Image non-blind deblurring is still an ill-posed problem. Uncertainty in solutions occurs when singular vectors of forward model matrix spanning the noise subspace have rather small singular values. This letter proposes a new image deblurring algorithm, called MNBC-Gibbs (multiple norms and boundary constraint enforced Gibbs sampling). To be more specific, the quadratic and sparseness-inducing norms are combined to construct regularization term, and the objective function is gradually minimized without requirement of regularization parameter choice. In particular, we propose an efficient Markov chain Monte Carlo (MCMC) method equipped with closed-form solution, artifacts processing and non-negative constraint to approximate the posterior distribution and estimate uncertainty for the unknown. Satisfactory deblurring results with sharp edges can be generated while maintaining smoothness without raising extra noise. The quantitative evaluations on different blur kernels and comparison with state-of-the-art image deblurring methods demonstrate the superiority of the proposed method. In addition, we show that our method can effectively deal with real blurry images.

中文翻译：

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多范数和边界约束通过高效的 MCMC 算法强制图像去模糊

图像非盲去模糊仍然是一个不适定的问题。当跨越噪声子空间的前向模型矩阵的奇异向量具有相当小的奇异值时，就会出现解的不确定性。这封信提出了一种新的图像去模糊算法，称为 MNBC-Gibbs（多重范数和边界约束强制 Gibbs 采样）。更具体地说，结合二次和稀疏诱导范数来构造正则化项，并且在不要求正则化参数选择的情况下逐渐最小化目标函数。特别是，我们提出了一种高效的马尔可夫链蒙特卡罗 (MCMC) 方法，该方法配备了封闭形式的解决方案、伪影处理和非负约束来近似后验分布并估计未知的不确定性。可以在保持平滑度的同时产生具有锐利边缘的令人满意的去模糊结果，而不会增加额外的噪音。对不同模糊核的定量评估以及与最先进的图像去模糊方法的比较证明了所提出方法的优越性。此外，我们表明我们的方法可以有效地处理真实的模糊图像。