Wavelet Transforms
To overcome noise problem in physical methods, we are developing multidimensional wavelet transforms to probe data that include
- multi-dimensional representation of signals
- development of customized wavelets
- enhancement in signal resolution in the wavelet domain
- development of noise thresholds
Inverse Problems and Uncertainty Analysis
In many physical systems, the data acquired from the experiments is the indirect information that needs to be transformed to obtain the final solution. But there is no unique solution that exist from the data, hence ill-posed problem, and one must find accurate solution among several candidates. Current methods compromise resolution to avoid instability. We are developing a “localized” approach, where
- a mechanism is designed to optimize the solution at each output point independently
- uncertainty in results is quantified for for reliability
Signal Science Lab 