Loopback matching algorithm with support set protection

Abstract

There was a drawback of deleting right support elements in some greedy iterative reconstruction algorithms.To resolve this problem,loopback matching algorithm with support set protection (LM-P) was proposed.First,LM-P ini-tialized elements of non-protected support set based on minimum residual inner product.Second,it computed the projec-tions of observations on the observation sub-matrix corresponding to non-protected support set elements.Then,an ele-ment in non-protected support set with the largest projection was added to the protected support set.An alternative multi-plicative iteration method was employed to obtain the whole protected support set.As to reconstruct a sparse signal whose nonzero elements are normally distributed and the signal sparsity is less than half the number of measurements,experimental results show that the reconstruction accuracy of LM-P algorithm exceeds 86%.For sparse signals with small noise,the reconstruction accuracy of LM-P can maintain over 99 %.Compared with OMP,CoSaMP,SP and GPA algo-rithms,LM-P's observations are smaller.LM-P also has good performance for image reconstruction.greedy iteration;support set;sparse signal;LM-P