Nonlinear Signal Processing: A Statistical Approach (Hardcover)

Gonzalo R. Arce

Nonlinear Signal Processing: A Statistical Approach (Hardcover)

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Description:

Nonlinear Signal Processing: A Statistical Approach focuses on unifying the study of a broad and important class of nonlinear signal processing algorithms which emerge from statistical estimation principles, and where the underlying signals are non-Gaussian, rather than Gaussian, processes. Notably, by concentrating on just two non-Gaussian models, a large set of tools is developed that encompass a large portion of the nonlinear signal processing tools proposed in the literature over the past several decades.

Key features include:

  • Numerous problems at the end of each chapter to aid development and understanding
  • Examples and case studies provided throughout the book in a wide range of applications bring the text to life and place the theory into context
  • A set of 60+ MATLAB software m-files allowing the reader to quickly design and apply any of the nonlinear signal processing algorithms described in the book to an application of interest is available on the accompanying FTP site.

 

Table of Contents:

Preface.

Acknowledgments.

Acronyms.

1. Introduction.

1.1 Non-Gaussian Random Processes.

1.1.1 Generalized Gaussian Distributions and Weighted Medians.

1.1.2 Stable Distributions and Weighted Myriads.

1.2 Statistical Foundations.

1.3 The Filtering Problem.

1.3.1 Moment Theory.

PART I: STATISTICAL FOUNDATIONS.

2. Non-Gaussian Models.

2.1 Generalized Gaussian Distributions.

2.2 Stable Distributions.

2.2.1 Definitions.

2.2.2 Symmetric Stable Distributions.

2.2.3 Generalized Central Limit Theorem.

2.2.4 Simulation of Stable Sequences.

2.3 Lower Order Moments.

2.3.1 Fractional Lower Order Moments.

2.3.2 Zero Order Statistics.

2.3.3 Parameter Estimation of Stable Distributions.

Problems.

3. Order Statistics.

3.1 Distributions of Order Statistics.

3.2 Moments of Order Statistics.

3.2.1 Order Statistics From Uniform Distributions.

3.2.2 Recurrence Relations.

3.3 Order Statistics Containing Outliers.

3.4 Joint Statistics of Ordered and Non-Ordered Samples.

Problems.

4. Statistical Foundations of Filtering.

4.1 Properties of Estimators.

4.2 Maximum Likelihood Estimation.

4.3 Robust Estimation.

Problems.

PART II: SIGNAL PROCESSING WITH ORDER STATISTICS.

5. Median and Weighted Median Smoothers.

5.1 Running Median Smoothers.

5.1.1 Statistical Properties.

5.1.2 Root Signals (Fixed Points).

5.2 Weighted Median Smoothers.

5.2.1 The Center Weighted Median Smoother.

5.2.2 Permutation Weighted Median Smoothers.

5.3 Threshold Decomposition Representation.

5.3.1 Stack Smoothers.

5.4 Weighted Medians in Least Absolute Deviation (LAD) Regression.

5.4.1 Foundation and Cost Functions.

5.4.2 LAD Regression with Weighted Medians.

5.4.3 Simulation.

Problems.

6. Weighted Median Filters.

6.1 Weighted Median Filters With Real-Valued Weights.

6.1.1 Permutation Weighted Median Filters.

6.2 Spectral Design of Weighted Median Filters.

6.2.1 Median Smoothers and Sample Selection Probabilities.

6.2.2 SSPs for Weighted Median Smoothers.

6.2.3 Synthesis of WM Smoothers.

6.2.4 General Iterative Solution.

6.2.5 Spectral Design of Weighted Median Filters Admitting Real-Valued Weights.

6.3 The Optimal Weighted Median Filtering Problem.

6.3.1 Threshold Decomposition for Real-Valued Signals.

6.3.2 The Least Mean Absolute (LMA) Algorithm.

6.4 Recursive Weighted Median Filters.

6.4.1 Threshold Decomposition Representation of Recursive WM Filters.

6.4.2 Optimal Recursive Weighted Median Filtering.

6.5 Mirrored Threshold Decomposition and Stack Filters.

6.5.1 Stack Filters.

6.5.2 Stack Filter Representation of Recursive WM Filters.

6.6 Complex Valued Weighted Median Filter.

6.6.1 Phase Coupled Complex WM Filters.

6.6.2 Marginal Phase Coupled Complex WM Filter.

6.6.3 Complex Threshold Decomposition.

6.6.4 Optimal Marginal Phase Coupled Complex WM.

6.6.5 Spectral Design of Complex Valued Weighted Medians.

6.7 Weighted Median Filters for Multichannel Signals.

6.7.1 Marginal WM Filter.

6.7.2 Vector WM Filter.

6.7.3 Weighted Multichannel Median Filtering Structures.

6.7.4 Filter Optimization.

Problems.

7. Linear Combination or Order Statistics.

7.1 L-Estimates of Location.

7.2 L-Smoothers.

7.3 Lℓ-Filters.

7.3.1 Design and Optimization of Lℓ Filters.

7.4 Ljℓ Permutation Filters.

7.5 Hybrid Median/Linear FIR Filters.

7.5.1 Median and FIR Affinity Trimming.

7.6 Linear Combination of Weighted Medians.

7.6.1 LCWM Filters.

7.6.2 Design of LCWM Filters.

7.6.3 Symmetric LCWM Filters.

Problems.

PART III: SIGNAL PROCESSING WITH THE STABLE MODEL.

8. Myriad Smoothers.

8.1 FLOM Smoothers.

8.2 Running Myriad Smoothers.

8.3 Optimality of the Sample Myriad.

8.4 Weighted Myriad Smoothers.

8.5 Fast Weighted Myriad Computation.

8.6 Weighted Myriad Smoother Design.

8.6.1 Center Weighted Myriads for Image Denoising.

8.6.2 Myriadization.

Problems.

9. Weighted Myriad Filters.

9.1 Weighted Myriad Filters with Real-Valued Weights.

9.2 Fast Real-Valued Weighted Myriad Computation.

9.3 Weighted Myriad Filter Design.

9.3.1 Myriadization.

9.3.2 Optimization.

Problems.

References.

Appendix A: Software Guide.

Index.

商品描述(中文翻譯)

描述：



《非線性信號處理：統計方法》專注於統一研究一類重要的非線性信號處理算法，這些算法源於統計估計原理，並且底層信號是非高斯過程，而不是高斯過程。值得注意的是，通過專注於兩個非高斯模型，我們開發了一套工具，涵蓋了過去幾十年來文獻中提出的大部分非線性信號處理工具。


主要特點包括：



  • 每章末尾提供大量問題，以幫助讀者發展和理解

  • 書中提供了各種應用領域的例子和案例研究，使理論具體化並置於上下文中

  • 附帶的FTP站點上提供了60多個MATLAB軟件m文件，讀者可以快速設計和應用書中描述的任何非線性信號處理算法到感興趣的應用中


 



目錄：


前言。

致謝。


縮寫詞。


1. 引言。


1.1 非高斯隨機過程。


1.1.1 广义高斯分布和加权中位数。


1.1.2 稳定分布和加权万象。


1.2 统计基础。


1.3 过滤问题。


1.3.1 矩理论。


第一部分：统计基础。


2. 非高斯模型。


2.1 广义高斯分布。


2.2 稳定分布。


2.2.1 定义。


2.2.2 对称稳定分布。


2.2.3 广义中心极限定理。


2.2.4 稳定序列的模拟。


2.3 低阶矩。


2.3.1 分数低阶矩。


2.3.2 零阶统计量。


2.3.3 稳定分布的参数估计。


问题。


3. 阶统计量。


3.1 阶统计量的分布。


3.2 阶统计量的矩。


3.2.1 来自均匀分布的阶统计量。


3.2.2 递推关系。


3.3 包含异常值的阶统计量。


3.4 有序和非有序样本的联合统计量。


问题。


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