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首页> 外文期刊>WSEAS Transactions on Signal Processing >Complexity Evaluation of Tensor Decomposition through 3D Inverse Spectrum Pyramid in respect of Deterministic Orthogonal Transforms
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Complexity Evaluation of Tensor Decomposition through 3D Inverse Spectrum Pyramid in respect of Deterministic Orthogonal Transforms

机译：确定性正交变换中三维逆谱金字塔的张量分解的复杂性评价

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摘要

Recently, orthogonal 3D tensor decompositions are widely involved in the processing of various kinds of 3D data such as multimedia signals, correlated image sequences, etc. The methods for tensor decomposition could be divided into two main groups: statistical, based on various modifications of the Principal Component Analysis and the Singular Value Decomposition, and deterministic, based on the pyramidal 3D Discrete Wavelet Transform decompositions, Curvelet/Contourlet Discrete Transform and the Shearlet Discrete Transform. The methods from the first group surpass these from the second in the higher decorrelation of the decomposition components, but these from the second group have much lower computational complexity. In this work are compared the structures and is evaluated the computational complexity of the tensor decompositions, mentioned above, with the decomposition developed by the authors, which is based on the Reduced 3D Inverse Spectrum Pyramid (3D-RISP). The comparison results show that: the global computational complexity of the 3D-RISP is much lower than that of the remaining pyramidal decompositions; the compared schemes for recursive calculation have similar structures but this of the RISP does not need operations of the kind decimation and interpolation which are the reason for distortions in the reconstructed tensors.
机译：最近，正交的3D张量分解广泛涉及处理各种3D数据的处理，例如多媒体信号，相关图像序列等。张量分解的方法可以分为两个主要组：统计，基于各种修改主成分分析和奇异值分解，并基于金字塔3D离散小波变换分解，Curvelet / Contourlet离散变换和Shearlet离散变换。来自第一组的方法在分解组分的较高去相关性的第二次中超过了这些方法，但是从第二组的计算复杂性具有更低的较低。在该工作中，将结构进行比较，并评估上面提到的张量分解的计算复杂性，其中由作者开发的分解，这是基于减少的3D逆谱金字塔（3D-RISP）。比较结果表明：3D-RISP的全局计算复杂性远低于剩余的金字塔分解;用于递归计算的比较方案具有类似的结构，但是该RISP中的这种不需要种类抽取和插值的操作，这是重建张量的扭曲的原因。

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