In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [6] in order to remove mixed Poisson-Gaussian (MPG) noise. In the existing splitting algorithm for TV-IC, an inner loop by Newton method had to be adopted for one nonlinear optimization subproblem, which increased the computation cost per outer loop. By introducing a new bilinear constraint and applying the alternating direction method of multipliers (ADMM), all subproblems of the proposed algorithms named as BCA (short for Bilinear Constraint based ADMM algorithm) and BCA$ _{f} $ (short for a variant of BCA with $ {\bf f} $ully splitting form) can be very efficiently solved. Especially for the proposed BCA$ _{f} $, they can be calculated without any inner iterations. The convergence of the proposed algorithms are investigated, where particularly, a Huber type TV regularizer is adopted to guarantee the convergence of BCA$ _f $. Numerically, compared to existing primal-dual algorithms for the TV-IC model, the proposed algorithms, with fewer tunable parameters, converge much faster and produce comparable results meanwhile.

中文翻译：

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基于双线性约束的ADMM去除泊松-高斯混合噪声

在本文中，我们为总变化正则化小数卷积（TV-IC）模型提出了新的算子分解算法[6]以消除混合的泊松－高斯（MPG）噪声。在现有的TV-IC分裂算法中，一个非线性优化子问题必须采用牛顿法的内环，这增加了每个外环的计算成本。通过引入新的双线性约束并应用乘数的交替方向方法（ADMM），提出的算法的所有子问题均称为BCA（B inlinear C onstraint基于A的缩写）DMM算法）和BCA $ _ {f} $（具有$ {\ bf f} $ ully split形式的BCA变体的缩写）可以非常有效地解决。特别是对于建议的BCA $ _ {f} $，无需任何内部迭代即可计算它们。研究了所提出算法的收敛性，特别是采用了Huber型电视调节器来保证BCA $ _f $的收敛性。在数值上，与现有的TV-IC模型的原始对偶算法相比，所提出的算法具有更少的可调参数，收敛速度更快，同时产生可比的结果。