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Wavelet-domain approximation and compression of piecewise smooth images
Michael B Wakin1, Justin K Romberg, Hyeokho Choi
1epartment of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA. wakin@ece.rice.edu
Summary
This study introduces a new wavelet framework for image compression, improving efficiency for images with smooth regions and edges. The geometric model uses wavelets and wedgeprints for near-optimal rate-distortion performance.
Area of Science:
- Image processing and computer vision
- Signal processing
- Data compression
Background:
- Wavelet transforms offer sparse representations for smooth images, aiding approximation and compression via techniques like zerotrees.
- This sparsity is limited in piecewise smooth images due to edge discontinuities, hindering efficient wavelet-based compression.
- Current methods achieve suboptimal rate-distortion (R-D) performance for specific image classes.
Purpose of the Study:
- To develop a geometric modeling framework for wavelets to enhance compression of piecewise smooth images.
- To address the limitations of existing wavelet-based methods in representing edge structures.
- To achieve near-optimal rate-distortion performance for image compression.
Main Methods:
- Developed a geometric modeling framework for wavelets, interpretable as an extended zerotree model or a new atomic representation.
- Introduced wedgeprints, anisotropic atoms adapted to edge singularities, alongside wavelets.
- Implemented a novel quadtree pruning strategy utilizing both zerotrees and wedgeprints.
Main Results:
- Achieved near-optimal asymptotic rate-distortion performance of D(R) <= (log R)2 /R2 for piecewise smooth C2/C2 images.
- Demonstrated a prototype image coder with improved efficiency for images containing smooth regions and edges.
- Extended the algorithm for natural image compression, yielding promising results in mean-square error and visual quality.
Conclusions:
- The proposed geometric wavelet framework effectively handles edge structures in piecewise smooth images.
- This approach significantly improves the efficiency and performance of image compression algorithms.
- The method shows potential for practical application in natural image compression.
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