Integer Matrix Transform for Video Compression
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Solution Overview
Problem
Conventional video compression systems face limitations in achieving a balance between vector length, block size, transform element size, and inner product norms, leading to inaccuracies and complexity in real-time video transmission.
Innovation Solution
The use of a transform matrix with integer elements for encoding and decoding video images, specifically designed to maintain orthogonality and similar norms across vectors, which allows for efficient data transformation and inverse transformation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional real-number transform matrices are used, then transform accuracy is maintained, but computational complexity and processing time increase
Solution Approach 1:
The patent changes the parameter type of transform matrix elements from real numbers to integers. This parameter change enables the use of integer arithmetic operations (addition, subtraction, multiplication by small constants) instead of complex floating-point operations, significantly reducing computational complexity while maintaining sufficient transform accuracy for video compression applications.
Solution Approach 2:
The patent employs a simplified integer transform matrix design that prioritizes computational efficiency over mathematical perfection. The integer matrix uses smaller, simpler numbers that can be processed quickly with standard hardware arithmetic, accepting that the transform is an approximation rather than an exact mathematical operation, thereby using 'cheap' computational resources effectively.
2Productivity
If larger block sizes are used, then compression efficiency improves, but transform element size and inner product norms become unbalanced
Solution Approach 1:
The patent segments the transform matrix into structured components with specific patterns. The integer transform matrix is designed with a block structure where elements follow predictable patterns (e.g., symmetric arrangements, repeated values), allowing the system to handle larger block sizes while maintaining element balance through this segmented design approach.
Solution Approach 2:
The patent applies different integer values to different positions in the transform matrix based on local requirements. The matrix design assigns specific integer constants to positions where they are needed to maintain orthogonality and norm balance, while using simpler values elsewhere, thereby achieving local optimization of transform quality across the entire matrix.
3Device complexity
If integer transform matrices are used, then computational complexity reduces, but orthogonality and norm similarity must be carefully maintained
Solution Approach 1:
The patent designs the integer transform matrix so that all rows (and columns) have equal norm, creating an equipotential structure. This is achieved by ensuring each row contains the same set of integer values with appropriate signs, making the matrix close to orthogonal while maintaining integer constraints. This equipotential design simplifies the maintenance of orthogonality properties.
Solution Approach 2:
The patent introduces controlled asymmetry in the integer matrix through sign variations. While the absolute values follow symmetric patterns, the signs are strategically varied to achieve the desired orthogonality properties. This asymmetric sign pattern allows the matrix to maintain integer simplicity while satisfying the reliability requirements of orthogonality and norm consistency.
Data Source
AI summary
A video decoding method, system and computer program product perform inverse transforming of transform coefficients for a video image. The inverse transforming is performed with a processing circuit on a first block of transform coefficients by a transform matrix having a plurality of vectors. The coefficients are transformed into a corresponding second block of residual pixel values for the video image. The transform matrix consists of integer elements, and includes a 4 point transform as whole or partial vectors of the transform matrix. The first row of the 4 point transform includes elements a a a a. The second row includes b c −c −b. The third row includes a −a −a a. The fourth row includes c −b b −c, wherein a, b and c comply with |b2+c2−(a2+a2)|/(a2+a2)<0.003, b/c being in an inclusive range of 2.1 through 2.4, and each of a, b and c being integer.