基本信息
- 原书名：A Wavelet Tour of Signal Processing, 3rd ed., Third Edition: The Sparse Way
- 原出版社： Academic Press
- 作者： Stephane Mallat
- 丛书名： 经典原版书库
- 出版社：机械工业出版社
- ISBN：9787111288619
- 上架时间：2011-5-20
- 出版日期：2010 年1月
- 开本：32开
- 页码：805
- 版次：3-1
- 所属分类：数学 > 分析 > 傅里叶分析与小波分析
教材
内容简介
书籍
数学书籍
这本经典教材的全新版本全面论述了稀疏表示的重要概念、技术和应用，反映了该主题在当今信号处理领域所起的关键作用。书中清楚地给出了傅里叶、小波和时频变换的标准表示，以及用快速算法构造的正交基。作者在解释了稀疏的主要概念后将其运用于信号压缩、噪声衰减和逆问题，同时给出了冗余字典、超分辨和压缩感知中的稀疏表示。.
全书以十分直观和近乎谈话的方式，以信号处理的问题为背景，叙述了小波的理论和应用，使读者可以透过复杂的数学公式来窥探小波的精髓，而又不致陷入小波纯数学理论的迷宫。本书是按研究生教材的要求编写的，既可以让应用数学系的学生了解数学公式的工程意义，也可以让计算机及电子工程系的学生了解工程问题的数学描述。对于小波理论与应用的研究人员，本书更是一本极具价值的参考书。..
本书网站http://www.ceremade.dauphine.fr/~peyre/wavelet-tour/上有本书中的插图、勘误等。
新增内容
·字典中的稀疏信号表示。
·压缩感知、超分辨和源分离。
·曲线波和条带波的几何图像处理。
·提升小波变换用于计算机图像处理。
·时频语音信号处理和去噪。
·JPEG 2000图像压缩。
数学书籍
这本经典教材的全新版本全面论述了稀疏表示的重要概念、技术和应用，反映了该主题在当今信号处理领域所起的关键作用。书中清楚地给出了傅里叶、小波和时频变换的标准表示，以及用快速算法构造的正交基。作者在解释了稀疏的主要概念后将其运用于信号压缩、噪声衰减和逆问题，同时给出了冗余字典、超分辨和压缩感知中的稀疏表示。.
全书以十分直观和近乎谈话的方式，以信号处理的问题为背景，叙述了小波的理论和应用，使读者可以透过复杂的数学公式来窥探小波的精髓，而又不致陷入小波纯数学理论的迷宫。本书是按研究生教材的要求编写的，既可以让应用数学系的学生了解数学公式的工程意义，也可以让计算机及电子工程系的学生了解工程问题的数学描述。对于小波理论与应用的研究人员，本书更是一本极具价值的参考书。..
本书网站http://www.ceremade.dauphine.fr/~peyre/wavelet-tour/上有本书中的插图、勘误等。
新增内容
·字典中的稀疏信号表示。
·压缩感知、超分辨和源分离。
·曲线波和条带波的几何图像处理。
·提升小波变换用于计算机图像处理。
·时频语音信号处理和去噪。
·JPEG 2000图像压缩。
目录
Preface to the Sparse Edition .
Notations
CHAPTER 1 Sparse Representations
1.1 Computational Harmonic Analysis
1.2 Approximation and Processing in Bases
1.3 Time-Frequency Dictionaries
1.4 Sparsity in Redundant Dictionaries
1.5 Inverse Problems
1.6 Travel Guide
CHAPTER 2 The Fourier Kingdom
2.1 Linear Time-lnvariant Filtering
2.2 Fourier Integrals
2.3 Properties
2.4 Two-Dimensional Fourier Transform
2.5 Exercises
CHAPTER 3 Discrete Revolution
3.1 Sampling Analog Signals
3.2 Discrete Time-Invariant Filters
3.3 Finite Signals
3.4 Discrete Image Processing
Notations
CHAPTER 1 Sparse Representations
1.1 Computational Harmonic Analysis
1.2 Approximation and Processing in Bases
1.3 Time-Frequency Dictionaries
1.4 Sparsity in Redundant Dictionaries
1.5 Inverse Problems
1.6 Travel Guide
CHAPTER 2 The Fourier Kingdom
2.1 Linear Time-lnvariant Filtering
2.2 Fourier Integrals
2.3 Properties
2.4 Two-Dimensional Fourier Transform
2.5 Exercises
CHAPTER 3 Discrete Revolution
3.1 Sampling Analog Signals
3.2 Discrete Time-Invariant Filters
3.3 Finite Signals
3.4 Discrete Image Processing
前言
I cannot help but find striking resemblances between scientific communities and schools of fish. We interact in conferences and through articles, and we move together while a global trajectory emerges from individual contributions. Some of us like to be at the center of the school, others prefer to wander around, and a few swim in multiple directions in front. To avoid dying by starvation in a progressively narrower and specialized domain, a scientific community needs also to move on. Computational harmonic analysis is still very much alive because it went beyond wavelets. Writing such a book is about decoding the trajectory of the school and gathering the pearls that have been uncovered on the way. Wavelets are no longer the central topic, despite the previous edition's original title. It is just an important tool, as the Fourier transform is. Sparse representation and processing are now at the core. .
In the 1980s, many researchers were focused on building time-frequency decom-positions, trying to avoid the uncertainty barrier, and hoping to discover the ultimate representation. Along the way came the construction of wavelet orthogonal bases,which opened new perspectives through collaborations with physicists and math-ematicians. Designing orthogonal bases with Xlets became a popular sport with compression and noise-reduction applications. Connections with approximations and sparsity also became more apparent. The search for sparsity has taken over,leading to new grounds where orthonormal bases are replaced by redundant dictio-naries of waveforms.
During these last seven years, I also encountered the industrial world. With a lot of naiveness, some bandlets, and more mathematics, I cofounded a start-up with Christophe Bernard, Jerome Kalifa, and Erwan Le Pennec. It took us some time to learn that in three months good engineering should produce robust algo-rithms that operate in real time, as opposed to the three years we were used to having for writing new ideas with promising perspectives. Yet, we survived because mathematics is a major source of industrial innovations for signal process-ing. Semiconductor technology offers amazing computational power and flexibility. However, ad hoc algorithms often do not scale easily and mathematics accelerates the trial-and-error development process. Sparsity decreases computations, memory,and data communications. Although it brings beauty, mathematical understanding is not a luxury. It is required by increasingly sophisticated information-processing devices.
New Additions
Putting sparsity at the center of the book implied rewriting many parts and adding sections. Chapters 12 and 13 are new. They introduce sparse represen-tations in redundant dictionaries, and inverse problems, super-resolution, and compressive sensing. Here is a small catalog of new elements in this third edition:
·Radon transform and tomography
·Lifting for wavelets on surfaces, bounded domains, and fast computations
·JPEG-2000 image compression
·Block thresholding for denoising
·Geometric representations with adaptive triangulations, curvelets, and bandlets
·Sparse approximations in redundant dictionaries with pursuit algorithms
·Noise reduction with model selection in redundant dictionaries
·Exact recovery of sparse approximation supports in dictionaries
·Multichannel signal representations and processing
·Dictionary learning
·Inverse problems and super-resolution
·Compressive sensing
·Source separation
Teaching
This book is intended as a graduate4evel textbook. Its evolution is also the result of teaching courses in electrical engineering and applied mathematics. A new website provides software for reproducible experimentations, exercise solutions,together with teaching material such as slides with figures and MATLAB software for numerical classes of http://wavelet-tour, com.
In the 1980s, many researchers were focused on building time-frequency decom-positions, trying to avoid the uncertainty barrier, and hoping to discover the ultimate representation. Along the way came the construction of wavelet orthogonal bases,which opened new perspectives through collaborations with physicists and math-ematicians. Designing orthogonal bases with Xlets became a popular sport with compression and noise-reduction applications. Connections with approximations and sparsity also became more apparent. The search for sparsity has taken over,leading to new grounds where orthonormal bases are replaced by redundant dictio-naries of waveforms.
During these last seven years, I also encountered the industrial world. With a lot of naiveness, some bandlets, and more mathematics, I cofounded a start-up with Christophe Bernard, Jerome Kalifa, and Erwan Le Pennec. It took us some time to learn that in three months good engineering should produce robust algo-rithms that operate in real time, as opposed to the three years we were used to having for writing new ideas with promising perspectives. Yet, we survived because mathematics is a major source of industrial innovations for signal process-ing. Semiconductor technology offers amazing computational power and flexibility. However, ad hoc algorithms often do not scale easily and mathematics accelerates the trial-and-error development process. Sparsity decreases computations, memory,and data communications. Although it brings beauty, mathematical understanding is not a luxury. It is required by increasingly sophisticated information-processing devices.
New Additions
Putting sparsity at the center of the book implied rewriting many parts and adding sections. Chapters 12 and 13 are new. They introduce sparse represen-tations in redundant dictionaries, and inverse problems, super-resolution, and compressive sensing. Here is a small catalog of new elements in this third edition:
·Radon transform and tomography
·Lifting for wavelets on surfaces, bounded domains, and fast computations
·JPEG-2000 image compression
·Block thresholding for denoising
·Geometric representations with adaptive triangulations, curvelets, and bandlets
·Sparse approximations in redundant dictionaries with pursuit algorithms
·Noise reduction with model selection in redundant dictionaries
·Exact recovery of sparse approximation supports in dictionaries
·Multichannel signal representations and processing
·Dictionary learning
·Inverse problems and super-resolution
·Compressive sensing
·Source separation
Teaching
This book is intended as a graduate4evel textbook. Its evolution is also the result of teaching courses in electrical engineering and applied mathematics. A new website provides software for reproducible experimentations, exercise solutions,together with teaching material such as slides with figures and MATLAB software for numerical classes of http://wavelet-tour, com.
媒体评论
Mallat的教材是该领域无可争议的经典参考书，它是唯一一本能够从深度和广度全面覆盖该领域关键资料的著作。...
——Laurent Demanet，斯坦福大学
——Laurent Demanet，斯坦福大学
