Consistent reconstruction of partially measured Mueller matrices: enpolarizing, depolarizing, and retarding descriptors

Many polarimetric imaging systems, such as division-of-focal-plane cameras or miniaturized endoscopic instruments, deliver incomplete Mueller matrices, typically restricted to the upper-left 3×3 block sensitive to linear polarization. Directly padding the missing entries with zeros often leads to unphysical 4×4 matrices and distorts depolarization metrics. Here we present a practical reconstruction strategy that, from any measured 3×3 block, synthesizes a physically admissible 4×4 Mueller matrix by selecting, among the infinitely many compatible completions, a statistical model whose associated covariance matrix H has rank at most two (no more than two spectral components) while exhibiting maximal polarimetric purity. We summarize the algorithm in a form directly translatable into numerical code, illustrate its behavior with synthetic examples, and discuss its use as a “polarimetric denoising” tool in imaging. This work focuses on the operational aspects and imaging-oriented implications of the method, while a companion journal article provides the full mathematical details.