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The existing back-track iterative reconstruction algorithms for reconstructing the original signal fast and well always require the prior information of signal sparsity for accurate recovery. But sometimes it's hard to meet the requirement in practice. Aiming at this problem, a new blind sparsity back-track reconstruction algorithm based on smooth l0 -norm constraint is proposed and its convergence is demonstrated. The new algorithm does not need the sparse prior and the smooth l0-norm issued to estimate the sparsity of signal and determine the support set in the truncation process. The new algorithm is effective as other back-track ones and is able to avoid recovery failure due to unknown or underestimated sparsity as well. The theoretical analysis and experiment simulation prove that the performance of the new algorithm is better than that of the existing back-track iterative reconstruction algorithms in the sparsity unknown conditions. [ABSTRACT FROM AUTHOR]