Shearlet Transform for Image Denoising

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Resource Overview

Application Context: Shearlet transform is an effective method for achieving localized and optimally sparse representations with simple mathematical construction and fast algorithmic implementation. These advantages make shearlet transform an attractive candidate for image representation. Key Technologies: (a) Decomposition of noisy images. (b) Obtaining shearlet coefficients through different subbands and directional filtering orientations using adaptive directional selection.

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Application Background

Shearlet transform serves as a highly effective mathematical tool for achieving localized and optimally sparse representations. Its simple mathematical structure allows efficient implementation through fast computational algorithms, typically involving multi-scale directional filtering operations. These advantages establish shearlet transform as a compelling choice for image representation tasks.

Key Technologies

(a) First, we perform decomposition of the noisy input image using a shearlet transform framework, which involves multi-resolution analysis through pyramidal filtering and directional localization via shearing operations.

(b) Subsequently, we extract shearlet coefficients by applying directional filters at various orientations and scales. This process utilizes adaptive directional sampling to capture image features across different subbands, where thresholding techniques can be applied to coefficients for effective noise reduction.

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