This work introduces the three-dimensional steerable discrete cosine transform (3D-SDCT), which is obtained from the relationship between the discrete cosine transform (DCT) and the graph Fourier transform of a signal on a path graph. One employs the fact that the basis vectors of the 3D-DCT constitute a possible eigenbasis for the Laplacian of the product of such graphs. The proposed transform employs a rotated version of the 3D-DCT basis. We then evaluate the applicability of the 3D-SDCT in the field of 3D medical image compression. We consider the case where we have only one pair of rotation angles per block, rotating all the 3D-DCT basis vectors by the same pair. The obtained results show that the 3D-SDCT can be efficiently used in the referred application scenario and it outperforms the classical 3D-DCT.

中文翻译：

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3D 可控离散余弦变换在 3D 图像压缩中的应用

这项工作介绍了三维可控离散余弦变换（3D-SDCT），它是从离散余弦变换（DCT）和路径图上的信号的图傅立叶变换之间的关系中获得的。一个人利用这样一个事实，即 3D-DCT 的基向量构成了这些图的乘积的拉普拉斯算子的可能特征基础。提议的变换采用了 3D-DCT 基础的旋转版本。然后我们评估 3D-SDCT 在 3D 医学图像压缩领域的适用性。我们考虑每个块只有一对旋转角度的情况，将所有 3D-DCT 基向量旋转同一对。获得的结果表明，3D-SDCT 可以有效地用于引用的应用场景，并且优于经典的 3D-DCT。