








[Using Bayesian Techniques to Solve Inverse Problems]Project title: Using Bayesian Techniques to Solve Inverse ProblemsPersons to contact: Prof. Per Christian Hansen, building 305, room 105, phone +45 4525 3097  pch@imm.dtu.dk or Prof. Ole Winther, building 321, room 115, phone +45 4525 3895  owi@imm.dtu.dk Background: Inverse problems appear in modelling of for example tomography and geophysical problems. The inverse problem can be recast into a statistical one by expressing all information, i.e., observed data and regularization, in terms of probability distributions. Using Bayes theorem, the information can be combined to make inference about the problem. Inference means both finding a solution, assigning errors bars to it and estimating other quantities like measurement noise. Project formulation: A number of projects are possible. For example, it can be studied how the linear algebra formulation of inverse problem can be translated to Bayesian theory. By combining these, algorithms that exploit the best of both views should be developed. In other cases variational techniques (i.e., approximate the complicated distribution with a simpler tractable one) and Monte Carlo techniques (i.e., sample the distribution) can be used. It can be studied how these scale and perform for large artificial and realworld problems. Forudsætninger: 02401 Dataanalyse og indledende statistik eller tilsvarende, samt et videregående fag i numerisk analyse/scientific computing. Antal deltagere: 13. Consult DTU campus catalogue: IMM Master in Engineering courses. 
