Improved Reconstruction Algorithm of Wireless Sensor Network Based on BFGS Quasi-Newton Method

Abstract

Aiming at the problems of low reconstruction rate and poor reconstruction precision when reconstructing sparse signals in wireless sensor networks, a sparse signal reconstruction algorithm based on the Limit-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton method is proposed. The L-BFGS quasi-Newton method uses a two-loop recursion algorithm to find the descent direction dk directly by calculating the step difference between m adjacent iteration points, and a matrix Hk approximating the inverse of the Hessian matrix is constructed. It solves the disadvantages of BFGS requiring the calculation and storage of Hk, reduces the algorithm complexity, and improves the reconstruction rate. Finally, the experimental results show that the L-BFGS quasi-Newton method has good experimental results for solving the problem of sparse signal reconstruction in wireless sensor networks.

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“…LBFGS is an abbreviation for limited-memory Broyden-Fletcher-Goldfarb-Shanno, an optimization algorithm based on BFGS, but using limited Random Access Memory (RAM) [27,28], as it does not store a matrix approximating the inverse of the Hessian ∇2 f(x), instead using an intermediate approximation [28,29]. The calculation is based on an initial approximation and an update rule that models local curvature information [27,28].…”

“…LBFGS is an abbreviation for limited-memory Broyden-Fletcher-Goldfarb-Shanno, an optimization algorithm based on BFGS, but using limited Random Access Memory (RAM) [27,28], as it does not store a matrix approximating the inverse of the Hessian ∇2 f(x), instead using an intermediate approximation [28,29]. The calculation is based on an initial approximation and an update rule that models local curvature information [27,28]. The original Broyden-Fletcher-Goldfarb-Shanno method, called full BFGS (BFGS), pro-posed by these four authors in 1970, keeps the aforementioned matrix in memory, whose computational cost of updating is high, of the order of O(n2) [28,29].…”

“…As for the convergence of the BFGS method, if the function has a continuous second derivative and the function is strongly convex, the sequence of successive values of x k tends towards the global minimizer, and furthermore, when it is assumed that the Hessian satisfies the Lipschitz condition, the rate of convergence is super linear [28,29]-i.e., faster than linear. The convergence of the LBFGS algorithm depends on the quality of the Hessian approximation, which is difficult to achieve, and it has been observed in numerical observations that an appropriate guess of the initial Hessian has a significant impact on the search direction and convergence [27,28].…”