A new piecewise quadratic approximation approach for L0 norm minimization problem
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摘要:
In this paper,we consider the problem of finding sparse solutions for underdetermined systems of linear equations,which can be formulated as a class of L0 norm minimization problem.By using the least absolute residual approximation,we propose a new piecewise quadratic function to approximate the L0 norm.Then,we develop a piecewise quadratic approximation (PQA) model where the objective function is given by the summation of a smooth non-convex component and a non-smooth convex component.To solve the (PQA) model,we present an algorithm based on the idea of the iterative thresh01ding algorithm and derive the convergence and the convergence rate.Finally,we carry out a series of numerical experiments to demonstrate the performance of the proposed algorithm for (PQA).We also conduct a phase diagram analysis to further show the superiority of (PQA) over L1 and L1/2 regularizations.