Low Complexity Secondary Transform for Video Compression
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Solution Overview
Problem
Existing image and video encoders face high computational complexity due to the use of secondary transforms like rotational transforms, which are not optimized for orthogonality, leading to sub-optimal quantization performance and increased energy consumption.
Innovation Solution
A low-complexity, almost-orthogonal secondary transform using a rotational transform matrix is implemented, which maximizes orthogonality and reduces computational complexity by factorizing Given's rotation matrices into lifting matrices, approximating parameters as rationals to minimize the number of elemental adders required for multiplication.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a rotational transform matrix is used for secondary transform, then quantization performance is improved, but computational complexity increases
Solution Approach 1:
The rotational transform matrix is segmented into multiple lifting matrices that can be applied sequentially. Instead of computing one large rotational transform, the transform is divided into smaller lifting steps, each operating on specific coefficient groups, thereby reducing per-step complexity while maintaining overall quantization performance.
Solution Approach 2:
The transform parameters are changed by selecting specific lifting matrix configurations and rotation angles that optimize the balance between orthogonality (for quantization performance) and computational simplicity. The lifting factorization allows parameters to be tuned for minimal complexity while preserving essential transform properties.
2Device complexity
If Given's rotation matrices are factorized into lifting matrices, then the number of elemental adders is reduced, but transform accuracy may be compromised
Solution Approach 1:
The lifting matrices are designed to replicate the essential functionality of Given's rotation matrices through approximation. By copying the structural properties and orthogonal characteristics of the original rotation matrices in a simplified lifting form, the transform accuracy is preserved while using fewer computational elements.
Solution Approach 2:
Simplified lifting matrices with fewer elemental adders are used as approximate replacements for the full Given's rotation matrices. These simplified transforms achieve sufficient accuracy for compression applications without requiring the complete computational resources of the original rotation matrices.
3Device complexity
If approximation of parameters as rationals is used, then multiplication complexity is minimized, but orthogonality degree is reduced
Solution Approach 1:
Transform parameters are changed from exact irrational values to rational approximations that facilitate simple multiplication operations. The lifting matrix parameters are selected as rational numbers that closely approximate the optimal rotation angles, enabling efficient hardware implementation while maintaining sufficient orthogonality for effective compression.
Data Source
AI summary
A method for encoding video or images includes receiving input data associated with a block within a video or image frame and performing a transform of the input data to produce a first set of output coefficients. The method also includes receiving the first set of output coefficients and performing a second transform to produce a second set of output coefficients. The method further includes quantizing the second set of output coefficients. The second transform is performed using a rotational transform matrix that is selected to maximize a degree of orthogonality of the rotational transform matrix.