## Inversions and imaging

A personal website of Yu ZHONG

*This personal website is designated to present my research works and further research interests.*

Basically, I am a scientific researcher mainly working on computational methods for

*and***inverse problems***associated to ***imaging problems****physical waves and fields**. I here to share my research works and my further research interests, the purposes of which are mainly for personal recording and for intriguing more research exchanges among scientists in this challenging area.## What are inverse problems?

Inverse problems and forward problems are like the two sides of a coin, reflecting the same (physical) behaviors from the different facets. For instance, when knowing distance from place A to place B and the walking speed of a person, to find the time needed for this person to walk from A to B could be defined as a forward problem. Then, the corresponding inverse problem might be to find the walking speed of the person when knowing the distance and the time costed. That is, usually in inverse problems, the known quantities are those could be directly measured, by which unknown quantities that could not be directly measured then is calculated (estimated).

For more information, one may refer to the inverse problems entry in Wikipedia. Otherwise, a short video by Prof. Roy Pike of King's College London might give you some good hints.

For more information, one may refer to the inverse problems entry in Wikipedia. Otherwise, a short video by Prof. Roy Pike of King's College London might give you some good hints.

## What are physical waves and fields?

Physical waves and fields are generated by active sources, and they propagate/diffuse/distribute around but not necessarily limited to the domain closely surrounding the sources. Since these waves and fields are generated by active sources, they are carrying energies from the sources, and they interact with the media within which they propagate/diffuse/distribute. So, in short, the waves and fields represent the interactions between the media and the active sources. The usual waves and fields that are "experienced" in our daily life include acoustic waves, electromagnetic waves, X-ray, seismic waves, besides which gravitational fields, quantum fields, etc., are also important research subjects.

## What to do with inverse problems?

-As mentioned above, the purpose of solving inverse problems is usually to estimate physical quantities that could not be directly measured. To inverse problems with physical waves and fields, it means that one estimate some media properties that relate to the interactions between such media and the waves and fields being used, by some measurements on the boundaries or distant away from the interested media domain. Such problems are of great interests due to the fact that waves and fields can penetrate the media being investigated without compromising the integrity of such media.

However, such problems are usually ill-posed (unstable) and nonlinear, i.e., the solutions of such problems might only be found, within reasonable amounts of computational time and resources, by using properly tailored numerical solvers that are able to address the instability and non-linearity.

However, such problems are usually ill-posed (unstable) and nonlinear, i.e., the solutions of such problems might only be found, within reasonable amounts of computational time and resources, by using properly tailored numerical solvers that are able to address the instability and non-linearity.