Non-blind and Blind Deconvolution Under Poisson Noise Using Fractional-Order Total Variation

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.