Rotational transform for image and video compression

To improve video coding efficiency, the Rotational Transform (ROT) was proposed for adaptive switching between different transforms cores. The Karhunen Loeve Transform (KLT) is known to be optimal for given residual but requires much side information to be signaled to the decoder. The Discrete Cosine transform (DCT) is known to be close to optimal but for strongly directional components, it is sub-optimal. The main idea of ROT is that small modification of DCT coefficients can improve energy compaction. The ROT is implemented as a secondary transform applied after the primary DCT. The ROT matrix is sparse and thus enjoys relatively small computational complexity and memory usage increment. The encoder tries every rotational transform from the dictionary. Only one number, the ROT index, needs to be signaled to the decoder. Because the ROT is an orthogonal transform, encoder search is greatly simplified: distortion can be estimated in frequency domain and no inverse transformation is needed. This makes the ROT an efficient way to improve image/video compression. The ROT Coding gain for Intra slice is 2-3% in the HM 1.0 software implementation.