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## New algorithms for best local cosine basis search (2004)

Venue: | In Proc. ICASSP-2004 |

Citations: | 9 - 8 self |

### Citations

186 |
Signal Processing with Lapped Transforms
- Malvar
- 1992
(Show Context)
Citation Context ...r compression [11], noise removal [5,6,9], and time-frequency analysis [3, 12]. The original paper on best basis search [2] exploited the fact that 1-D wavelet packet bases [1] and local cosine bases =-=[8]-=- can be organized on a single dyadic tree, making it possible to find the best basis (for an additive cost) via an efficient dynamic programming algorithm. In the case of local cosines, however, it re... |

132 |
Entropy Based Algorithms for Best Basis Selection
- Coifman, Wickerhauser
- 1992
(Show Context)
Citation Context ...ette, IN 47907 Urbana, IL 61801 ABSTRACT We propose a best basis search algorithm for local cosine dictionaries. We improve upon the classical best local cosine basis selection based on a dyadic tree =-=[2]-=-, by considering a larger dictionary of bases. This results in more compact representations, lower costs, and approximate shift-invariance. We also provide a version of our algorithm which is strictly... |

113 |
A wavelet tour of signal processing, second edition
- Mallat
- 1999
(Show Context)
Citation Context ...ch Foundation grant, and an NSF CAREER award CCR-0237633. All plots were generated with the help of Wavelab 802 [4]. 2. BACKGROUND The general best basis search problem is formulated, for example, in =-=[2, 7]-=-. We consider a dictionary D that is the union of orthonormal bases for C N , D = [ B λ , where each basis B λ is a family λ∈Λ of N vectors, B λ = {g λ m}1≤m≤N . The cost of representing a signal f in... |

91 | Wavelet analysis and signal processing
- Coifman, Meyer, et al.
- 1992
(Show Context)
Citation Context ...nstrated to be effective for compression [11], noise removal [5,6,9], and time-frequency analysis [3, 12]. The original paper on best basis search [2] exploited the fact that 1-D wavelet packet bases =-=[1]-=- and local cosine bases [8] can be organized on a single dyadic tree, making it possible to find the best basis (for an additive cost) via an efficient dynamic programming algorithm. In the case of lo... |

57 |
wavelet packet bases in a rate-distortion sense
- Best
- 1993
(Show Context)
Citation Context ...ms where the aim is to adaptively select, from a library of orthonormal bases, the basis which minimizes a cost for a given signal. Such methods have been demonstrated to be effective for compression =-=[11]-=-, noise removal [5,6,9], and time-frequency analysis [3, 12]. The original paper on best basis search [2] exploited the fact that 1-D wavelet packet bases [1] and local cosine bases [8] can be organiz... |

55 | On denoising and best signal representation
- Krim, Tucker, et al.
- 1999
(Show Context)
Citation Context ...to adaptively select, from a library of orthonormal bases, the basis which minimizes a cost for a given signal. Such methods have been demonstrated to be effective for compression [11], noise removal =-=[5,6,9]-=-, and time-frequency analysis [3, 12]. The original paper on best basis search [2] exploited the fact that 1-D wavelet packet bases [1] and local cosine bases [8] can be organized on a single dyadic t... |

24 | On the statistics of best bases criteria
- Krim, Pesquet
- 1995
(Show Context)
Citation Context ...to adaptively select, from a library of orthonormal bases, the basis which minimizes a cost for a given signal. Such methods have been demonstrated to be effective for compression [11], noise removal =-=[5,6,9]-=-, and time-frequency analysis [3, 12]. The original paper on best basis search [2] exploited the fact that 1-D wavelet packet bases [1] and local cosine bases [8] can be organized on a single dyadic t... |

19 | Orthonormal shift-invariant adaptive local trigonometric decomposition
- Cohen, Raz, et al.
- 1997
(Show Context)
Citation Context ...he original signals and time-frequency representations of the best local cosine basis with smallest cell size M = 16: (a) The signal from Fig. 1(d); (b) the shift-invariant local cosine decomposition =-=[3]-=-; (c) a copy of Fig. 1(f), i.e., the best multitree local cosine basis; (d-f) a similar experiment for a signal where the two local cosine bumps are shifted by different amounts.s3.3. Shift-Invariance... |

17 |
Signal estimation using adapted treestructured bases and the MDL principle
- Moulin
- 1996
(Show Context)
Citation Context ...to adaptively select, from a library of orthonormal bases, the basis which minimizes a cost for a given signal. Such methods have been demonstrated to be effective for compression [11], noise removal =-=[5,6,9]-=-, and time-frequency analysis [3, 12]. The original paper on best basis search [2] exploited the fact that 1-D wavelet packet bases [1] and local cosine bases [8] can be organized on a single dyadic t... |

14 | Anisotropic 2D wavelet packets and rectangular tiling: theory and algorithms
- Xu, Do
- 2003
(Show Context)
Citation Context ...ion of a wide class of 2-D optimal basis search algorithms. In [10], we use these 2-D algorithms to find the best rectangular tiling of an image, and to find the best anisotropic wavelet packet basis =-=[13]-=-. Note that the original best basis paper [2] proposed using an entropy cost. Since then, a number of papers have proposed different criteria, e.g., based on the MDL principle [5, 9], Bayesian estimat... |

8 | Adapted bases of time-frequency local cosines
- Villemoes
(Show Context)
Citation Context ...of orthonormal bases, the basis which minimizes a cost for a given signal. Such methods have been demonstrated to be effective for compression [11], noise removal [5,6,9], and time-frequency analysis =-=[3, 12]-=-. The original paper on best basis search [2] exploited the fact that 1-D wavelet packet bases [1] and local cosine bases [8] can be organized on a single dyadic tree, making it possible to find the b... |

5 | Optimal tilings and best basis search in large dictionaries
- Huang, Pollak, et al.
- 2003
(Show Context)
Citation Context ...ncy pictures, and approximate shift-invariance. We show that this algorithm can moreover be made strictly shiftinvariant by using a procedure similar to the one developed in [3]. In a companion paper =-=[10]-=-, we show that our dynamic programming algorithm is a 1-D version of a wide class of 2-D optimal basis search algorithms. In [10], we use these 2-D algorithms to find the best rectangular tiling of an... |