The adaptive multidimensional data acquisition in physical experiments

Abstract Modern physical experiments produce a lot of information in digital form, which must be stored and quickly processed. The process of data accumulation is often too long, especially when the experimenter has to scan many independent parameters. To solve this problem, we proposed a method of adaptive data acquisition. The whole multidimensional domain is iteratively divided into several subdomains and inside each subdomain the sample grid is adapted to the smoothness of an unknown data function. The grid is denser where the data function is highly alternated and sparser in the opposite, smoother parts. We choose cubic splines as the basic approximation functions. The procedure takes into account the presence of noise: the iterations have more stages when the noise is weak, and hence the unknown structure is revealed with many details, limited only by the technical resolution of the instrument. However, when the noise is high, the resolution is limited due to smoothing, the degree of which depends on the intensity of noise. The proposed algorithm is transformed in simple software and is illustrated by computer simulation.