Precision of proportion estimation with binary compressed Raman spectrum

  • Réfrégier Philippe
  • Scotté Camille
  • De Aguiar Hilton
  • Rigneault Herve
  • Galland Frédéric

  • 1103055 -Information theoretical analysis
  • 1104280 -Noise in imaging systems
  • 0704560 -Data processing by optical means
  • 3006450 -Spectroscopy Raman


The precision of proportion estimation with binary filtering of a Raman spectrum mixture is analyzed when the number of binary filters is equal to the number of present species and when the measurements are corrupted with Poisson photon noise. It is shown that the Cramer–Rao bound provides a useful methodology to analyze the performance of such an approach, in particular when the binary filters are orthogonal. It is demonstrated that a simple linear mean square error estimation method is efficient (i.e., has a variance equal to the Cramer–Rao bound). Evolutions of the Cramer–Rao bound are analyzed when the measuring times are optimized or when the considered proportion for binary filter synthesis is not optimized. Two strategies for the appropriate choice of this considered proportion are also analyzed for the binary filter synthesis.