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The best neighborhood matching (BNM) algorithm is an efficient approach for image restoration. However, its high computation overhead imposes an obstacle to its application. In this paper, a fast image restoration approach named jump and look around BNM (JLBNM) is proposed to reduce computation overhead of the BNM. The main idea of JLBNM is to employ two kinds of search mechanisms so that the whole search process can be sped up. Some optimization techniques for the restoration algorithm JLBNM are also developed, including adaptive threshold in the matching stage, the terminal threshold in the searching stage, and the application of an appropriate matching function in both the matching and recovering stages. Theoretical analysis and experiment results have shown that JLBNM not only can provide high quality for image restoration but also has low computation overhead.