Signal Reconstruction Under Incomplete And Inaccurate Measurements

For signal f?F???R^N,we do incomplete and inaccurate linear measurement y=F_?f + ?(F_??R^|?|×N,|?|<<N,??R^|?| is measurement error).So,in the sense of l₂ norm,is it possible for us to reconstruct f perfectly from incomplete and inaccurate measurement y?In fact,if the signal cluster F has sparse structure under some certain representation,then it is possible to reconstruct the original signal with a very high accuracy from very few random measurements.Sparsity requirement sim-plify the problem into a constrained l₀ minimization problem,while l₀ minimization is a NP-hard problem,it's solution requires searching for all column combinations of F.This paper mainly considers the approximation of l₀ problem.Considering that signals usually have different sparsity at different locations,we propose an adaptive variable exponential generalized quasi norm ?g?_lp?g?^S to approximate ?g?_l0.We trans-form the non-convex generalized quasi norm minimization problem into a sequence of convex quadratic programming by using iterative techniques.In the iteration,we let?p?g??_??0 to complete the approximation of the l₀ minimization.In this paper,we apply the proposed l₀ approximation algorithm to three typical compressed sensing problems.The numerical results show that our algorithm still performs well under very few measurements.Moreover,it is more stable than similar non-convex algorithms.