IEEE Trans Image Process. 2017 May;26(5):2296-2310. doi: 10.1109/TIP.2017.2679442. Epub 2017 Mar 8.
In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. 3D DCT approximations are formalized in terms of high-order tensor theory. The formulation is extended to higher dimensions with arbitrary lengths. Several multiplierless 8×8 ×8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case. The proposed methods complexity cost was assessed, presenting considerably lower arithmetic operations when compared with the exact 3D DCT. The proposed approximations were embedded into 3D DCT-based video coding scheme and a modified quantization step was introduced. The simulation results showed that the approximate 3D DCT coding methods offer almost identical output visual quality when compared with exact 3D DCT scheme. The proposed 3D approximations were also employed as a tool for visual tracking. The approximate 3D DCT-based proposed system performs similarly to the original exact 3D DCT-based method. In general, the suggested methods showed competitive performance at a considerably lower computational cost.
在本文中，我们介绍了低复杂度多维离散余弦变换（DCT）逼近方法。3D DCT 逼近方法通过高阶张量理论来形式化。该方法可以扩展到任意长度的更高维度。提出了几种无乘法器的 8×8×8 近似方法，并讨论了一般多维情况下的计算复杂度。评估了所提出方法的复杂度成本，与精确的 3D DCT 相比，其计算复杂度明显更低。所提出的近似方法被嵌入到基于 3D DCT 的视频编码方案中，并引入了修改的量化步长。仿真结果表明，与精确的 3D DCT 方案相比，基于近似 3D DCT 的编码方法提供了几乎相同的输出视觉质量。所提出的 3D 近似方法也被用作视觉跟踪的工具。基于近似 3D DCT 的提出系统的性能与原始基于精确 3D DCT 的方法相似。总的来说，所提出的方法在计算成本显著降低的情况下表现出了竞争力。
