Reversible Overlap Operator for Lossless Image Compression
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Solution Overview
Problem
Current lapped transforms with linear phase have not been formulated for efficient lossless (reversible) compression of data, and existing reversible constructions are limited in their compression rate vs. distortion performance, particularly in digital picture compression where linear phase functions are required.
Innovation Solution
The development of efficient reversible lapped transforms using pre- and post-filters, referred to as overlap operators, which are realized through planar rotational transforms and unit determinant planar scaling transforms, enabling lossless image compression with improved computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If lapped biorthogonal transform (LBT) is used for image compression, then rate-distortion performance is improved, but lossless compression is not achievable because integer-reversible constructions were not known
Solution Approach 1:
The LBT is segmented into two separate transforms: a forward integer reversible LBT (IR-LBT) for encoding and an inverse IR-LBT for decoding. This segmentation allows each transform to be independently designed for reversibility while maintaining the overall compression performance of the original LBT.
Solution Approach 2:
The transform parameters are changed to enable integer arithmetic operations. Specifically, the LBT matrices are modified to have integer elements and unit determinants, allowing exact reversible transformation without floating-point rounding errors, thus achieving lossless compression.
2Stability of the object's composition
If modulated lapped transform (MLT) with orthogonal basis functions is used, then reversible constructions are available, but linear phase (symmetric) functions required for picture compression are not provided
Solution Approach 1:
The invention uses asymmetric integer reversible filter pairs (analysis and synthesis filters) to construct the IR-LBT. The analysis filter and synthesis filter are designed as asymmetric counterparts that work together to provide both linear phase properties and exact reversibility through integer arithmetic operations.
3Loss of information
If restricted pre and post filters are chosen for reversibility, then lossless compression is achieved, but compression performance (rate vs. distortion) is limited
Solution Approach 1:
The integer reversible overlap operator designed in this invention serves multiple functions simultaneously: it provides the pre-filtering operation, enables exact reversibility through integer arithmetic, maintains linear phase properties, and optimizes compression performance. This universal operator eliminates the need for separate specialized filters for each function.
4Object-affected harmful factors
If lapped transform with overlap operator is used, then blocking effect is reduced, but computational complexity increases
Solution Approach 1:
The overlapping operations in the lapped transform are merged into a single integer reversible overlap operator that combines the pre-filtering and overlap functions. This merging reduces the number of separate computational steps while maintaining the blocking effect reduction benefits of the lapped transform structure.
Data Source
AI summary
An efficient lapped transform is realized using pre- and post-filters (or reversible overlap operators) that are structured of unit determinant component matrices. The pre- and post-filters are realized as a succession of planar rotational transforms and unit determinant planar scaling transforms. The planar scaling transforms can be implemented using planar shears or lifting steps. Further, the planar rotations and planar shears have an implementation as reversible/lossless operations, giving as a result, a reversible overlap operator.