Fluorescence localization microscopy is extensively used to study the details of spatial architecture of subcellular compartments. This modality relies on determination of spatial positions of fluorophores, labeling an extended biological structure, with precision exceeding the diffraction limit. Several established models describe influence of pixel size, signal-to-noise ratio and optical resolution on the localization precision. The labeling density has been also recognized as important factor affecting reconstruction fidelity of the imaged biological structure. However, quantitative data on combined influence of sampling and localization errors on the fidelity of reconstruction are scarce. It should be noted that processing localization microscopy data is similar to reconstruction of a continuous (extended) non-periodic signal from a non-uniform, noisy point samples. In two dimensions the problem may be formulated within the framework of matrix completion. However, no systematic approach has been adopted in microscopy, where images are typically rendered by representing localized molecules with Gaussian distributions (widths determined by localization precision).