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## Matching pursuits with time-frequency dictionaries (1993)

Venue: | IEEE Transactions on Signal Processing |

Citations: | 1666 - 13 self |

### Citations

2600 |
Ten lectures on wavelets
- Daubechies
- 1992
(Show Context)
Citation Context ...2, where get) E L 2 (R) and _ 1 _ (t - pa j I1U) ika-j!J.~r gj.p.k(t) = J;;J g a j e . (101) The dual window g(t) has an exponential decay and its Fourier transform g(w) also has an exponential decay =-=[5]-=-. For any fE L 2 (R), +00 +00MALLAT AND ZHANG: MATCHING PURSUITS WITH TIME-FREQUENCY DICTIONARIES 34\3 With a change of variable, one can derive that for any } E Z +00 +00 +00 +00 <f, gyo> = I; I; <f... |

884 | Vector Quantization.
- Gray
- 1984
(Show Context)
Citation Context ... of the codebook. The inner product (j, g-yo> is quantized by approximating it to the closest scalar stored in the codebook. Vector quantizations algorithms can be extended with a multistage strategy =-=[9]-=-. After quantizing a given vector, the remaining error is quantized once more, and the process continues iteratively. A matching pursuit is similar to a multistage shape-gain vector quantizer. However... |

814 | The Wavelet Transform, Time-Frequency Localization and - Daubechies - 1990 |

675 | Entropy-based algorithms for best basis selection
- Coifman, Wickerhauser
- 1992
(Show Context)
Citation Context ...rithm that chooses at each iteration a waveform that is best adapted to approximate part of the signal. Section VIII compares this locally adaptive method to the algorithm of Coifman and Wickerhauser =-=[4]-=-, which selects the basis that is best adapted to the global signal properties, among all bases of a wavepacket family, Numerical results show that the global optimization does not perform well for hi... |

550 | Projection pursuit regression
- Friedman, StŸtzle
- 1981
(Show Context)
Citation Context ...nlinear, like an orthogonal expansion, it maintains an energy conservation which guaranties its convergence. It is closely related to projection pursuit strategies, developed by Friedman and Stuetzle =-=[7]-=- for statistical parameter estimation. The general algorithm in the Hilbert space framework is explained in Section III and the finite dimensional case is further studied in Section IV. The applicatio... |

389 |
Wavelets and signal processing,”
- Rioul, Vetterli
- 1991
(Show Context)
Citation Context ...omposition might have very different properties. Window Fourier transforms and wavelet transforms are examples of time-frequency signal decomposition that have been studied thoroughly [2], [5], [13], =-=[15]-=-. To extract informations from complex signals, it is often necessary to adapt the time-frequency decomposition to the particular signal structures. This section discusses the adaptivity requirements.... |

345 | Ondelettes et Operateurs. - Meyer - 1990 |

218 |
Time-frequency Distributions - A Review,
- Cohen
- 1989
(Show Context)
Citation Context ...y atoms, the decomposition might have very different properties. Window Fourier transforms and wavelet transforms are examples of time-frequency signal decomposition that have been studied thoroughly =-=[2]-=-, [5], [13], [15]. To extract informations from complex signals, it is often necessary to adapt the time-frequency decomposition to the particular signal structures. This section discusses the adaptiv... |

133 | Wavelets: A Tutorial in Theory and Applications, - Chui - 1992 |

54 | On a conjecture of Huber concerning the convergence of projection pursuit regression. - Jones - 1987 |

43 |
Size Properties of Wavelet Packets
- Coifman, Meyer, et al.
- 1992
(Show Context)
Citation Context ...are not as well localized in time and frequency as Gabor functions. When the scale 2 J increases, these atoms have a complicated time-frequency localization studied by Coifman, Meyer and Wickerhauser =-=[3]-=-. The time-frequency image obtained with this wavepacket dictionary is similar to the energy distribution in Fig. l(b), obtained with Gabor dictionary. Some signal features do not appear as clearly be... |

29 | Product code vector quantizers for waveform and voice coding,” - Sabin, Gray - 1984 |

22 |
Wavelets associated with representations of the affine Weyl-Heisenberg group
- Torresani
- 1991
(Show Context)
Citation Context ...ncy w = ~. Its energy is concentrated in a neighborhood of ~, whose size is proportional to 1/s. The family 5) = (g'Y(t»'Y E[ is extremely redundant, and its properties have been studied by Torresani =-=[17]-=-. To represent efficiently any function f (t), we must select an appropriate countable subset of atoms (g'Yu(t»nEN, with 'Yn = (SfP Un' ~n), so thatf(t) can be written (6)MALLAT AND ZHANG: MATCHING P... |

10 | Matrix Computations", The Johns Hopkins - Golub, Loan - 1989 |

8 |
Signal representation via adaptive normalized Gaussian functions. Signal Processing 36
- Qian, Chen
- 1994
(Show Context)
Citation Context ...ly to the Wigner distribution or Cohen's class distributions, this energy distribution does not include interference terms and thus provides a clear picture in the time-frequency plane. Qian and Chen =-=[14]-=- have developed independently a similar algorithm to expand signals over time-frequency atoms. A fast implementation of the matching pursuit for dictionary of Gabor time-frequency atoms is described i... |

5 | Projection Pursuit", The - Huber - 1985 |

5 | Wavelets associated with representations of the ane Weyl-Heisenberg group - Torresani - 1991 |

2 | Wavelets: A Tutorial in Theory and Applications - K, Chui - 1992 |

2 |
Projection pursuit
- unknown authors
- 1985
(Show Context)
Citation Context ... , X d • This decomposition is obtained with a strategy similar to the matching pursuit approach. Readers further interested by projections pursuits are referred to a tutorial review written by Huber =-=[10]-=-. The mathematical similarities of the two algorithms allow us to transpose a result of Jones [11] that proves the convergence of projection pursuit algorithms. Let us recall that V is the closed line... |

1 |
Local time-frequency multilayer orthogonal transforms
- Mallat, Zhang
- 1992
(Show Context)
Citation Context ...m increases. Let us mention that the algorithm can be modified by selecting several vectors from the dictionary at each iterations and projecting the residue over the space generated by these vectors =-=[12]-=-, but we shall not further develop this approach here. Functional approximations through such iterated orthogonal projections has previously been studied in statistics by Friedman and Stuetzle [7], un... |

1 |
x +00 +00 m=-ooq=-oo S~ 27r X exp i -2--2
- Hermann
- 1990
(Show Context)
Citation Context ...he decomposition might have very different properties. Window Fourier transforms and wavelet transforms are examples of time-frequency signal decomposition that have been studied thoroughly [2], [5], =-=[13]-=-, [15]. To extract informations from complex signals, it is often necessary to adapt the time-frequency decomposition to the particular signal structures. This section discusses the adaptivity require... |