Molecular imaging in nano MRI / Michael Ting.

Format:

Book

Author/Creator:

Ting, Michael, author.

Series:

Focus series in waves

Language:

English

Subjects (All):

Magnetic resonance imaging.

Molecular diagnosis.

Physical Description:

x, 76 p : illustrations ; 24 cm.

Place of Publication:

London : ISTE ; Hoboken, NJ : John Wiley & Sons, 2014.

Summary:

Magnetic resonance imaging (MRI), a non-destructive technique that can produce 2D images or 3D volumes with a typical spatial resolution in the mm range, has enjoyed considerable success in the field of medical imaging. There is interest in non-destructive 3D imaging on a finer scale, in the nm range, since this would open up the possibility of molecular imaging. Being able to determine the structure of molecules would help the development of drugs. Other possible applications include high-density storage and quantum computing. For nano MRI to fulfill its potential as a 3D imaging technique that can visualize the atomic structure of molecules, it is necessary to consider the reconstruction of spares images. Many works have leveraged the assumption of sparsity in order to achieve an improved performance that would not otherwise be possible. This book reviews the latest results on molecular imaging for nano MRI. Chapter 1 introduces Magnetic Resonance Force Microscopy (MRFM), a promising candidate in the quest for achieving MRI on the atomic scale. Chapter 2 introduces the topic of sparse image reconstruction, and briefly reviews the literature. Algorithms developed with molecular image reconstruction in mind are presented in Chapters 3 to 5. Finally, a simulation study is conducted in Chapter 6 to compare the reconstruction algorithms. Book jacket.

Contents:

Chapter 1 Nano MRI 1

Chapter 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

Chapter 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 MAPI versus MAP2 31

3.6 Simulation example 33

3.7 Future directions 41

Chapter 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

Chapter 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

Chapter 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.

Notes:

Includes bibliographical references (pages 73-76) and index.

ISBN:

9781848214743

184821474X

OCLC:

859185634