In order to solve the high complexity of classical image processing, a quantum scheme for image sharpness estimation based on the Laplacian operator is proposed. The mean of grayscale gradients of all pixels is regarded as the sharpness estimation metric. A new quantum image representation model is presented by extending the Novel Enhanced Quantum Representation (NEQR) model, which is greatly useful for quantum image convolution. In quantum platforms, it has been shown that the mean calculation of numbers is rather difficult because the numbers are stored in a quantum superposition state. In order to solve this problem, we put forward an algorithm which essential idea is cyclically shifting the superposition state and iteratively calculating the mean of the new one and the original state. The mean can be obtained from the superposition state by only one quantum measurement. By analyzing the space complexity and time complexity, the scheme is far superior to classical ones in terms of resource consumption and execution speed. In addition, the results of simulation experiments show that for noiseless images, the performance of the scheme is consistent with subjective visual perception of images sharpness.

中文翻译：

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基于拉普拉斯算子的量子图像清晰度估计

针对经典图像处理复杂度高的问题，提出了一种基于拉普拉斯算子的图像锐度估计量子方案。所有像素的灰度梯度的平均值被视为锐度估计度量。通过扩展新型增强量子表示（NEQR）模型，提出了一种新的量子图像表示模型，该模型对量子图像卷积非常有用。在量子平台中，已经证明数字的平均计算相当困难，因为数字存储在量子叠加态中。为了解决这个问题，我们提出了一种算法，其基本思想是循环移动叠加态并迭代计算新态和原态的均值。仅通过一次量子测量就可以从叠加态中获得平均值。通过分析空间复杂度和时间复杂度，该方案在资源消耗和执行速度上都远优于经典方案。此外，仿真实验结果表明，对于无噪声图像，该方案的性能与主观视觉感知的图像清晰度一致。