# The lifting scheme: a construction of second generation wavelets

@article{Sweldens1995TheLS, title={The lifting scheme: a construction of second generation wavelets}, author={Wim Sweldens}, journal={Siam Journal on Mathematical Analysis}, year={1995}, volume={29}, pages={511-546} }

We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included.

## 2,406 Citations

### The lifting scheme based on the second generation wavelets

- Computer ScienceWuhan University Journal of Natural Sciences
- 2008

This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets.

### A novel design of lifting scheme from general wavelet

- MathematicsIEEE Trans. Signal Process.
- 2001

A novel algorithm that is used to lift the vanishing moments of the wavelet from general wavelet and not only from the Lazy wavelet is proposed, which only needs to solve simple linear equations to obtain the lifting coefficients.

### Representation and compression of operators in bases of second-generation wavelets using the lifting scheme

- Engineering6th International Conference on Signal Processing, 2002.
- 2002

Focuses on the representation of differential operator in second-generation wavelet (SGW) domain. One kind of polynomial biorthogonal interpolating wavelet (PBIW) using the lifting scheme is…

### The Red-Black Wavelet Transform

- Engineering
- 1997

A new kind of second generation wavelets on a rectangular grid is presented using a 2D lifting scheme which is based on a red-black blocking scheme and shows less anisotropy than classical tensor product wavelets.

### Singularity detecting with the second generation wavelet

- Computer ScienceWuhan University Journal of Natural Sciences
- 2008

Two examples are given to prove the second-generation wavelets's potentialities in the singularity detection of signal: a wavelet with vanishing moment and symmetry can be constructed according to the problem.

### Lifting scheme: a new philosophy in biorthogonal wavelet constructions

- MathematicsOptics + Photonics
- 1995

It is shown how lifting leads to a faster, fully in- plane implementation of the wavelet transform, and can be used in the construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one function.

### Wavelets Based on Lifting Scheme and Its Application on Image Processing

- Computer Science2008 International Symposium on Knowledge Acquisition and Modeling
- 2008

This paper aims at analysis the second generation wavelets based on the lifting scheme, which increases the number of the vanishing moments to increase the compress result.

### Parallel Computation of Wavelet Transforms Using the Lifting Scheme

- Computer ScienceThe Journal of Supercomputing
- 2004

This paper describes a message–passing parallel implementation in which high efficiency is achieved by a modified data–swapping approach allowing communications to overlap computations.

### The simplest dual method for constructing lifting scheme of wavelets

- Mathematics2011 International Conference on Electrical and Control Engineering
- 2011

The simplest dual method is introduced as a novel method for constructing the lifting scheme of any biorthogonal wavelets with the unique result and relatively simple structures only if the low pass…

### Building your own wavelets at home

- Mathematics
- 2000

We give an practical overview of three simple techniques to construct wavelets under general circumstances: interpolating subdivision, average interpolation, and lifting. We include examples…

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