[Using Bayesian Techniques to Solve Inverse
Project title: Using Bayesian Techniques to Solve Inverse
Persons to contact: Prof. Per Christian Hansen,
building 305, room 105, phone +45 4525 3097 -
Prof. Ole Winther,
building 321, room 115, phone +45 4525 3895 -
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 real-world problems.
02401 Dataanalyse og indledende statistik eller tilsvarende, samt et
videregående fag i numerisk analyse/scientific computing.
Antal deltagere: 1-3.
Consult DTU campus catalogue: IMM
Master in Engineering courses.