Rekonstruktioalgoritmien

Rekonstruktioalgoritmien are algorithms used to reconstruct a full image or signal from a limited or incomplete set of measurements. This is a common problem in various scientific and engineering fields, where obtaining a complete dataset might be impossible, too expensive, or too time-consuming. The core idea is to infer the missing information based on the available data and prior knowledge about the object or phenomenon being studied.

A classic example is in medical imaging, such as Magnetic Resonance Imaging (MRI). An MRI scanner does not directly capture a full image. Instead, it collects data in a transformed domain (k-space). Rekonstruktioalgoritmien are then applied to this collected data to generate the diagnostic images. Similarly, in computed tomography (CT), projections from various angles are used to reconstruct a 3D image of the internal structure.

Other applications include signal processing, where a complete signal needs to be recovered from undersampled or noisy data, and in fields like astronomy for reconstructing images from telescope observations. The effectiveness of a rekonstruktioalgoritmi often depends on the quality of the acquired data, the assumptions made about the underlying structure, and the mathematical techniques employed. Common approaches involve mathematical optimization, statistical inference, and signal processing techniques. The goal is to achieve a reconstruction that is both accurate and visually interpretable, representing the original object or signal as faithfully as possible.