A general weighted median filter structure admitting negative weights
A general weighted median filter structure admitting negative weights
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DOI：
10.1109/78.735296
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发表时间：
1998-12-01
影响因子：
5.4
通讯作者：
Arce, GR
中科院分区：
文献类型：
--
作者：
Arce, GR
加权中值平滑器是由 Edgemore 在 100 多年前的最小绝对回归背景下引入的，在过去的二十年中在信号处理领域受到了相当多的关注。尽管加权中值平滑器比传统的线性有限脉冲响应 (FIR) 滤波器具有优势，但本文表明它们缺乏充分解决许多信号处理问题的灵活性。事实上，加权中值平滑器类似于仅限于具有正权重的归一化 FIR 线性滤波器。本文还表明，就像将均值推广到丰富的线性 FIR 滤波器类别一样，中值也可以推广到更丰富的允许正权重和负权重的滤波器类别。概括起来很自然，而且出奇地简单。为了分析和设计此类滤波器，开发了一种允许实值输入信号的新阈值分解理论。然后，使用新的阈值分解框架来开发快速自适应算法，以优化设计实值滤波器系数。新的加权中值滤波器公式带来了更强大的估计器，能够有效解决信号处理中的许多基本问题，而先前的加权中值平滑器结构无法充分解决这些问题。
Weighted median smoothers, which were introduced by Edgemore in the context of least absolute regression over 100 Sears ago, have received considerable attention in signal processing during the past two decades, Although weighted median smoothers offer advantages over traditional linear finite impulse response (FIR) filters, it is shown in this paper that they lack the flexibility to adequately address a number of signal processing problems. In fact, weighted median smoothers are analogous to normalized FIR linear filters constrained to have only positive weights. In this paper, it is also shown that much like the mean is generalized to the rich class of linear FIR filters, the median can be generalized to a richer class of filters admitting positive and negative weights. The generalization follows naturaly and is surprisingly simple. In order to analyze and design this class of filters, a new threshold decomposition theory admitting real-valued input signals is developed. The new threshold decomposition framework is then used to develop fast adaptive algorithms to optimally design the real-valued filter coefficients. The new weighted median filter formulation leads to significantly more powerful estimators capable of effectively addressing a number of fundamental problems in signal processing that could not adequately be addressed by prior weighted median smoother structures.