In a wide range of applications such as astronomy, biology, and medical imaging, acquired data are usually corrupted by Poisson noise and blurring artifacts. Poisson noise often occurs when photon counting is involved in such imaging modalities as X-ray, positron emission tomography, and fluorescence microscopy. Meanwhile, blurring is also inevitable due to the physical mechanism of an imaging system, which can be modeled as a convolution of the image with a point spread function. In this paper, we consider both non-blind and blind image deblurring models that deal with Poisson noise. In the pursuit of high-order smoothness of a restored image, we propose a fractional-order total variation regularization to remove the blur and Poisson noise simultaneously. We develop two efficient algorithms based on the alternating direction method of multipliers, while an expectation-maximization algorithm is adopted only in the blind case. A variety of numerical experiments have demonstrated that the proposed algorithms can efficiently reconstruct piecewise smooth images degraded by Poisson noise and various types of blurring, including Gaussian and motion blurs. Specifically for blind image deblurring, we obtain significant improvements over the state of the art.

在天文学，生物学和医学成像等广泛的应用中，采集的数据通常会受到泊松噪声和伪影模糊的破坏。当光子计数涉及X射线，正电子发射断层扫描和荧光显微镜等成像方式时，通常会产生泊松噪声。同时，由于成像系统的物理机制，模糊也是不可避免的，可以将其建模为具有点扩展函数的图像卷积。在本文中，我们同时考虑了处理泊松噪声的非盲和盲图像去模糊模型。为了追求还原图像的高阶平滑度，我们提出了分数阶总变化正则化以同时消除模糊和泊松噪声。我们基于乘法器的交替方向方法开发了两种有效的算法，而期望最大化算法仅在盲情况下才采用。各种数值实验表明，所提出的算法可以有效地重建因泊松噪声和各种类型的模糊而退化的分段平滑图像，包括高斯和运动模糊。特别是对于盲图像去模糊，我们在现有技术上获得了重大改进。