Sparse Signal Processing
作者/authors
摘要/abstract
Conventional sampling techniques are based on Shannon-Nyquist theory which states that the required sampling rate for perfect recovery of a band-limited signal is at least twice its bandwidth. The band-limitedness property of the signal plays a significant role in the design of conventional sampling and reconstruction systems. As the natural signals are not necessarily band-limited, a low-pass filter is applied to the signal prior to its sampling for the purpose of antialiasing. Most of the signals we are faced with are sparse rather than band-limited (or low pass). It means that they have a small number of non-zero coefficients in some domain such as time, discrete cosine transform (DCT), discrete wavelet transform (DWT), or discrete fourier transform (DFT). This characteristic of the signal is the foundation for the emerging of a new signal sampling theory called Compressed Sampling, an extension of random sampling. In this chapter, an overview of compressed sensing, together with a summary of its popular recovery techniques, is presented. Moreover, as a well-known example of structured sparsity, the block sparse recovery problem is investigated and the related recovery approaches are illustrated.
目录/contents
1 Abstract Exact and Approximate Sampling Theorems ................ 1
M.M. Dodson
2 Sampling in Reproducing Kernel Hilbert Space ........................ 23
J.R. Higgins
3 Boas-Type Formulas and Sampling in Banach Spaces
with Applications to Analysis on Manifolds ............................. 39
Isaac Z. Pesenson
4 On Window Methods in Generalized Shannon Sampling
Operators .................................................................... 63
Andi Kivinukk and Gert Tamberg
5 Generalized Sampling Approximation for Multivariate
Discontinuous Signals and Applications to Image Processing ......... 87
Carlo Bardaro, Ilaria Mantellini, Rudolf Stens, Jörg Vautz,
and Gianluca Vinti
6 Signal and System Approximation from General Measurements ..... 115
Holger Boche and Ullrich J. Mönich
7 Sampling in Image Representation and Compression.................. 149
John J. Benedetto and Alfredo Nava-Tudela
8 Sparse Signal Processing................................................... 189
Masoumeh Azghani and Farokh Marvasti
9 Signal Sampling and Testing Under Noise ............................... 215
Mirosław Pawlak
10 Superoscillations ............................................................ 247
Paulo J.S.G. Ferreira
11 General Moduli of Smoothness and Approximation
by Families of Linear Polynomial Operators ............................ 269
K. Runovski and H.-J. Schmeisser
12 Variation and Approximation in Multidimensional Setting
for Mellin Integral Operators ............................................. 299
Laura Angeloni and Gianluca Vinti
13 The Lebesgue Constant for Sinc Approximations ...................... 319
Frank Stenger, Hany A.M. El-Sharkawy, and Gerd Baumann
14 Six (Seven) Problems in Frame Theory .................................. 337
Ole Christensen
15 Five Good Reasons for Complex-Valued Transforms
in Image Processing ........................................................ 359
Brigitte Forster
16 Frequency Determination Using the Discrete Hermite Transform ... 383
Dale H. Mugler and Stuart Clary
17 Fractional Operators, Dirichlet Averages, and Splines................. 399
Peter Massopust
18 A Distributional Approach to Generalized Stochastic
Processes on Locally Compact Abelian Groups ......................... 423
H.G. Feichtinger and W. Hörmann
19 On a Discrete Turán Problem for `-1 Radial Functions ............... 447
Elena E. Berdysheva and Hubert Berens