The discrete shearlet transform: a new directional transform and compactly supported shearlet frames

Area of Science:

• Image Processing
• Computer Vision
• Applied Mathematics

Background:

• Analyzing intrinsic geometrical features of images is crucial for various applications.
• Existing directional image representation schemes have limitations.
• The discrete wavelet transform (DWT) is a common but not always optimal method.

Purpose of the Study:

• To develop and evaluate the discrete shearlet transform (DST) for image processing.
• To assess DST's performance in multiscale directional representation.
• To compare DST with existing transforms like DWT in image approximation and denoising.

Main Methods:

• Development of the discrete shearlet transform (DST) within a discrete framework.
• Implementation based on multiresolution analysis (MRA).
• Performance assessment through image approximation and denoising experiments.

Main Results:

• DST provides efficient multiscale directional representation.
• DST-based image approximation outperforms DWT.
• DST's computational cost is comparable to DWT.
• DST demonstrates favorable performance in image denoising compared to other transforms.

Conclusions:

• The discrete shearlet transform (DST) is an effective tool for image processing applications.
• DST offers advantages over DWT in image approximation and competitive performance in denoising.
• The developed DST provides a robust method for analyzing intrinsic geometrical features of images.