High-Precision 4×4 DST7 and DCT8 Matrices for Fast Video Transforms
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Solution Overview
Problem
Existing video coding technologies face challenges in maintaining fast transform implementations as precision increases, as the mathematical properties of integer transform matrices used in moderate precision do not necessarily hold for higher precisions, leading to increased complexity.
Innovation Solution
Modifying the integer coefficients of 4×4 DST7 and DCT8 transform matrices by adjusting one value to ensure that the sum of two values equals a third value, allowing for fast implementations at higher precisions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If integer transform matrices are used with higher precision to improve compression efficiency, then compression performance is improved, but computational complexity increases and fast implementation properties are lost
Solution Approach 1:
The patent modifies the integer coefficients of the transform matrix by changing specific parameter values to satisfy the fast implementation condition (a+b=d). This allows higher precision transform (using 16-bit integers instead of 32-bit) while maintaining the computational efficiency of fast implementation algorithms.
Solution Approach 2:
The patent applies local modification to specific coefficients in the transform matrix rather than changing all coefficients. By selectively adjusting certain integer values (a, b, c, d) to satisfy the fast implementation property, it maintains overall transform accuracy while enabling fast computation.
2Productivity
If integer coefficients are modified to maintain fast implementation properties, then computational efficiency is preserved, but transform accuracy may be compromised
Solution Approach 1:
The patent carefully selects parameter modifications that maintain the fast implementation property (a+b=d) while minimizing impact on transform accuracy. The modified integer coefficients are chosen to closely approximate the original floating-point values, ensuring both computational efficiency and transform precision are maintained.
Data Source
AI summary
A method for reconstructing a block of a picture comprising: applying an inverse transform to a block of transform coefficients using a first matrix of integer coefficients representative of the inverse transform, wherein the first matrix of integer coefficients is the inverse of a second matrix of integer coefficients representative of a transform inverted to obtain the inverse transform, the second matrix of integer coefficients being derived from a third matrix of integer coefficients, the absolute values of the integer coefficients of the third matrix taking their values in a set of four different values, the derivation comprising a modification of one value of the set to ensure that a sum of two values of the set equals a third value of the set.