线性反问题的Chebyshev惯性Landweber算法
Chebyshev Inertial Landweber Algorithm for Linear Inverse Problems
摘要：
定义在复/实Hilbert空间上的Landweber算法是求解线性逆问题的一种梯度下降算法。我们的贡献是提出了一种新的方法来加速收敛的Landweber算法。本文首先将Chebyshev惯性迭代理论推广到Hilbert空间上的Landweber算法。上界的收敛速度阐明了所提出的方法的全局收敛速度。切比雪夫惯性Landweber算法可以应用到广泛的类的信号恢复问题的希尔伯特空间，包括连续信号的反卷积。在本文中开发的理论讨论自然会导致一种新的实用信号恢复算法。作为示范，推导了一种基于投影Landweber算法的MIMO检测算法。与MMSE检测器相比，所提出的MIMO检测算法实现了更小的符号出错率。
英文摘要：
The Landweber algorithm defined on complex/real Hilbert spaces is a gradient descent algorithm for linear inverse problems. Our contribution is to present a novel method for accelerating convergence of the Landweber algorithm. In this paper, we first extend the theory of the Chebyshev inertial iteration to the Landweber algorithm on Hilbert spaces. An upper bound on the convergence rate clarifies the speed of global convergence of the proposed method. The Chebyshev inertial Landweber algorithm can be applied to wide class of signal recovery problems on a Hilbert space including deconvolution for continuous signals. The theoretical discussion developed in this paper naturally leads to a novel practical signal recovery algorithm. As a demonstration, a MIMO detection algorithm based on the projected Landweber algorithm is derived. The proposed MIMO detection algorithm achieves much smaller symbol error rate compared with the MMSE detector.
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