Molecular Imaging in Nano MRI

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 are
sparse structures. This work reviews the latest results on molecular imaging for nano MRI. Sparse image reconstruction methods can be categorized as either non-Bayesian or Bayesian. A comparison of the performance and complexity of several such algorithms is given.

Introduction ix

Chapter 1. Nano MRI 1

Chapter 2. Sparse Image Reconstruction 7

Chapter 3. Iterative Thresholding Methods 15

Chapter 4. Hyperparameter Selection Using the SURE Criterion 43

Chapter 5. Monte Carlo Approach: Gibbs Sampling 53

Chapter 6. Simulation Study 65

Bibliography 73

Index 77

Michael Ting is currently a software engineer at Criteo in Paris, France, having received a PhD in Electrical Engineering: Systems, from the University of Michigan, USA, in 2006. His doctoral work focused on signal processing for MRFM. He is a Senior Member of the IEEE and is a co-author of a US patent. His research interests include detection and estimation theory, inverse problems, system identification, and time series analysis.