Improvement of measurement reduction if the feature of interest of the research object belongs to a known convex closed set

The article considers the use of information that the input signal or the characteristic of interest of the research object belongs to a given set in measurement reduction method for probabilistic measurement model. A probabilistic reduction estimate that has lower mean squared error than previusly known ones is proposed and researched. Futhermore, as an example the article considers reduction of a quantum optical measurement — an image of the research object obtained using illumination with natural light and light with suppressed photon count fluctuations. The dependency of reduction result quality on fluctuation suppression and some image features (contrast, average brightness). It is shown that the dependence of noise covariation operator on the estimated signal does not noticeably degrade measurement reduction quality.