Fractional-order calculus is an extension of integer order calculus. In signal processing, fractional-order calculus can non-linearly enhance the low-frequency signal and suppress the high-frequency signal. In this paper, a new fractional-order local minimum pixel prior (FOLMP) is proposed by combining fractional-order calculus with the local minimum pixel prior. The FOLMP of the sharp images includes fewer non-zero pixels than the blur images. A new blur kernel estimation algorithm is proposed by combining L0 regularized FOLMP with the maximum posterior probability. Furthermore, the kernel similarity is employed to adjust the iteration times to accelerate the computational efficiency. Comparative experiments show that the proposed algorithm can perform better on different types of datasets than the most advanced algorithms. In addition, non-overlapping image patches are adopted to compute the FOLMP, and the kernel similarity is used to suppress excessive iterations. Therefore, the proposed algorithm is several times or even tens of times more efficient than the classical prior-based methods.
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