arXiv subjects

Tingzhu Huang

Publications and source records attributed to Tingzhu Huang.

3 recordsLinked to original sources

arXiv2017

On weaving g-frames for Hilbert spaces

Weaving frames are powerful tools in wireless sensor networks and pre-processing signals. In this paper, we introduce the concept of weaving for g-frames in Hilbert spaces. We first give some properties of weaving g-frames and present two necessary conditions in terms of frame bounds for weaving g-frames. Then we study the properties of weakly woven g-frames and give a sufficient condition for weaving g-frames. It is shown that weakly woven is equivalent to woven. Two sufficient conditions for weaving g-Riesz bases are given. And a weaving equivalent of an unconditional g-basis for weaving g-Riesz bases is considered. Finally, we present Paley-Wiener-type perturbation results for weaving g-frames.

math.FA↗

arXiv2017

Enhanced joint sparsity via Iterative Support Detection

Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressed sensing (CS), statistics, and machine learning. Traditional convex models suffer from the suboptimal performance though enjoying tractable computation. In this paper, we propose a new non-convex joint sparsity model, and develop a corresponding multi-stage adaptive convex relaxation algorithm. This method extends the idea of iterative support detection (ISD) from the single vector estimation to the multi-vector estimation by considering the joint sparsity prior. We provide some preliminary theoretical analysis including convergence analysis and a sufficient recovery condition. Numerical experiments from both compressive sensing and feature learning show the better performance of the proposed method in comparison with several state-of-the-art alternatives. Moreover, we demonstrate that the extension of ISD from the single vector to multi-vector estimation is not trivial. In particular, while ISD does not work well for reconstructing the signal channel sparse Bernoulli signal, it does achieve significantly improved performance when recovering the multi-channel sparse Bernoulli signal thanks to its ability of natural incorporation of the joint sparsity structure.

math.NA↗

arXiv2015

A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems

In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine factorization techniques of both implicit and explicit type, recursive combinatorial algorithms, multilevel mechanisms and overlapping strategies to maximize sparsity in the inverse factors and consequently reduce the factorization costs. Numerical experiments demonstrate the good potential of the proposed solver to precondition effectively general linear systems, also against other state-of-the-art iterative solvers of both implicit and explicit form.

math.NA↗