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.
Table of Content
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
About the author
Michael Ting is currently a software engineer at Criteo in Paris, France, having received a Ph D 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.
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