论文标题
Chebyshev惯性地网算法线性逆问题
Chebyshev Inertial Landweber Algorithm for Linear Inverse Problems
论文作者
论文摘要
在复杂/真实希尔伯特空间上定义的Landweber算法是线性反问题的梯度下降算法。我们的贡献是提出一种加速Landweber算法收敛的新方法。在本文中，我们首先将Chebyshev惯性迭代的理论扩展到希尔伯特空间上的Landweber算法。收敛速率上的上限阐明了所提出方法的全局收敛速度。 Chebyshev惯性陆地算法可以应用于希尔伯特空间的广泛信号恢复问题，包括连续信号的反卷积。本文进行的理论讨论自然会导致一种新颖的实用信号恢复算法。作为演示，得出了基于预计的Landweber算法的MIMO检测算法。与MMSE检测器相比，提出的MIMO检测算法达到的符号错误率要小得多。
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.
