Independent measurement of biogenic silica in sediments by FTIR spectroscopy and PLS regression

We present an independent calibration model for the determination of biogenic silica (BSi) in sediments, developed from analysis of synthetic sediment mixtures and application of Fourier transform infrared spectroscopy (FTIRS) and partial least squares regression (PLSR) modeling. In contrast to current FTIRS applications for quantifying BSi, this new calibration is independent from conventional wet-chemical techniques and their associated measurement uncertainties. This approach also removes the need for developing internal calibrations between the two methods for individual sediments records. For the independent calibration, we produced six series of different synthetic sediment mixtures using two purified diatom extracts, with one extract mixed with quartz sand, calcite, 60/40 quartz/calcite and two different natural sediments, and a second extract mixed with one of the natural sediments. A total of 306 samples—51 samples per series—yielded BSi contents ranging from 0 to 100 %. The resulting PLSR calibration model between the FTIR spectral information and the defined BSi concentration of the synthetic sediment mixtures exhibits a strong cross-validated correlation ( R2cv = 0.97) and a low root-mean square error of cross-validation (RMSECV = 4.7 %). Application of the independent calibration to natural lacustrine and marine sediments yields robust BSi reconstructions. At present, the synthetic mixtures do not include the variation in organic matter that occurs in natural samples, which may explain the somewhat lower prediction accuracy of the calibration model for organic-rich samples.

Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.