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Abstract. This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab is the geometric equivalent of a cost criterion, that quantifies "data mismatch". Sparsity is imposed by the introduction of appropriately designed weighted ℓ 1 balls. The algorithm develops around projections onto the sequence of the generated hyperslabs as well as the weighted ℓ 1 balls. The resulting scheme exhibits linear dependence, with respect to the unknown system's order, on the number of multiplications/additions and an O(L log 2 L) dependence on sorting operations, where L is the length of the system/signal to be estimated. Numerical results are also given to validate the performance of the proposed method against the LASSO algorithm and two very recently developed adaptive sparse LMS and LS-type of adaptive algorithms, which are considered to belong to the same algorithmic family.

In this paper, a sparsity promoting 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. In addition, sparsity is also imposed by employing variable metric projections onto weighted 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

Empirical mode decomposition (EMD) is a relatively new, data-driven adaptive technique for analyzing multicomponent signals. Although it has many interesting features and often exhibits an ability to decompose nonlinear and non-stationary signals, it lacks a strong theoretical basis which would allow a performance analysis and hence the enhancement and optimization of the method in a systematic way.In this paper, the optimization of EMD is attempted in an alternative manner. Using specially defined multicomponent signals, the optimum outputs can be known in advance and used in the optimization of the EMD free parameters within a genetic algorithm framework. The contributions of this paper are twofold.Firstly, the optimization of both the interpolation points and the piecewise interpolating polynomials for the formation of the upper and lower envelopes of the signal reveal important characteristics of the method which where previously hidden. Secondly, basic directions for the estimates of the optimized parameters are developed, leading to significant performance improvements.

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