Challenges in the decomposition of 2D NMR spectra of mixtures of small molecules.

Analytical methods for mixtures of small molecules require specificity (is a certain molecule present in the mix?) and speciation capabilities. NMR spectroscopy has been a tool of choice for both of these issues since its early days, due to its quantitative (linear) response, sufficiently high resolving power and capabilities of inferring molecular structures from spectral features (even in the absence of a reference database). However, the analytical performances of NMR spectroscopy are being stretched by the increased complexity of the samples, the dynamic range of the components, and the need for a reasonable turnover time.

Detecting single-trial EEG evoked potential using a wavelet domain linear mixed model: application to error potentials classification.

Objective: The main goal of this work is to develop a model for multisensor signals, such as magnetoencephalography or electroencephalography (EEG) signals that account for inter-trial variability, suitable for corresponding binary classification problems. An important constraint is that the model be simple enough to handle small size and unbalanced datasets, as often encountered in BCI-type experiments.

Approach: The method involves the linear mixed effects statistical model, wavelet transform, and spatial filtering, and aims at the characterization of localized discriminant features in multisensor signals.

Optimal Window and Lattice in Gabor Transform. Application to Audio Analysis.

This article deals with the use of optimal lattice and optimal window in Discrete Gabor Transform computation. In the case of a generalized Gaussian window, extending earlier contributions, we introduce an additional local window adaptation technique for non-stationary signals. We illustrate our approach and the earlier one by addressing three time-frequency analysis problems to show the improvements achieved by the use of optimal lattice and window: close frequencies distinction, frequency estimation and SNR estimation.

A review of blind source separation in NMR spectroscopy.

Fourier transform is the data processing naturally associated to most NMR experiments. Notable exceptions are Pulse Field Gradient and relaxation analysis, the structure of which is only partially suitable for FT. With the revamp of NMR of complex mixtures, fueled by analytical challenges such as metabolomics, alternative and more apt mathematical methods for data processing have been sought, with the aim of decomposing the NMR signal into simpler bits.

Effective processing of pulse field gradient NMR of mixtures by blind source separation.

NMR diffusometry and its flagship layout, diffusion-ordered spectroscopy (DOSY), are versatile for studying mixtures of bioorganic and synthetic molecules, but a limiting factor of its applicability is the requirement of a mathematical treatment capable of distinguishing molecules with similar spectra or diffusion constants. We present here a processing strategy for DOSY, a synergy of two high-performance blind source separation (BSS) techniques: non-negative matrix factorization (NMF) using additional sparse conditioning (SC), and the JADE (joint approximate diagonalization of eigenmatrices) declination of independent component analysis (ICA). While the first approach has an intrinsic affinity for NMR data, the latter one can be orders of magnitude computationally faster and can be used to simplify the parametrization of the former.