We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data with the examples of several images and discuss further possible utilizations in other fields of data processing.

The most realistic information about a transparent sample such as a live cell can be obtained using bright-field light microscopy. Under high-intensity pulsing LED illumination, we captured a primary 12-bit-per-channel (bpc) response from an observed sample using a bright-field microscope equipped with a high-resolution (4872 × 3248) image sensor. In order to suppress data distortions originating from the light interactions with elements in the optical path, poor sensor reproduction (geometrical defects of the camera sensor and some peculiarities of sensor sensitivity), we propose a spectroscopic approach for the correction of these uncompressed 12 bpc data by simultaneous calibration of all parts of the experimental arrangement. Moreover, the final intensities of the corrected images are proportional to the photon fluxes detected by a camera sensor. It can be visualized in 8 bpc intensity depth after the Least Information Loss compression.