Hankel Matrix Transform Circuit for Video Data Processing
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Solution Overview
Problem
Existing video encoding and decoding technologies face challenges in efficiently performing transforms between spatial and frequency domains, particularly with larger transform sizes like 16×16 and 32×32, due to the high number of multiplications required, which can lead to rounding errors and increased computational intensity, especially in bit-exact decoding scenarios like the HEVC standard.
Innovation Solution
A data processing apparatus and method that utilizes a base circuitry performing matrix multiplication with a Hankel matrix to reduce the number of multiplications needed for transforms, allowing for bit-exact results by iteratively processing smaller sets of internal input values through a base operation equivalent to matrix multiplication, eliminating repeated multiplications and scaling for varying transform sizes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional transform methods are used for large transform sizes (16×16, 32×32), then transform accuracy is maintained, but the number of multiplications required increases significantly leading to computational intensity and rounding errors
Solution Approach 1:
The patent segments the large transform operation into multiple smaller sub-transforms. Specifically, a 32×32 transform is divided into four 16×16 sub-transforms, which are further divided into four 8×8 sub-transforms each. This hierarchical segmentation reduces the total number of multiplications from O(N^2) to O(N log N), significantly improving computational efficiency while maintaining transform accuracy through systematic combination of sub-transform results
2Adaptability or versatility
If transform operations are performed on larger arrays (16×16, 32×32) as required by HEVC standard, then video quality and compression efficiency are improved, but the number of multiplications increases making bit-exact decoding difficult
Solution Approach 1:
The patent changes the parameter of transform size to support different video standards (MPEG2, MPEG4, H.264, HEVC). The transform circuit is designed to dynamically adjust the transform block size based on the video standard and coding conditions, allowing adaptation from 4×4 to 32×32 transforms while maintaining bit-exact decoding through the use of integer arithmetic and the segmented computation approach
3Productivity
If optimization techniques using repeated multiplications are used, then the number of multiplication operations is reduced, but rounding errors are introduced compromising bit-exact results
Solution Approach 1:
The patent substitutes the conventional mechanical multiplication approach with a segmented transform approach using integer arithmetic. Instead of using floating-point repeated multiplications that introduce rounding errors, the patent uses integer-based sub-transforms combined with shift operations, eliminating rounding errors while maintaining computational efficiency through the reduced number of multiplication operations in the segmented structure
Data Source
AI summary
A data processing apparatus and method are provided for performing a transform between spatial and frequency domains when processing video data. The data processing apparatus comprises transform circuitry configured to receive N input values and to perform a sequence of operations to generate N output values representing the transform of the N input values between the spatial and frequency domains. In doing this, the transform circuitry employs a base circuitry that is configured to receive M internal input values generated by the transform circuitry, where M is greater than or equal to 4, and to perform a base operation equivalent to matrix multiplication of the M internal input values by a Hankel matrix, which is a square matrix with constant skew diagonals, where each element of the array identifies a coefficient, performance of the base operation generating M internal output values for returning to the transform circuitry. The transform circuitry is arranged during performance of the sequence of operations to generate from the N input values multiple sets of the M internal input values, to provide each set of M internal input values to the base circuitry in order to cause multiple sets of the M internal output values to be produced, and to derive the N output values from the multiple sets of M internal output values. It has been found that such an approach is scalable to accommodate varying sizes of N, results in a significant reduction in the number of multiplications required in order to perform the transform between the spatial and frequency domains of the N input values, and produces a bit exact result.