四阶张量分解在视频压缩领域的应用

Application of fourth-order tensor decomposition in video compression

根据张量概念及其基本运算,构建出新的四阶张量乘法、张量模乘、一些特殊的四阶张量.并基于块循环三阶张量的离散傅里叶变换提出新的四阶张量奇异值分解,理论证明该分解具有很好的稀疏性和保范性.通过对人工数据和视频数据进行压缩试验,验证了在保留视频结构完整性的同时,四阶张量分解算法的有效性和可行性.

Based on the concept of tensor and its basic operations,the new fourth-order tensor multiplication,tensor module multiplication and some special fourth-order tensors are constructed.Also,a fourth-order tensor singular value decomposition based on the DFT of the block circulant third-order tensor is generated.The theory proves that the algorithm has good sparseness and norm-preserving ability.Through the compression test of artificial example and video data,the results prove the effectiveness and feasibility of the fourth-order tensor decomposition algorithm,while at the same time maintain the structural integrity of the video tensor.