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Bayesian Approach to Limited-Angle Reconstruction in Computed Tomography
[chapter]
1987
Maximum-Entropy and Bayesian Spectral Analysis and Estimation Problems
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The null-space components of deterministic solutions are usually zero, giving rise to unavoidable artifacts. ...
There exists a null subspace in the Hilbert space of possible source functions about which the available projection measurements provide no information. ...
Thus the concept of null space and the Bayesian methods proposed for overcoming its limitations are relevant to a large variety of image-restoration problems. ...
doi:10.1007/978-94-009-3961-5_15
fatcat:5n2jkljfn5dxbnf5aezuuxyaci
Bayesian approach to limited-angle reconstruction in computed tomography
1983
Journal of the Optical Society of America
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The null-space components of deterministic solutions are usually zero, giving rise to unavoidable artifacts. ...
There exists a null subspace in the Hilbert space of possible source functions about which the available projection measurements provide no information. ...
Thus the concept of null space and the Bayesian methods proposed for overcoming its limitations are relevant to a large variety of image-restoration problems. ...
doi:10.1364/josa.73.001501
fatcat:tfy2bwgib5hcrbglr65pvndmfa
Ghost images and feasibility of reconstructions with the Richardson-Lucy algorithm
1994
Image Reconstruction and Restoration
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The question was: What is the null space (ghost images) of the Richardson-Lucy (RL) algorithm?. ...
We introduce the concept of a "nearly null" space, with an unsharp distinction between the "measurement" and the "null" components of an image and generate a reduced resolution Hubble Point Spread Function ...
INTRODUCTION In the workshop on "The Restoration of HST Images and Spectra II" that took place at the Space Telescope Science Institute in November 1993, a question was raised as to what is the null space ...
doi:10.1117/12.188042
fatcat:vr4puhf6xrawlbpt5237pc466i
Iterative statistical approach to blind image deconvolution
2000
Optical Society of America. Journal A: Optics, Image Science, and Vision
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To facilitate computation we use an iterative method, which is an extension of the traditional expectation-maximization method, instead of direct optimization. ...
We employ a statistical point of view of the data and use a modified maximum a posteriori approach to identify the most probable object and blur given the observed image. ...
For image restoration, it could lead to better results because we can restore the portion of the object in the null space of the blur. 16 It could also lead to faster convergence as the prior knowledge ...
doi:10.1364/josaa.17.001177
pmid:10883969
fatcat:j2n7aweunjbnbnwtn5efyvo5yu
Multichannel blind deconvolution of spatially misaligned images
2005
IEEE Transactions on Image Processing
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Index Terms-Image restoration, maximum a posteriori (MAP) estimator, multichannel blind deconvolution, subspace methods, variational integral. ...
This stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise. ...
[21] , [22] suggested two MC restoration algorithms that, contrary to the previous two indirect algorithms, estimate directly the original image from the null space or from the range of a special matrix ...
doi:10.1109/tip.2005.849322
pmid:16028551
fatcat:mbdaswcmi5fkbmrop35ezcxoru
Interval estimate with probabilistic background constraints in deconvolution
2012
Optical Society of America. Journal A: Optics, Image Science, and Vision
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2012 pre-print arXiv:1211.3662v1 fatcat:j5glyvee7bhsddxdnsst5rp5yy
Confidence intervals reveal the uncertainties due to the background constraint are calculated and significance levels for sources retrieved from restored images are provided. ...
We elaborate our objective -- the interval estimate of the unknown object from observed data and our approach -- monte-carlo experiment and analysis of marginal distributions of image values. ...
While in Bayesian statistics the maximum a posteriori (MAP) algorithm maximizes the conditional probability density of the object intensity to achieve a MAP estimate [11] . ...
doi:10.1364/josaa.29.002688
pmid:23455920
fatcat:kfo5gmlembcnjezbkoi2byijzy
Enhanced fog detection and free-space segmentation for car navigation
2011
Machine Vision and Applications
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Then, the method restores the contrast of the road by only assuming that the road is flat and, at the same time, detects the vertical objects. ...
The proposed method is complementary to existing free-space area detection methods relying on color segmentation and stereovision. ...
This is especially the case on the sidewalks and curbs which are detected as a part of the free-space area by the algorithm (see Fig. 14c for example), which was expected due to the definition chosen ...
doi:10.1007/s00138-011-0383-3
fatcat:sdov4uljirfgpjc4x7cy66qqyy
Spatio-temporal fMRI analysis using Markov random fields
1998
IEEE Transactions on Medical Imaging
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Index Terms-Bayesian framework, functional magnetic resonance imaging (fMRI) analysis, Markov random fields (MRF's), signal analysis, signal restoration. ...
We propose to embed the fMRI analysis problem into a Bayesian framework consisting of two steps: i) data restoration and ii) data analysis. ...
This affine transformation is estimated by maximizing the image cross correlation [32] with the Simplex algorithm. ...
doi:10.1109/42.746636
pmid:10048860
fatcat:5hkmpunh7vcdncr3lyruqars4m
A recursive soft-decision approach to blind image deconvolution
2003
IEEE Transactions on Signal Processing
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An optimization scheme is developed where a new cost function is projected and minimized with respect to the image and blur domains. ...
This paper presents a new approach to blind image deconvolution based on soft-decision blur identification and hierarchical neural networks. ...
Expectation maximization (EM) is often used in conjunction with ML to maximize the log-likelihood function of the parameter set from their solution spaces. ...
doi:10.1109/tsp.2002.806985
fatcat:zkuepn5v7befdpfnix4shki4ba
Bayesian and regularization methods for hyperparameter estimation in image restoration
1999
IEEE Transactions on Image Processing
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We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. ...
In this paper, we propose the application of the hierarchical Bayesian paradigm to the image restoration problem. ...
The initial restoration for the MAP algorithm was the EM solution for the 10, 20, and 30 dB problems, respectively. ...
doi:10.1109/83.743857
pmid:18267470
fatcat:njm2cxjglffethnsqpxyzigto4
Fast and efficient MRF-based blotch detection algorithm for degraded film sequences
2007
2007 International Symposium on Intelligent Signal Processing and Communication Systems
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detection algorithms. ...
This paper proposes an efficient blotch detection algorithm based on a Markov Random Field (MRF) model with less computational complexity and with lower false alarm rate than the existing MRF-based blotch ...
detection r c and false alarm r f are defined as [1] : r c = C b N c , r f = F b N 1 N 2 − N c . (9) In our experiment, the search space used for the full search block matching algorithm was ±5 pixels ...
doi:10.1109/ispacs.2007.4445833
fatcat:th7s3cfjgzhlzkoyaadoqhx6we
Space-variant generalised Gaussian regularisation for image restoration
2018
Computer Methods in Biomechanics and Biomedical Engineering Imaging & Visualization
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2019 pre-print arXiv:1906.10517v1 fatcat:oumqmd6kq5g47lexyqzqkrnebyOther Versions
The restored image is efficiently computed by means of an iterative numerical algorithm based on the alternating direction method of multipliers. ...
We propose a new space-variant regularization term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalized ...
Acknowledgments: Research was supported by the "National Group for Scientific Computation (GNCS-INDAM)" and by ex60 project by the University of Bologna "Funds for selected research topics". ...
doi:10.1080/21681163.2018.1471620
fatcat:rw4gqzdx7fhn7ndkfbacfcr3ha
Blur identification by residual spectral matching
1993
IEEE Transactions on Image Processing
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The PSF estimate is selected to provide the best match between the restoration residual power spectrum and its expected value, derived under the assumption that the candidate PSF is equal to the true PSF ...
The a priori knowledge required is the noise variance and the original image spectrum. ...
The Expectation-Maximization (EM) algorithm has been applied in the space [ l l ] and frequency domain [12] for iterative maximization of the likelihood function. ...
doi:10.1109/83.217219
pmid:18296204
fatcat:kc2vf25zb5hjzds53oiz6bljbu
Speckle Control with a Remapped-Pupil PIAA Coronagraph
2012
Publications of the Astronomical Society of the Pacific
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, and demonstrate the benefit of the PIAA for high contrast imaging at small angular separation. ...
The PIAA is a now well demonstrated high contrast technique that uses an intermediate remapping of the pupil for high contrast coronagraphy (apodization), before restoring it to recover classical imaging ...
Using an iterative speckle nulling algorithm, the voltage map that cancels speckles within the control region of the DM has been identified. ...
doi:10.1086/668848
fatcat:hkbzq7pfwvesrb5rqhc3z3bxgm
Fast Blotch Detection Algorithm for Degraded Film Sequences Based on MRF Models
2007
2007 IEEE International Conference on Image Processing
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This paper proposes a fast blotch detection algorithm based on a Markov Random Field (MRF) model with less computational load and with lower false alarm rate than the existing MRF-based algorithms. ...
The experimental results show that our proposed method provides the computational simplicity and an efficient detecting performance for the blotches. ...
In our experiment, the search space used for the full search block matching algorithm was ±5 pixels. A block size of 8 × 8 was used. ...
doi:10.1109/icip.2007.4379371
dblp:conf/icip/NamAK07
fatcat:ixrlvzvkjbawhcxtoo7wkmfzxm
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