Measurement reduction to the form typical for the measurement of the object transparency distribution in the presence of subjective information about its sparsity in a given basis

When studying light-sensitive or rapidly evolving objects the number of illumination photons interacting with the object is often low, which causes poor quality of the reconstructed image of the research object. In this situation the mathematical techniques of measurement data processing should not only provide minimal error, but also use all available information about the research object for further reduction of the error. The source of information that is used alongside measurement data to estimate the distribution of the optical characteristics of the object could be researcher's notions about the possible form of the distribution of characteristics of interest of the research object and about the plausible noise realizations. The article considers a version of the mathematical method of measurement reduction that allows to use such information, which is modeled using the mathematical formalism of subjective modeling, and to verify using measurement data their concordance with the subjective information provided by the researcher.