käänteistehtäviä

Käänteistehtäviä refers to inverse problems in mathematics and science. An inverse problem is one where the parameters of a system are determined from observations of its effects. This is in contrast to a forward problem, where the parameters of a system are known, and its effects are predicted. For example, in a forward problem, one might know the properties of a material and predict how sound waves travel through it. In the corresponding inverse problem, one would measure the sound waves and use that information to deduce the material's properties.

The concept of inverse problems is fundamental in many scientific disciplines. In geophysics, seismic data is used to infer the structure of the Earth's interior. In medical imaging, techniques like CT scans and MRI rely on solving inverse problems to reconstruct images of the inside of the body from external measurements. In engineering, inverse problems are used in areas such as structural health monitoring and system identification.

Inverse problems are often more challenging than forward problems. They can be ill-posed, meaning that a solution may not exist, may not be unique, or may be highly sensitive to small changes in the data. This often requires the use of regularization techniques to find stable and meaningful solutions. The development of robust algorithms and computational methods for solving inverse problems is an active area of research.