A unified approach to noniterative linear signal restoration
A unified approach to noniterative linear signal restoration
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DOI：
10.1109/tassp.1984.1164323
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
J. Sanz;Thomas S. Huang
中科院分区：
文献类型：
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作者：
J. Sanz;Thomas S. Huang
本文的主要目标是描述一个统一的框架，几个非迭代算法的信号外推文献报道。这种统一是通过积分方程和希尔伯特空间理论实现的。这种统一的重要性在于，我们可以利用这些理论中的大量技术来解决外推问题。我们将表明，所谓的两步程序外推与不同的基础模型可以统一的非迭代算法解决希尔伯特空间中的优化问题。特别地，我们证明了离散-连续模型下的两步程序[1]，[2]属于求解第一类线性积分方程的一般类众所周知的算法：给定g（x），x \in A找到f（t），t \in \Omega使得g（x）= \int\min{\Omega} K（x，t）f（t）dt，x \in A（1）另外，我们将证明长球展开法也是著名的Picard本征函数法在一般积分问题（1）中的一个特例。这种理论统一，连同[3]中提出的迭代最小二乘算法，证明了大多数著名的带限外推程序可以被认为是积分方程和算子理论中标准技术的特殊情况。
The main goal of this paper is to describe a unified framework for several noniterative algorithms for signal extrapolation reported in the literature. This unification is achieved through integral equation and Hilbert space theories. The importance of this unification is that we can bring to bear the vast body of techniques in these theories to the solution of the extrapolation problem. We will show that the so-called two-step procedures for extrapolation with different underlying models can be unified by means of noniterative algorithms for solving optimization problems in Hilbert spaces. In particular, we show that two-step procedures under a discrete-continuous model [1], [2] belong to a general class of well-known algorithms for solving linear integral equations of the first kind: given g(x), x \in A find f(t), t \in \Omega such that g(x) = \int\min{\Omega} K(x,t)f(t)dt, x \in A (1) In addition, we will show that the prolate spheroidal expansion technique is also a special case of the well-known Picard's eigenfunction procedure for the general integral problem (1). This theoretical unification, together with that presented in [3] for iterative least-squares algorithms, demonstrates that most of the well-known procedures for band-limited extrapolation can be considered as special cases of standard techniques in integral equations and operator theory.