Signal reconstruction is a significantly important theoretical issue for compressed sensing. Considering the situation of signal reconstruction with unknown sparsity, the conventional signal reconstruction algorithms usually perform low accuracy. In this work, a sparsity adaptive signal reconstruction algorithm using sensing dictionary is proposed to achieve a lower reconstruction error. The sparsity estimation method is combined with the construction of the support set based on sensing dictionary. Using the adaptive sparsity method, an iterative signal reconstruction algorithm is proposed. The sufficient conditions for the exact signal reconstruction of the algorithm also is proved by theory. According to a series of simulations, the results show that the proposed method has higher precision compared with other state-of-the-art signal reconstruction algorithms especially in a high compression ratio scenarios.

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