论文标题
通过Bregman近端DCAS进行非平滑正规化的盲卷卷积
Blind Deconvolution with Non-smooth Regularization via Bregman Proximal DCAs
论文作者
论文摘要
盲反卷积是一种恢复原始信号而不知道卷积过滤器的技术。它自然地将其作为在某些假设下的四分之一目标函数的最小化。由于其可区分的部分没有Lipschitz的连续梯度，因此现有的一阶方法在理论上不受支持。在本文中，我们采用了基于布雷格曼的近端方法，理论上在$ l $ -Smothable（$ L $ -SMAD）属性下可以保证其融合。我们首先将目的函数重新将凸功能差异（DC）函数重新出发，并应用Bregman近端DC算法（BPDCA）。该直流分解满足$ l $ -SMAD物业。该方法以外推（BPDCAE）的速度扩展到BPDCA，以更快地收敛。当我们的正常器具有足够简单的结构时，每次迭代都会以封闭形式的表达求解，因此我们的算法可以有效地解决大规模问题。我们还提供了平衡的稳定性分析，并通过图像脱张的数值实验来证明所提出的方法。结果表明，BPDCAE成功恢复了原始图像，并优于其他现有算法。
Blind deconvolution is a technique to recover an original signal without knowing a convolving filter. It is naturally formulated as a minimization of a quartic objective function under some assumption. Because its differentiable part does not have a Lipschitz continuous gradient, existing first-order methods are not theoretically supported. In this paper, we employ the Bregman-based proximal methods, whose convergence is theoretically guaranteed under the $L$-smooth adaptable ($L$-smad) property. We first reformulate the objective function as a difference of convex (DC) functions and apply the Bregman proximal DC algorithm (BPDCA). This DC decomposition satisfies the $L$-smad property. The method is extended to the BPDCA with extrapolation (BPDCAe) for faster convergence. When our regularizer has a sufficiently simple structure, each iteration is solved in a closed-form expression, and thus our algorithms solve large-scale problems efficiently. We also provide the stability analysis of the equilibrium and demonstrate the proposed methods through numerical experiments on image deblurring. The results show that BPDCAe successfully recovered the original image and outperformed other existing algorithms.
