Register now After registration you will be able to apply for this opportunity online.
This opportunity is not published. No applications will be accepted.
Multi-Resolution Analysis and Synthesis of Random Fields
In applications ranging from image reconstruction to uncertainty quantification, random fields have to be generated. In this context, the potential of multi-resolution analysis, also known as wavelet transforms, shall be explored.
Keywords: random field generator, multi-level Monte Carlo, wavelets, multi-resolution analysis
For example, flows in the porous subsurface are subject to high uncertainties in the parameter fields that determine flow and transport. To generate realistic parameter field scenarios or realizations, field generators that randomly replicate features of reference fields or mathematical models are needed. In multi-resolution analysis (MRA), a one-, two-, or three-dimensional field is decomposed into a global mean value plus some fluctuations at different scales. These fluctuations are typically referred to as detail differences or simply details and are represented by wavelets. MRA and wavelets are widely applied in signal/image compression (jpeg standard). In the present project, our aim is the formulation of an MRA-based random field generator.
For example, flows in the porous subsurface are subject to high uncertainties in the parameter fields that determine flow and transport. To generate realistic parameter field scenarios or realizations, field generators that randomly replicate features of reference fields or mathematical models are needed. In multi-resolution analysis (MRA), a one-, two-, or three-dimensional field is decomposed into a global mean value plus some fluctuations at different scales. These fluctuations are typically referred to as detail differences or simply details and are represented by wavelets. MRA and wavelets are widely applied in signal/image compression (jpeg standard). In the present project, our aim is the formulation of an MRA-based random field generator.
- Literature review
- Inspection of statistical dependence of details and coarse level coefficients belonging to different MRA levels
- Generation of synthetic fields based on a statistical model for MRA details
- Documentation of results
- Literature review - Inspection of statistical dependence of details and coarse level coefficients belonging to different MRA levels - Generation of synthetic fields based on a statistical model for MRA details - Documentation of results
Interested candidates please send a short statement of motivation and a recent transcript of records to meyerda ethz ch.
Interested candidates please send a short statement of motivation and a recent transcript of records to meyerda ethz ch.