论文标题
从非线性转换恢复信号的固定点框架
A Fixed Point Framework for Recovering Signals from Nonlinear Transformations
论文作者
论文摘要
我们考虑在建模先验信息的凸约限制下，从非线性转换中恢复信号的问题。由于非线性，标准的可行性和优化方法不适合解决此问题。我们表明，在许多常见应用中，转换模型可以与涉及牢固非专业运算符的固定点方程相关联。反过来，恢复问题被简化为可触犯的公共固定点公式，该公共固定点公式通过可证明的收敛性，块状词汇算法有效地解决。展示了信号和图像恢复的应用。还解决了不一致的问题。
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the nonlinearities. We show that, in many common applications, the transformation model can be associated with fixed point equations involving firmly nonexpansive operators. In turn, the recovery problem is reduced to a tractable common fixed point formulation, which is solved efficiently by a provably convergent, block-iterative algorithm. Applications to signal and image recovery are demonstrated. Inconsistent problems are also addressed.
