The Discrete Shearlet Transform: A New Directional Transform and Compactly Supported Shearlet Frames

It is now widely acknowledged that analyzing the intrinsic geometrical features of the underlying image is essential in many applications including image processing. In order to achieve this, several directional image representation schemes have been proposed. In this paper, we develop the discrete...

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Bibliographic Details
Published in:IEEE transactions on image processing 2010-05, Vol.19 (5), p.1166-1180
Main Author: LIM, Wang-Q
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation
Approximation error
Computational efficiency
Discrete shearlet transform
Discrete transforms
Discrete wavelet transforms
Exact sciences and technology
Frames
Geometry
Image analysis
image approximations
Image denoising
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Image representation
Information, signal and communications theory
Mathematical analysis
Multiresolution analysis
Numerical Analysis, Computer-Assisted
Pattern Recognition, Automated - methods
Representations
Reproducibility of Results
Sensitivity and Specificity
shearlets
Signal and communications theory
Signal processing
Signal Processing, Computer-Assisted
Signal representation. Spectral analysis
Signal, noise
Telecommunications and information theory
Transforms
wavelets
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Summary:It is now widely acknowledged that analyzing the intrinsic geometrical features of the underlying image is essential in many applications including image processing. In order to achieve this, several directional image representation schemes have been proposed. In this paper, we develop the discrete shearlet transform (DST) which provides efficient multiscale directional representation and show that the implementation of the transform is built in the discrete framework based on a multiresolution analysis (MRA). We assess the performance of the DST in image denoising and approximation applications. In image approximations, our approximation scheme using the DST outperforms the discrete wavelet transform (DWT) while the computational cost of our scheme is comparable to the DWT. Also, in image denoising, the DST compares favorably with other existing transforms in the literature.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2010.2041410