Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford UniversityThe new edition of ...this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.Features:* Balances presentation of the mathematics with applications to signal processing* Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox* Companion website for instructors and selected solutions and code available for studentsNew in this edition* Sparse signal representations in dictionaries* Compressive sensing, super-resolution and source separation* Geometric image processing with curvelets and bandlets* Wavelets for computer graphics with lifting on surfaces* Time-frequency audio processing and denoising* Image compression with JPEG-2000* New and updated exercisesA Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering.Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company.Companion website: A Numerical Tour of Signal Processing
Includes all the latest developments since the book was published in 1999, including itsapplication to JPEG 2000 and MPEG-4Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolboxBalances presentation of the mathematics with applications to signal processing
This volume provides an overview of X-ray technology and the historical development of modern CT systems. The main focus of the book is a detailed derivation of reconstruction algorithms in 2D and ...modern 3D cone-beam systems. A thorough analysis of CT artifacts and a discussion of practical issues such as dose considerations give further insight into current CT systems. Although written mainly for graduate students of biomedical engineering, medical physics, medicine (radiology), mathematics, electrical engineering, and physics, practitioners in these fields will also benefit from this book.
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph ...signal processing. However, a meaningful graph is not always readily available from the data, nor easy to define depending on the application domain. In particular, it is often desirable in graph signal processing applications that a graph is chosen such that the data admit certain regularity or smoothness on the graph. In this paper, we address the problem of learning graph Laplacians, which is equivalent to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology. To this end, we adopt a factor analysis model for the graph signals and impose a Gaussian probabilistic prior on the latent variables that control these signals. We show that the Gaussian prior leads to an efficient representation that favors the smoothness property of the graph signals. We then propose an algorithm for learning graphs that enforces such property and is based on minimizing the variations of the signals on the learned graph. Experiments on both synthetic and real world data demonstrate that the proposed graph learning framework can efficiently infer meaningful graph topologies from signal observations under the smoothness prior.
The quaternion least mean square (QLMS) algorithm is introduced for adaptive filtering of three- and four-dimensional processes, such as those observed in atmospheric modeling (wind, vector fields). ...These processes exhibit complex nonlinear dynamics and coupling between the dimensions, which make their component-wise processing by multiple univariate LMS, bivariate complex LMS (CLMS), or multichannel LMS (MLMS) algorithms inadequate. The QLMS accounts for these problems naturally, as it is derived directly in the quaternion domain. The analysis shows that QLMS operates inherently based on the so called ldquoaugmentedrdquo statistics, that is, both the covariance E { xx H } and pseudocovariance E { xx T } of the tap input vector x are taken into account. In addition, the operation in the quaternion domain facilitates fusion of heterogeneous data sources, for instance, the three vector dimensions of the wind field and air temperature. Simulations on both benchmark and real world data support the approach.
Research in graph signal processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper, we first provide an overview of core ideas in GSP and their ...connection to conventional digital signal processing, along with a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas. We then summarize recent advances in developing basic GSP tools, including methods for sampling, filtering, or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning.
Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well ...established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture radar
Call for Papers: Photonic Signal Processing
IEEE journal of selected topics in quantum electronics,
2022-Nov.-Dec., Volume:
28, Issue:
6: High Density Integr. Multipurpose Photon. Circ.
Journal Article
Detecting respiration and heartbeat information from human chest movement is crucial for non‐contact vital sign detection. Due to the small frequency difference between respiration and heartbeat ...signals and the relatively low amplitude of the heartbeat signal, it is challenging to separate and extract them completely. This letter proposes a successive variational mode extraction method based on spectrum trend for the extraction of respiration and heartbeat signals. The proposed method adaptively determines the initial centre frequency and extraction order of the desired signal modes by analyzing the spectrum trend of the signal to be decomposed. Additionally, a recursive framework is introduced to sequentially extract the desired signal modes. Both simulation and practical experiment results show that the method is effective in extracting respiration and heartbeat signals, significantly improving the accuracy of estimating respiration and heartbeat frequencies.
This letter proposes a successive variational mode extraction method based on spectrum trend for the extraction of respiration and heartbeat signals. The method determines the initial centre frequency and extraction order of the desired modes based on the spectrum trend information of the input signal, and introduces a recursive framework to extract the desired modes sequentially. Experimental results show that the method improves the extraction accuracy of respiration and heartbeat signals.
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