Improved EMD Using doubly-iterative sifting and high order spline interpolation

Empirical mode decomposition (EMD) is a signal analysis method which has received much attention lately due to its application in a number of fields. The main disadvantage of EMD is that it lacks a theoretical analysis and, therefore, our understanding of EMD comes from an intuitive and experimental validation of the method. Recent research on EMD revealed improved criteria for the interpolation points selection. More specifically, it was shown that the performance of EMD can be significantly enhanced if, as interpolation points, instead of the signal extrema, the extrema of the subsignal having the higher instantaneous frequency are used. Even if the extrema of the subsignal with the higher instantaneous frequency are not known in advance, this new interpolation points criterion can be effectively exploited in doubly-iterative sifting schemes leading to improved decomposition performance. In this paper, the possibilities and limitations of the developments above are explored and the new methods are compared with the conventional EMD

A Sparsity-Aware Adaptive Algorithm for Distributed Learning

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed convex set, known as property set, is constructed based on the received measurements; this defines the region in which the solution is searched for. In this paper, the property sets take the form of hyperslabs. The goal is to find a point that belongs to the intersection of these hyperslabs. To this end, sparsity encouraging variable metric projections onto the hyperslabs have been adopted. Moreover, sparsity is also imposed by employing variable metric projections onto weighted $\ell_1$ balls. A combine adapt cooperation strategy is adopted. Under some mild assumptions, the scheme enjoys monotonicity, asymptotic optimality and strong convergence to a point that lies in the consensus subspace. Finally, numerical examples verify the validity of the proposed scheme, compared to other algorithms, which have been developed in the context of sparse adaptive learning

Assisted Dictionary Learning for fMRI Data Analysis

Extracting information from functional magnetic resonance (fMRI) images has been a major area of research for more than two decades. The goal of this work is to present a new method for the analysis of fMRI data sets, that is capable to incorporate a priori available information, via an efficient optimization framework. Tests on synthetic data sets demonstrate significant performance gains over existing methods of this kind.Comment: 5 pages, 2 figure

Sparsity-promoting adaptive algorithm for distributed learning in diffusion networks

In this paper, a sparsity-promoting adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale, i.e., at each time instant and at each node, a closed convex set, namely a hyperslab, is constructed around the current measurement point. This defines the region in which the solution lies. The algorithm seeks a solution in the intersection of these hyperslabs by a sequence of projections. Sparsity is encouraged in two complimentary ways: a) by employing extra projections onto a weighted ℓ1 ball, that complies with our desire to constrain the respective weighted ℓ1 norm and b) by adopting variable metric projections onto the hyperslabs, which implicitly quantify data mismatch. A combine-adapt cooperation strategy is adopted. Under some mild assumptions, the scheme enjoys a number of elegant convergence properties. Finally, numerical examples verify the validity of the proposed scheme, compared to other algorithms, which have been developed in the context of sparse adaptive learning.compared to other algorithms, which have been developed in the context of sparse adaptive learning