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Band selection plays an important role in hyperspectral imaging for reducing the data and improving the efficiency of data acquisition and analysis whilst significantly lowering the cost of the imaging system.Without the category labels, it is challenging to select an effective and low-redundancy band subset. In this paper, a new unsupervised band selection algorithm is proposed based on a new band search criterion and an improved Determinantal Point Processes (DPP). First, to preserve the original information of hyperspectral image, a novel band search criterion is designed for searching the bands with high information entropy and low noise. Unfortunately, finding the optimal solution based on the search criteria to select a low-redundancy band subset is a NP-hard problem. To solve this problem, we consider the correlation of bands from both original hyperspectral image and its spatial information to construct a double-graph model to describe the relationship between spectral bands. Besides, an improved DPP algorithm is proposed for the approximate search of a low-redundancy band subset from the double-graph model. Experiment results on several well-known datasets show that the proposed optical band selection algorithm achieves better performance than many other state-of-the-art methods.