Precision of proportion estimation with binary compressed Raman spectrum

Abstract

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.

Fast compressive Raman bio-imaging via matrix completion

“…3.C, the output of the matrix completion was passed to a standard SVD algorithm, to generate the eigenimages, in turn used for generating the spectra (Fig. 3.B) for input of the supervised approach [15,16]. For the spectral sampling domain, we have used two spectral basis set for the spectral domain: a canonical (Fig.…”

“…Compressive Raman is based on concepts of the emerging field of compressive sensing, which exploits new sampling paradigms based on experimental undersampling followed by computational reconstruction. In general, two strategies exist in compressive Raman: supervised [12,[15][16][17] and unsupervised compression [13,18]. Both concepts are based on the fact that the hyperspectrum H typically contains a small number of distinguishable chemical signatures, that is, it is extremely "chemically sparse" (Fig.…”

“…Mathematically, this is equivalent to say that H is a low-rank matrix. Hence, from few data samples, the complete hyperspectrum can be reconstructed without loss of fidelity [12,15]. On the one hand, the unsupervised approach is the most appealing as it re- * h.aguiar@phys.ens.fr quires low a priori information for computational reconstruction.…”

“…The supervised method exploits the eigenspectra of H ( Fig. 1.B, rightmost spectra), as a priori information, to develop optimized spectral filters for fast, accurate, and precise chemical abundances determination [15,20]. Nevertheless, this supervised method fails in chemically changing environments, as the "eigenspectra library" may evolve.…”

High-Sensitivity High-Speed Compressive Spectrometer for Raman Imaging

“…Each spatial pixel can then be written as x = F P c, where proportions c are estimated from simple inversion of F P . The key step for proportion estimation is to develop filters that are robust against noise 18,21 . We use as a metric the variance of the Cramer-Rao bound (CRB) to determine the optimized spectral filters.…”