四维矩阵离散余弦变换的整数实现

Integer implementation of four-dimensional matrix DCT

根据四维矩阵离散余弦变换变换核的定义,可以将四维矩阵DCT的变换核降维看作二维矩阵。这些二维矩阵属于酉矩阵。并根据可逆整型变换矩阵分解的原理,首先计算四维矩阵离散余弦浮点变换的整数可逆分解,得到整数到整数的可逆变换矩阵。然后利用得到的分解矩阵对视频序列进行变换,最后将得到的系数用基于稳健统计的矢量量化方法进行量化编码。实验结果表明,在相同压缩比的情况下,整数到整数的四维矩阵离散余弦变换与浮点变换相比,恢复图像的PSNR有1 dB以上的提高,主观质量也有改善。

According to the definition of 4D matrix DCT, the transfer core matrix can be considered as two-dimensional unitary matrix. Float 4D-MDCT inversible factorization was conducted and integer to integer inversible transform metrix was obtained. Then this implementation of 4D-MDCT was applied to video sequnces and the integer trasform coefficients were quantized by the vector quantizer based on robust statistics. Experiment results indicate that the PSNR of the reconstructed image through this scheme improves more than ldB than that of the reconstructed image of float scheme and the subject quality of the image is also improved.