Low Complexity Large Transform for Video Coding
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The implementation of large block size discrete cosine transforms in video coding standards like HEVC increases complexity significantly, leading to feasibility issues due to high computational requirements.
Innovation Solution
A low complexity large transform method is introduced, combining Hadamard transforms with discrete cosine transforms (DCT) and inverse DCT (IDCT) to reduce computational complexity, using (n/m) m×m Hadamard transforms and (m*m) (n/m)×(n/m) DCT/IDCT, where m<n, to generate and reconstruct n×n transform coefficient blocks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If large block size transforms (16×16, 32×32, 64×64 DCT) are used, then coding efficiency is improved, but implementation complexity increases significantly
Solution Approach 1:
The patent segments the large n×n transform into smaller m×m Hadamard transforms and (n/m)×(n/m) DCTs. For example, a 16×16 transform is divided into four 4×4 Hadamard transforms and sixteen 2×2 DCTs, reducing computational complexity while maintaining transform effectiveness.
Solution Approach 2:
The patent creates a composite transform method by combining Hadamard transforms and DCTs. This hybrid approach uses the properties of both transform types to achieve the benefits of large block transforms with reduced computational requirements, effectively creating a new transform methodology.
2Measurement precision
If direct matrix multiplication is used for large transforms, then transform accuracy is maintained, but computational complexity increases exponentially
Solution Approach 1:
The patent breaks down the direct matrix multiplication into sequential stages of smaller transforms. Instead of computing one large n×n matrix multiplication, the method performs multiple smaller m×m Hadamard transforms followed by (n/m)×(n/m) DCTs, dramatically reducing the number of multiplications required.
Solution Approach 2:
The patent applies Hadamard transforms as a preliminary step before applying DCTs. This preliminary action pre-processes the input data in a way that simplifies the subsequent DCT computation, reducing the overall computational burden while preserving transform accuracy.
3Productivity
If fast algorithms are used for transforms, then computational speed is improved, but complexity still increases with block size
Solution Approach 1:
The patent segments the transform computation into manageable stages using fast Hadamard transforms and fast DCT algorithms. By dividing the large transform into smaller independent transforms, the method achieves O(N log N) complexity growth rather than O(N³), improving scalability with block size.
Solution Approach 2:
The patent combines fast Hadamard transform algorithms with fast DCT algorithms to create a composite fast transform method. This combination leverages the efficiency of both algorithm types to achieve high computational speed while keeping the complexity growth manageable as block size increases.
Data Source
AI summary
Methods of encoding a video stream in a video encoder and decoding an encoded video stream in a video decoder using a low complexity large transform are provided. An encoding method includes receiving an n×n residual block in a transform component of the video encoder, and transforming the n×n residual block using an n×n transform to generate an n×n transform coefficient block, wherein the n×n transform is based on (n/m*n/m) m×m Hadamard transforms and (m*m) (n/m)×(n/m) discrete cosine transforms, wherein m<n. A decoding method includes receiving an n×n transform coefficient block in an inverse transform component of the video decoder, and applying an n×n inverse transform to the n×n transform coefficient block to reconstruct an n×n residual block, wherein the n×n inverse transform is based on (n/m*n/m) m×m Hadamard transforms and (m*m) (n/m)×(n/m) inverse discrete cosine transforms, wherein m<n.