Estimation of sparse nonnegative sources from noisy overcomplete mixtures using MAP

Sparse signal reconstruction via collaborative neurodynamic optimization

In this paper, we formulate a mixed-integer problem for sparse signal reconstruction and reformulate it as a global optimization problem with a surrogate objective function subject to underdetermined linear equations. We propose a sparse signal reconstruction method based on collaborative neurodynamic optimization with multiple recurrent neural networks for scattered searches and a particle swarm optimization rule for repeated repositioning. We elaborate on experimental results to demonstrate the outperformance of the proposed approach against ten state-of-the-art algorithms for sparse signal reconstruction.

Library-assisted nonlinear blind separation and annotation of pure components from a single 1H nuclear magnetic resonance mixture spectra

Due to its capability for high-throughput screening ¹H nuclear magnetic resonance (NMR) spectroscopy is commonly used for metabolite research. The key problem in ¹H NMR spectroscopy of multicomponent mixtures is overlapping of component signals and that is increasing with the number of components, their complexity and structural similarity. It makes metabolic profiling, that is carried out through matching acquired spectra with metabolites from the library, a hard problem. Here, we propose a method for nonlinear blind separation of highly correlated components spectra from a single ¹H NMR mixture spectra. The method transforms a single nonlinear mixture into multiple high-dimensional reproducible kernel Hilbert Spaces (mRKHSs). Therein, highly correlated components are separated by sparseness constrained nonnegative matrix factorization in each induced RKHS. Afterwards, metabolites are identified through comparison of separated components with the library comprised of 160 pure components. Thereby, a significant number of them are expected to be related with diabetes type 2. Conceptually similar methodology for nonlinear blind separation of correlated components from two or more mixtures is presented in the Supplementary material. Single-mixture blind source separation is exemplified on: (i) annotation of five components spectra separated from one ¹H NMR model mixture spectra; (ii) annotation of fifty five metabolites separated from one ¹H NMR mixture spectra of urine of subjects with and without diabetes type 2. Arguably, it is for the first time a method for blind separation of a large number of components from a single nonlinear mixture has been proposed. Moreover, the proposed method pinpoints urinary creatine, glutamic acid and 5-hydroxyindoleacetic acid as the most prominent metabolites in samples from subjects with diabetes type 2, when compared to healthy controls.

Computing sparse representations of multidimensional signals using Kronecker bases

Recently there has been great interest in sparse representations of signals under the assumption that signals (data sets) can be well approximated by a linear combination of few elements of a known basis (dictionary). Many algorithms have been developed to find such representations for one-dimensional signals (vectors), which requires finding the sparsest solution of an underdetermined linear system of algebraic equations. In this letter, we generalize the theory of sparse representations of vectors to multiway arrays (tensors)--signals with a multidimensional structure--by using the Tucker model. Thus, the problem is reduced to solving a large-scale underdetermined linear system of equations possessing a Kronecker structure, for which we have developed a greedy algorithm, Kronecker-OMP, as a generalization of the classical orthogonal matching pursuit (OMP) algorithm for vectors. We also introduce the concept of multiway block-sparse representation of N-way arrays and develop a new greedy algorithm that exploits not only the Kronecker structure but also block sparsity. This allows us to derive a very fast and memory-efficient algorithm called N-BOMP (N-way block OMP). We theoretically demonstrate that under the block-sparsity assumption, our N-BOMP algorithm not only has a considerably lower complexity but is also more precise than the classic OMP algorithm. Moreover, our algorithms can be used for very large-scale problems, which are intractable using standard approaches. We provide several simulations illustrating our results and comparing our algorithms to classical algorithms such as OMP and BP (basis pursuit) algorithms. We also apply the N-BOMP algorithm as a fast solution for the compressed sensing (CS) problem with large-scale data sets, in particular, for 2D compressive imaging (CI) and 3D hyperspectral CI, and we show examples with real-world multidimensional signals.

On consciousness, resting state fMRI, and neurodynamics

BACKGROUND

During the last years, functional magnetic resonance imaging (fMRI) of the brain has been introduced as a new tool to measure consciousness, both in a clinical setting and in a basic neurocognitive research. Moreover, advanced mathematical methods and theories have arrived the field of fMRI (e.g. computational neuroimaging), and functional and structural brain connectivity can now be assessed non-invasively.

RESULTS

The present work deals with a pluralistic approach to "consciousness'', where we connect theory and tools from three quite different disciplines: (1) philosophy of mind (emergentism and global workspace theory), (2) functional neuroimaging acquisitions, and (3) theory of deterministic and statistical neurodynamics - in particular the Wilson-Cowan model and stochastic resonance.

CONCLUSIONS

Based on recent experimental and theoretical work, we believe that the study of large-scale neuronal processes (activity fluctuations, state transitions) that goes on in the living human brain while examined with functional MRI during "resting state", can deepen our understanding of graded consciousness in a clinical setting, and clarify the concept of "consiousness" in neurocognitive and neurophilosophy research.