Sparse Signal Processing
作者/authors
M Azghani, F Marvasti
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
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