Compressed sensing theory shows that sparse signals can be accurately reconstructed from under-determined linear systems,which makes compressed sensing theory widely used in various aspects.How to reconstruct sparse signals is the core problem of compressed sensing.In this paper,the minimization of LASSO of fractional function is mainly studied,and it is concluded that if its data is k-compressible,the sparsity of the optimal solution of LASSO minimization of fractional function does not exceed[(1+δ)(βδ+α/ψλ)2k].In addition,the L2/L1 error bounds of the optimal solution xλ and the approximate solution of the original signal x(k) are also discussed,and the degree to which the error bounds are de-pendent on the parameters k and λ are generated.The results of this paper can provide some references for the theoretical research of non-convex compressed sensing.
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