Non-Redundant Complex Wavelet Transform for Image Compression
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Solution Overview
Problem
Existing image and video compression methods, such as JPEG2000, suffer from lack of shift invariance, directionality, and explicit phase information due to real wavelet transforms, which complicates geometric modeling and is not suitable for applications like digital still cameras and wireless-linked Internet transmission.
Innovation Solution
A separable two-dimensional non-redundant complex wavelet image transform using one-dimensional triband transforms is implemented, which reduces redundancy and maintains complex wavelet properties, providing directionality and phase coherence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If real wavelet transforms are used in JPEG2000, then image compression is achieved, but shift invariance, directionality, and explicit phase information are lost
Solution Approach 1:
The patent changes the fundamental parameter of the wavelet transform from real-valued to complex-valued coefficients. This parameter change enables the transform to preserve explicit phase information, achieve shift invariance, and provide directionality while maintaining compression capabilities through the complex coefficient structure.
2Loss of information
If redundant complex wavelet transforms are used, then directionality and phase information are achieved, but redundancy increases encoding memory requirements
Solution Approach 1:
The patent extracts and discards the redundant negative frequency components from the complex wavelet transform, retaining only the essential positive frequency information. This extraction process eliminates the redundancy that would otherwise double the encoding memory requirements while preserving the directionality and phase information benefits of complex transforms.
3Quantity of substance
If non-redundant complex wavelet transform is implemented, then encoding memory use is reduced, but implementation complexity increases
Solution Approach 1:
The patent segments the complex wavelet transform implementation into distinct stages: (1) performing the full complex wavelet transform to obtain both positive and negative frequency components, (2) identifying and discarding the redundant negative frequency components, and (3) processing and encoding only the essential positive frequency components. This segmentation simplifies the overall implementation by breaking down the complex operation into manageable steps.
Data Source
AI summary
A method of image compression with non-redundant complex wavelet transforms applied using a triband decomposition. Variant transforms for real and complex inputs allow for elimination of redundancy.