PhD Scholarship in Inverse Problems with Besov Prior

Tuesday 02 Nov 21

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Apply no later than 15 December 2021
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We invite applications for a PhD position in the Section for Scientific Computing within the Department of Applied Mathematics and Computer Science. The position is part of the research initiative CUQI: Computational Uncertainty Quantification for Inverse problems funded by the Villum Foundation and headed by Professor Per Christian Hansen.

Image deblurring, tomographic imaging, source reconstruction, and fault inspection are examples of inverse problems. Uncertainty Quantification (UQ) uses methods from Bayesian inference to characterize and study the sensitivity of a reconstruction taking into account errors and inaccuracies in the data, the mathematical and physical models, the regularization terms, etc. Our goal is to create a platform for modeling and computations related to applying UQ to a range of inverse problems in academia and industry.

Responsibilities and qualifications
You will be part of a large team consisting of experts in many areas of inverse problems and scientific computing. Together with the team, you will contribute to the project’s goal by developing theory and computational methods that can handle the challenges we face in developing a versatile platform.

In many inverse problems, we need to go beyond Gaussian priors in order to handle more advanced spatial correlations. This PhD position will focus on handling inverse problems with Besov priors. In the CUQI platform we will use Besov priors that are suited for producing piecewise smooth reconstructions and for detection of edges and interfaces. This involves the use of linear combinations of wavelets/frames with random coefficients. This project requires knowledge of functional analysis and numerical computation and, preferably, harmonic analysis. Moreover, experience with inverse problems or Bayesian inference will be a plus.

You must have a two-year master's degree (120 ECTS points) or a similar degree with an academic level equivalent to a two-year master's degree. 

Approval and Enrolment
The scholarships for the PhD degree are subject to academic approval, and the candidates will be enrolled in one of the general degree programmes at DTU. For information about our enrolment requirements and the general planning of the PhD study programme, please see the DTU PhD Guide.

Assessment
The assessment of all applicants will be made by Associate Professor Yiqiu Dong and Associate Professor Jakob Lemvig.

We offer
DTU is a leading technical university globally recognized for the excellence of its research, education, innovation and scientific advice. We offer a rewarding and challenging job in an international environment. We strive for academic excellence in an environment characterized by collegial respect and academic freedom tempered by responsibility.

Salary and appointment terms
The appointment will be based on the collective agreement with the Danish Confederation of Professional Associations. The allowance will be agreed upon with the relevant union. The period of employment is 3 years.

The workplace is DTU Lyngby Campus, Denmark.

You can read more about career paths at DTU here.

Further information
Further information about the positions and CUQI may be obtained from Associate Professor Yiqiu Dong, yido@dtu.dk.


You can read more about the Department of Applied Mathematics and Computer Science at www.compute.dtu.dk/english.

If you are applying from abroad, you may find useful information on working in Denmark and at DTU at DTU – Moving to Denmark.  

Application procedure

Your complete online application must be submitted no later than 15 December 2021 (Danish time). Applications must be submitted as one PDF file containing all materials to be given consideration. To apply, please open the link "Apply online", fill out the online application form, and attach all your materials in English in one PDF file. The file must include:

  • A letter motivating the application (cover letter)
  • Curriculum vitae
  • Grade transcripts and BSc/MSc diploma
  • Excel sheet with translation of grades to the Danish grading system (see guidelines and Excel spreadsheet here)

You may apply prior to ob­tai­ning your master's degree but cannot begin before having received it.

Applications received after the deadline will not be considered.

All interested candidates irrespective of age, gender, race, disability, religion or ethnic background are encouraged to apply.

DTU Compute
DTU Compute is a unique and internationally recognized academic department with 385 employees and 11 research sections spanning the science disciplines mathematics, statistics, computer science, and engineering. We conduct research, teaching and innovation of high international standard – producing new knowledge and technology-based solutions to societal challenges. We have a long-term involvement in applied and interdisciplinary research, big data and data science, artificial intelligence (AI), internet of things (IoT), smart and secure societies, smart manufacturing, and life science. At DTU Compute we believe in a diverse workplace with a flexible work-life balance.


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