In this paper, we consider the nonnegative tensor least squares problem, which arises in the color image restoration. Based on the BB stepsize technique, we design a nonmonotonic descent stepsize and then derive a new gradient projection algorithm to solve this problem. The convergence analysis of the new gradient projected algorithm is given. Some numerical examples show that the new method is feasible and effective. Especially, some simulation experiments in the color image restoration problems illustrate that our algorithm is more effective than the existed algorithms.

中文翻译：

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一种求解非负张量最小二乘问题的有效算法

在本文中，我们考虑了在彩色图像恢复中出现的非负张量最小二乘问题。基于 BB 步长技术，我们设计了一个非单调下降步长，然后推导出一种新的梯度投影算法来解决这个问题。给出了新的梯度投影算法的收敛性分析。一些数值例子表明新方法是可行和有效的。特别是在彩色图像恢复问题中的一些仿真实验表明，我们的算法比现有算法更有效。