Background removal from spectra by designing and minimising a non-quadratic cost function

One popular method for the recovery of an ideal intensity image from corrupted or indirect measurements is regularization: minimize an objective function that enforces a roughness penalty in addition to coherence with the data. Linear estimates are relatively easy to compute but generally introduce systematic errors; for example, they are incapable of recovering discontinuities and other important image attributes. In contrast, nonlinear estimates are more accurate but are often far less accessible. This is particularly true when the objective function is nonconvex, and the distribution of each data component depends on many image components through a linear operator with broad support. Our approach is based on an auxiliary array and an extended objective function in which the original variables appear quadratically and the auxiliary variables are decoupled. Minimizing over the auxiliary array alone yields the original function so that the original image estimate can be obtained by joint minimization. This can be done efficiently by Monte Carlo methods, for example by FFT-based annealing using a Markov chain that alternates between (global) transitions from one array to the other. Experiments are reported in optical astronomy, with space telescope data, and computed tomography.

One of the challenges of using Raman spectroscopy for biological applications is the inherent fluorescence generated by many biological molecules that underlies the measured spectra. This fluorescence can sometimes be several orders of magnitude more intense than the weak Raman scatter, and its presence must be minimized in order to resolve and analyze the Raman spectrum. Several techniques involving hardware and software have been devised for this purpose; these include the use of wavelength shifting, time gating, frequency-domain filtering, first- and second-order derivatives, and simple curve fitting of the broadband variation with a high-order polynomial. Of these, polynomial fitting has been found to be a simple but effective method. However, this technique typically requires user intervention and thus is time consuming and prone to variability. An automated method for fluorescence subtraction, based on a modification to least-squares polynomial curve fitting, is described. Results indicate that the presented automated method is proficient in fluorescence subtraction, repeatability, and in retention of Raman spectral lineshapes.

A parametric model is proposed for the warping function when aligning chromatograms. A very fast and stable algorithm results that consumes little memory and avoids the artifacts of dynamic time warping. The parameters of the warping function are useful for quality control. They also are easily interpolated, allowing alignment of batches of chromatograms based on warping functions for a limited number of calibration samples.