Scanning singular-value-decomposition method for restoration of images with space-variant blur

Fish, D.; Grochmalicki, Jan; Pike, E. R.

doi:10.1364/josaa.13.000464

Cited by 33 publications

(26 citation statements)

References 11 publications

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“…Regularization methods are generally used to control the increase of noise in the reconstructed source found by the semilinear method (Suyu et al 2006). Several optimization methods have been applied to problems with spatially variant blur including Landweber iteration (Nocedal & Wright (1999);Fish et al (1996);Trussel & Hunt (1978)), Richardson-Lucy deconvolution (Faisal et al 1995), and Lanczos-Tikhonov hybrid methods (Chung et al 2008) in the context of the standard image deconvolution problem. Following Rogers & Fiege (2011), we focus on the conjugate gradient method for least-squares problems (CGLS) and the steepest descent method (SD).…”

Section: A Small-scale Testmentioning

confidence: 99%

Strong Gravitational Lens Modeling With Spatially Variant Point-Spread Functions

Rogers

Fiege

2011

ApJ

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Astronomical instruments generally possess spatially variant point-spread functions, which determine the amount by which an image pixel is blurred as a function of position. Several techniques have been devised to handle this variability in the context of the standard image deconvolution problem. We have developed an iterative gravitational lens modeling code called Mirage that determines the parameters of pixelated source intensity distributions for a given lens model. We are able to include the effects of spatially variant point-spread functions using the iterative procedures in this lensing code. In this paper, we discuss the methods to include spatially variant blurring effects and test the results of the algorithm in the context of gravitational lens modeling problems.

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Section: A Small-scale Testmentioning

confidence: 99%

Strong Gravitational Lens Modeling With Spatially Variant Point-Spread Functions

Rogers

Fiege

2011

ApJ

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“…This approach does not satisfy us because the coordinate transformation functions need to be known explicitly. Another approach considered, for example, in (Fish et al, 1996), is based on the assumption that the blurring is approximately spatially invariant in small regions of the image domain. Each region is restored using its own spatially invariant PSF, and the results are then sewn together to obtain the restored image.…”

Section: Validation Of Linear Spatially Variant Blurring Modelmentioning

confidence: 99%

Methods for Postprocessing in Single-Step Diffuse Optical Tomography

Konovalov¹,

Vlasov²,

Mogilenskikh³

et al. 2008

Computer Vision

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“…Fortunately the matrix K can usually be represented by a compact data structure, such as when the blur is spatially invariant. Approximation techniques for more complicated spatially variant blurs include geometrical coordinate transformations [62,83,87], sectioning [37,97,98], PSF interpolation [14,33,67,68], and in some cases a sparse matrix data structure can be used for K [32,80].…”

Section: Introductionmentioning

confidence: 99%

Iterative Methods for Image Restoration

Berisha

Nagy

2014

Academic Press Library in Signal Processing: Volume 4 - Image, Video Processing and Analysis, Hardware, Audio, Acoustic and Spe

104

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Although image restoration methods based on spectral filtering techniques are very efficient, they can be applied only to problems with fairly simple spatially invariant blurring operators. Iterative methods, however, are much more flexible; they can be very efficient for spatially invariant as well as spatially variant blurs, they can incorporate a variety of regularization techniques and boundary conditions, and they can more easily incorporate additional constraints, such as nonnegativity. This chapter describes a variety of iterative methods used in image restoration, with a particular emphasis on efficiency, convergence behavior, and implementation. Discussion of MATLAB software implementing the methods is also provided.

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Scanning singular-value-decomposition method for restoration of images with space-variant blur

Cited by 33 publications

References 11 publications

Strong Gravitational Lens Modeling With Spatially Variant Point-Spread Functions

Strong Gravitational Lens Modeling With Spatially Variant Point-Spread Functions

Methods for Postprocessing in Single-Step Diffuse Optical Tomography

Iterative Methods for Image Restoration

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