# The dual-tree complex wavelet transform: a new technique for shift invariance and directional filters

@inproceedings{Kingsbury1998TheDC, title={The dual-tree complex wavelet transform: a new technique for shift invariance and directional filters}, author={Nick Kingsbury}, year={1998} }

A new implementation of the Discrete Wavelet Transform is presented, suitable for a range of signal and image processing applications. It employs a dual tree of wavelet lters to obtain the real and imaginary parts of complex wavelet coeecients. This introduces limited redundancy (4:1 for 2-dimensional signals) and allows the transform to provide approximate shift in-variance and directionally selective lters (properties lacking in the traditional wavelet transform) while preserving the usual…

No Paper Link Available

## Topics from this paper

## 653 Citations

Shift invariant properties of the dual-tree complex wavelet transform

- Mathematics, Computer Science1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)
- 1999

We discuss the shift invariant properties of a new implementation of the discrete wavelet transform, which employs a dual-tree of wavelet filters to obtain the real and imaginary parts of complex…

The Dual-Tree Complex Wavelet Transform – A Coherent Framework for Multiscale Signal and Image Processing

- 2005

The dual-tree complex wavelet transform ( CWT) is a relatively recent enhancement of the discrete wavelet transform (DWT) with important additional properties: It is nearly shift-invariant and…

The dual-tree complex wavelet transform

- Computer Science, MathematicsIEEE Signal Processing Magazine
- 2005

Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual- tree approach.

Complex Wavelets for Shift Invariant Analysis and Filtering of Signals

- Mathematics
- 2001

This paper describes a form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces…

Dual-Tree Complex Wavelet Transform in the problem of speech enhancement

- Mathematics
- 2015

The dual-tree complex wavelet transform is considered a relatively recent improvement for the discrete wavelet transform. In this paper, the applicability of such transform in the problem of speech…

Analytic Wavelet Packets—Combining the Dual-Tree Approach With Wavelet Packets for Signal Analysis and Filtering

- Mathematics, Computer ScienceIEEE Transactions on Signal Processing
- 2009

This paper provides a review of these problems as well as the undecimated wavelet transform which solves the problem of shift-variance and a filter swapping scheme is developed in order to create complex wavelet packets with analytic basis functions.

Dual-Tree Complex Wavelet Transform in the Frequency Domain and an Application to Signal Classification

- Computer ScienceInt. J. Wavelets Multiresolution Inf. Process.
- 2005

We examine Kingsbury's dual-tree complex wavelet transform in the frequency domain, where it can be formulated for standard wavelet filters without special filter design and apply the method to the…

A DUAL TREE COMPLEX WAVELET TRANSFORM CONSTRUCTION AND ITS APPLICATION TO IMAGE DENOISING

- 2010

This paper discusses the application of complex discrete wavelet transform (CDWT) which has significant advantages over real wavelet transform for certain signal processing problems. CDWT is a form…

A Study on the Performance Improvement of Over-sampled Discrete Wavelet Transform

- Computer Science
- 2014

This paper shows that the proposed non-separable based discrete wavelet transform is well applied with performance improvement of digital image and noise removal and satisfies shift invariance and directional selectivity.

Complex Wavelets – N Kingsbury 3 Complex Wavelets for Shift Invariant Analysis and Filtering of Signals 1

- 2001

This paper describes a form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces…

## References

SHOWING 1-6 OF 6 REFERENCES

A Theory for Multiresolution Signal Decomposition: The Wavelet Representation

- Computer Science, MathematicsIEEE Trans. Pattern Anal. Mach. Intell.
- 1989

It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/Sup j/ can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.

Motion estimation using a complex-valued wavelet transform

- Mathematics, Computer ScienceIEEE Trans. Signal Process.
- 1998

The accuracy, efficiency, and robustness of the new algorithm are demonstrated in comparison testing against hierarchical implementations of intensity gradient-based and fractional-precision block matching motion estimators.

Flexible design of multidimensional perfect reconstruction FIR 2-band filters using transformations of variables

- Mathematics, MedicineIEEE Trans. Image Process.
- 1993

An approach to designing multidimensional linear-phase FIR diamond subband filters having the perfect reconstruction property is presented. It is based on a transformation of variables technique and…

Pyramid-based texture analysis/synthesis

- Computer ScienceProceedings., International Conference on Image Processing
- 1995

This paper describes a method for synthesizing images that match the texture appearance of a given digitized sample that is based on a model of human texture perception, and has potential to be a practically useful tool for image processing and graphics applications.

Shiftable multi-scale trans- forms

- IEEE Trans. Information Theory,
- 1992

\Shiftable multi-scale transforms

- IEEE Trans. Information Theory
- 1992