of the source plane intensity distribution is used to find an initial approximation to the optimal lens parameters. The second stage of the optimization uses a pixelated source plane with the semilinear method to determine an optimal source. Regularization is handled by means of an iterative method and the generalized cross validation (GCV) and unbiased predictive risk estimator (UPRE) functions that are commonly used in standard image deconvolution problems. This approach simultaneously estimates the optimal regularization parameter and the number of degrees of freedom in the source. Using the GCV and UPRE functions we are able to justify an estimation of the number of source degrees of freedom found in previous work. We test our approach by applying our code to a subset of the lens systems included in the SLACS survey.

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Strong Gravitational Lens Modeling With Spatially Variant Point-Spread Functions

Cited by 3 publications

References 28 publications

Fast Approximations of Shift-Variant Blur

Fast Approximations of Shift-Variant Blur

Scalable Matrix-Free Adaptive Product-Convolution Approximation for Locally Translation-Invariant Operators

Global Optimization Methods for Gravitational Lens Systems With Regularized Sources

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