LLM Integer Cosine Transform and its Fast Algorithm

Existing video coding standards use only 4 × 4 and 8 × 8 transforms for energy compaction. Recent research has found that the use of larger transforms, such as 16 × 16, together with the existing transforms can improve coding performance especially in high-definition (HD) videos which are becoming more and more common. This raises the interest of seeking high-performance higher-order transforms with low computation requirement. In this paper, a method to derive orthogonal integer cosine transforms is proposed. The order-2N transform is defined using the order-N transform. A family of these integer transforms, Loeffler, Ligtenberg, and Moschytz (LLM) integer cosine transform, is derived using this method. Its fast algorithm structure is the same as LLM fast discrete cosine transform (DCT) algorithm but requires integer operations only. This new family of transforms is not only very close to the DCT but also has excellent coding performance.