Application Of Smoothing Absolute Function In Signal Reconstruction

This paper studies the sparse signal reconstruction in the field of compressed sensing.At the beginning,six smooth approximation functions of absolute value function are researched.After comparing the approaching effect of these functions,we deduce the smoothing l₁-norm model,and analyse the properties of it.Then,we use three-terms conjugate gradient algorithm to solve the problem,and prove global convergence of the algorithm under some appropriate assumptions.On the basis of a large number of simulation experiments,the numerical results show that our algorithm performs better comparing with NESTA algorithm on the effect of signal reconstruction.For l_p+l₂-quasi-normmodel,we still use smoothing absolute value functions to get the smoothing signal reconstruction model.A modified three-terms conjugate gradient is used to solve this problem.We also do numerical experiments as before,whose results reflect the influence of parameters on signal reconstruction.