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Book: Electro-Magentic Tissue Property MRI 
Jin Keun Seo, Eung Je Woo, Ulich Katcher, Yi Wang (Imperial College Press)


Computational Science & Engineering

The mission of Computational Science and Engineering (CSE) is to make scientific discoveries and breakthroughs by research in mathematics; to promote at the highest scientific level of research on mathematical modeling, PDE theory and analysis, numerical analysis, algorithmic development and simulation, as well as their application in nature, environment, life, science and engineering; and to advance the state-of-the-art in mathematical science by creating multi-disciplinary teams consisting of PDE theorists, numerical mathematicians and experts in computational science and engineering.

   Click : Survey of CSE graduate program

Inverse Problems and Medical Imaging: Pioneering the multi-disciplinary area

Over the past decade, there has been marked progress in electromagnetic property and mechanical property imaging techniques in which cross-sectional image reconstructions inside the human body are pursued. These techniques also have wider applications as imaging methods in medicine, biotechnology, non-destructive testing and the monitoring of industrial processes, and in other areas. Magnetic Resonance Electrical Impedance Tomography (MREIT) is an MR-based conductivity imaging technique at low frequencies. In MREIT, we inject currents into an imaging object after RF pulses and measure induced magnetic flux density data from MR phase images. Quasistatic Maxwell equations provide a relation between the measured magnetic flux density and the conductivity from which we can reconstruct cross-sectional conductivity images. Magnetic Resonance Electrical Property Tomography (MREPT) aims to reconstruct images of both conductivity and permittivity distributions inside the human body at MR frequency. In contrast to MREIT, MREPT does not require current injection since it is based on standard RF field mapping techniques to measure active magnetic RF field components. These modalities belong to interdisciplinary research areas incorporating mathematical theories and analyses of electromagnetism, MR physics and imaging methods, inverse problems and image reconstruction algorithms, numerical analyses and experimental techniques.

Machine Learning and Medical Image Computing

In March 2016, machine learning (ML) took a big leap forward when AlphaGo, a ML program for the game Go, defeated the world's best player, Lee Sedol, in Korea. This historic match has attracted significant attention in both the scientific and popular press because of the tough computational challenges associated with playing Go proficiently.  Go has a huge number of cases, which make its complexity vastly greater than that of chess; therefore, it was regarded to be almost impossible to handle by explicit mathematical means.  However, AlphaGo seemingly handled this huge complexity without explicit programming.

 What is ML? Arthur Lee Samuel(1901-1990), who wrote an early TEX manual (typing system)  in 1983, defined ML as the "field of study that gives computers the ability to learn without being explicitly programmed".  Numerous mathematical models with differing integrative levels have been developed to solve various real-world problems systematically and quantitatively. However, the corresponding problems in many cases are ill posed, with modeling inaccuracies and data uncertainties, which make them difficult to deal with using solely numerical means. ML has the potential to deal with these ill-posed problems using statistical reasoning. Supervised ML is concerned with training a program using existing data so as to enhance its ability to make the best predictions (or decisions) when faced with new data. In ML, the first step should be the formulation of forward models. Before programming, we should understand the information loss of the models and also potential data uncertainties, practical limitations associated with the data, and so on. 

George Box(1919-2013) emphasized a motivated iteration between theory and practice:   All models are wrong, but some are useful. The scientist cannot obtain a correct one by excessive elaboration. If you want to know what happens to a process when you interfere with it, you have to interfere with it, not passively observe it.   Science is a means whereby learning is achieved, not by mere theoretical speculation on the one hand, nor by the undirected accumulation of practical facts on the other, but rather by a motivated iteration between theory and practice. Given that many researchers are susceptible to biased hypotheses, the rule of parsimony seems to be necessary to falsify incorrect theories. A critical view is an important part of the scientific method, and acts as an early warning system to alleviate biased and erroneous development.

CSE  eeducation
Guideline for CSE Admission (PhD/MS)

We look for students with excellent academic standing, who are highly accomplished and self-motivated students. Successful candidates are supported for their tuition and living expenses by the CSE. For those who show high performance, the chance of oversea research training will also be provided. 

CSE Curriculum
(Ph.D. Degree Process Map)

Based on theory and practice taught in our courses, students will be able to develop numerical algorithms to perform computer simulation, and to visualize various engineering problems. Through the multi-stage process they will gain skills for practical applications. 

CSE Internship

CSE recruited 10 intern researchers and trained them basic mathematical concepts necessary for CSE subjects. They were undergraduate students of Mathematics, Engineering and Science with high scores of GPA. The program contributed to draw attention of students to CSE, a new discipline 

CSE Lecture note
PDE-based Image Processing

Image processing has been closely related to medical imaging in basic tasks such as denoising and deblurring. At present, such applications are rapidly increasing for automated or computer-aided surgery and therapy and diagnoses through classification, registration, and anomaly detection, for example. To meet various end users’ demands, new image models and computational algorithms incorporating a deep understanding of imaging processes and the innate nature of medical images are required. For this purpose, we plan to apply total variation, anisotropic diffusion and mean curvature motion along with recent examples of progress such as compressed sensing, sparse representation, and machine learning tools in an innovative manner. Such an approach will provide better quality images and reduce the computational costs.

Haeeun Han 


Haeeun Han 


Copyright 2013 Department of Computational Science and Engineering All Rights Reserved. 

Copyright 2013 Department of Computational Science and Engineering All Rights Reserved. 

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