A particle filtered matching pursuit for compressive sensing of blind sparsity signal polluted by non-Gaussion noise was proposed, while the conventional detectors(e.g. least-squares estimates) were known to be sensitive to the non-Gaussion nature of noise. The proposed algorithm which combined the Huber cost(loss) function with an l₁-norm did not need the sparse prior while it eliminated the interference of measuring noise by particle filter estimation. Meanwhile, sparsity adaptive matching pursuit was used to sift the effective support set so as to inverse the original states. Simulation results indicate that the proposed algorithm outperforms the existing greedy iterative inversions in the same condition, especially in the non-Gaussion noise situation.