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## Quantization noise shaping on arbitrary frame expansions (2005)

Venue: | In Proceedings of IEEE ICASSP 2005 |

Citations: | 11 - 6 self |

### Citations

10589 | Introduction to Algorithms
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...e optimal sequential quantizer. This can be determined by solving the traveling salesman problem (TSP). The TSP is of course NP-complete in general, but has been extensively studied in the literature =-=[6]-=-. Similarly, the optimal tree quantizer is defined by the solution of the minimum spanning tree problem. This is also a well studied problem, solvable in polynomial time [6]. Since any path is also a ... |

105 |
Ten lectures on wavelets. CBMS-NSF regional conference series in applied mathematics.
- Daubechies
- 1992
(Show Context)
Citation Context ...ed considerable attention in the last few years. Simple scalar quantization applied independently on each frame expansion coefficient, followed by linear reconstruction is well known to be suboptimal =-=[8, 7]-=-. Several algorithms have been proposed that improve performance although with significant complexity either at the quantizer [9] or ∗This work was supported in part by: participation in the Advanced ... |

41 |
Reduction of the MSE in r-times oversampled A/D conversion from O(1/r) to O(1/r 2
- Thao, Vetterli
- 1994
(Show Context)
Citation Context ...m, BAE Systems Inc., and MIT Lincoln Laboratory. The views expressed are those of the authors and do not reflect the official policy or position of the U.S. Government. 1 in the reconstruction method =-=[9, 11]-=-. More recently, frame quantization methods inspired by uniform oversampled noise shaping (referred to generically as Sigma-Delta noise shaping) have been proposed for finite uniform frames [1, 2] and... |

39 | Ö.: Sigma-Delta quantization and finite frames
- Benedetto, Powell, et al.
- 1990
(Show Context)
Citation Context ...od [9, 11]. More recently, frame quantization methods inspired by uniform oversampled noise shaping (referred to generically as Sigma-Delta noise shaping) have been proposed for finite uniform frames =-=[1, 2]-=- and for frames generated by oversampled filterbanks [3]. In [1, 2] the error due to the quantization of each expansion coefficient is subtracted from the next coefficient. The method is algorithmical... |

29 | Noise reduction in oversampled filter banks using predictive quantization
- Bölcskei, Hlawatsch
- 2001
(Show Context)
Citation Context ...red by uniform oversampled noise shaping (referred to generically as Sigma-Delta noise shaping) have been proposed for finite uniform frames [1, 2] and for frames generated by oversampled filterbanks =-=[3]-=-. In [1, 2] the error due to the quantization of each expansion coefficient is subtracted from the next coefficient. The method is algorithmically similar to classical first order noise shaping and us... |

14 |
Overcomplete expansions and robustness
- Cvetkovic, Vetterli
- 1996
(Show Context)
Citation Context ...ed considerable attention in the last few years. Simple scalar quantization applied independently on each frame expansion coefficient, followed by linear reconstruction is well known to be suboptimal =-=[8, 7]-=-. Several algorithms have been proposed that improve performance although with significant complexity either at the quantizer [9] or ∗This work was supported in part by: participation in the Advanced ... |

4 |
Quantized overcomplete expansions in IRN: analysis, synthesis, and algorithms
- Goyal, Vetterli, et al.
- 1998
(Show Context)
Citation Context ...t, followed by linear reconstruction is well known to be suboptimal [8, 7]. Several algorithms have been proposed that improve performance although with significant complexity either at the quantizer =-=[9]-=- or ∗This work was supported in part by: participation in the Advanced Sensors Collaborative Technology Alliance (CTA) sponsored by the U.S. Army Research Laboratory under Cooperative agreement DAAD19... |

1 |
and G.C Temes, editors. Oversampling Delta-Sigma Converters
- Candy
- 1992
(Show Context)
Citation Context ... show that if the frame forms an orthonormal basis, then direct scalar quantization is optimal in terms of minimizing the error magnitude. However, this is not the case for all other frame expansions =-=[1, 2, 3, 5, 7, 8, 9, 11]-=-. Noise shaping is one of the possible strategies to reduce the error magnitude. In order to generalize noise shaping to arbitrary frame expansions, we first present traditional oversampling and noise... |