Title Molecular Imaging in Nano MRI / Michael Ting

Published London, U.K. : ISTE ; Hoboken, N.J. : Wiley, 2014

Table of Contents
	Introduction					ix
ch. 1	Nano MRI					1
ch. 2	Sparse Image Reconstruction					7
2.1.	Introduction					7
2.2.	Problem formulation					8
2.3.	Validity of the observation model in MRFM					9
2.4.	Literature review					11
2.4.1.	Sparse denoising					11
2.4.2.	Variable selection					12
2.4.3.	Compressed sensing					12
2.5.	Reconstruction performance criteria					13
ch. 3	Iterative Thresholding Methods					15
3.1.	Introduction					15
3.2.	Separation of deconvolution and denoising					15
3.2.1.	Gaussian noise statistics					17
3.2.2.	Poisson noise statistics					19
3.3.	Choice of sparse denoising operator in the case of Gaussian noise statistics					20
3.3.1.	Comparison to the projected gradient method					23
3.4.	Hyperparameter selection					25
3.5.	MAP estimators using the LAZE image prior					26
3.5.1.	MAP1					28
3.5.2.	MAP2					30
3.5.3.	Comparison of MAP1 versus MAP2					31
3.6.	Simulation example					33
3.7.	Future directions					41
ch. 4	Hyperparameter Selection Using the SURE Criterion					43
4.1.	Introduction					43
4.2.	SURE for the lasso estimator					44
4.3.	SURE for the hybrid estimator					45
4.4.	Computational considerations					46
4.5.	Comparison with other criteria					47
4.6.	Simulation example					48
ch. 5	Monte Carlo Approach: Gibbs Sampling					53
5.1.	Introduction					53
5.2.	Casting the sparse image reconstruction problem in the Bayesian framework					54
5.3.	MAP estimate using the Gibbs sampler					56
5.3.1.	Conditional density of w					57
5.3.2.	Conditional density of a					58
5.3.3.	Conditional density of sigma2					58
5.3.4.	Conditional density of σ2					60
5.4.	Uncertainty in the blur point spread function					60
5.5.	Simulation example					60
ch. 6	Simulation Study					65
6.1.	Introduction					65
6.2.	Reconstruction simulation study					66
6.2.1.	Binary-valued x					67
6.2.2.	{0, ±1}-valued x					69
6.3.	Discussion					71
	Bibliography					73
	Index					77

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Description 1 online resource (x, 77 pages) Series Focus series Focus nanoscience and nanotechnology series. Contents 880-01 Cover; Title page; Contents; Introduction; Chapter 1. Nano MRI; Chapter 2. Sparse Image Reconstruction; 2.1. Introduction; 2.2. Problem formulation; 2.3. Validity of the observation model in MRFM; 2.4. Literature review; 2.4.1. Sparse denoising; 2.4.2. Variable selection; 2.4.3. Compressed sensing; 2.5. Reconstruction performance criteria; Chapter 3. Iterative Thresholding Methods; 3.1. Introduction; 3.2. Separation of deconvolution and denoising; 3.2.1. Gaussian noise statistics; 3.2.2. Poisson noise statistics 880-01/(S Machine generated contents note: ch. 1 Nano MRI -- ch. 2 Sparse Image Reconstruction -- 2.1. Introduction -- 2.2. Problem formulation -- 2.3. Validity of the observation model in MRFM -- 2.4. Literature review -- 2.4.1. Sparse denoising -- 2.4.2. Variable selection -- 2.4.3. Compressed sensing -- 2.5. Reconstruction performance criteria -- ch. 3 Iterative Thresholding Methods -- 3.1. Introduction -- 3.2. Separation of deconvolution and denoising -- 3.2.1. Gaussian noise statistics -- 3.2.2. Poisson noise statistics -- 3.3. Choice of sparse denoising operator in the case of Gaussian noise statistics -- 3.3.1. Comparison to the projected gradient method -- 3.4. Hyperparameter selection -- 3.5. MAP estimators using the LAZE image prior -- 3.5.1. MAP1 -- 3.5.2. MAP2 -- 3.5.3. Comparison of MAP1 versus MAP2 -- 3.6. Simulation example -- 3.7. Future directions -- ch. 4 Hyperparameter Selection Using the SURE Criterion -- 4.1. Introduction -- 4.2. SURE for the lasso estimator -- 4.3. SURE for the hybrid estimator -- 4.4. Computational considerations -- 4.5. Comparison with other criteria -- 4.6. Simulation example -- ch. 5 Monte Carlo Approach: Gibbs Sampling -- 5.1. Introduction -- 5.2. Casting the sparse image reconstruction problem in the Bayesian framework -- 5.3. MAP estimate using the Gibbs sampler -- 5.3.1. Conditional density of w -- 5.3.2. Conditional density of a -- 5.3.3. Conditional density of sigma2 -- 5.3.4. Conditional density of σ2 -- 5.4. Uncertainty in the blur point spread function -- 5.5. Simulation example -- ch. 6 Simulation Study -- 6.1. Introduction -- 6.2. Reconstruction simulation study -- 6.2.1. Binary-valued x -- 6.2.2. {0, ±1}-valued x -- 6.3. Discussion 3.3. Choice of sparse denoising operator in the case of Gaussian noise statistics3.3.1. Comparison to the projected gradient method; 3.4. Hyperparameter selection; 3.5. MAP estimators using the LAZE image prior; 3.5.1. MAP1; 3.5.2. MAP2; 3.5.3. Comparison of MAP1 versus MAP2; 3.6. Simulation example; 3.7. Future directions; Chapter 4. Hyperparameter Selection Using the SURE Criterion; 4.1. Introduction; 4.2. SURE for the lasso estimator; 4.3. SURE for the hybrid estimator; 4.4. Computational considerations; 4.5. Comparison with other criteria; 4.6. Simulation example Summary The authors describe a technique that can visualize the atomic structure of molecules, it is necessary, in terms of the image processing, to consider the reconstruction of sparse images. Many works have leveraged the assumption of sparsity in order to achieve an improved performance that would not otherwise be possible. For nano MRI, the assumption of sparsity is given by default since, at the atomic scale, molecules aresparse structures. This work reviews the latest results on molecular imaging for nano MRI. Sparse image reconstruction methods can be categorized as either non-B Bibliography Includes bibliographical references and index Notes Online resource; title from PDF title page (Wiley, viewed April 4, 2014) Subject Magnetic resonance imaging -- Computer programs Nanoscience. Nuclear magnetic resonance -- Computer programs TECHNOLOGY & ENGINEERING -- Engineering (General) TECHNOLOGY & ENGINEERING -- Reference. Nanoscience Form Electronic book ISBN 9781118760932 111876093X 9781118760895 1118760891 9781118760949 1118760948

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