本文提出一种实数运算的快速确定性算法，用于从已知上界M≥m的短支持向量x的DCT-II反变换重建，时间复杂度为O(M log M + m log₂(N/M))，且不采用逆FFT恢复x。
摘要：
本文提出了一种新的快速且确定性的算法，用于类型II离散余弦变换的反变换，以从已知上界M≥m的短支持长度m的向量x∈R^N（N=2^J）的离散余弦变换x^II^_hat进行重建。所提出的算法仅使用实数运算，其运行时间为O(M log M + m log₂(N/M))，并需要O(M + m log₂(N/M))个x^II^_hat的样本。当m,M趋近于N时，其运行时间和采样要求接近常规IDCT-II对于全支持向量的性能。本文所提出的算法不采用逆FFT算法来恢复x。
英文摘要：
In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II for reconstructing the input vector $\mathbf x\in\mathbb R^N$, $N=2^J$, with short support of length $m$ from its discrete cosine transform $\mathbf x^{\widehat{\mathrm{II}}}=C^{\mathrm{II}}_N\mathbf x$ if an upper bound $M\geq m$ is known. The resulting algorithm only uses real arithmetic, has a runtime of $\mathcal{O}\left(M\log M+m\log_2\frac{N}{M}\right)$ and requires $\mathcal{O}\left(M+m\log_2\frac{N}{M}\right)$ samples of $\mathbf x^{\widehat{\mathrm{II}}}$. For $m,M\rightarrow N$ the runtime and sampling requirements approach those of a regular IDCT-II for vectors with full support. The algorithm presented hereafter does not employ inverse FFT algorithms to recover $\mathbf x$.
Extensions on Low-complexity DCT Approximations for Larger Blocklengths Based on Minimal Angle Similarity
Programa de Pós-Graduação em Estatística, Universidade Federal de Pernambuco（统计硕士课程，巴伊亚联邦大学）；Universidade Federal de Santa Maria（圣玛丽亚联邦大学）；Universidade Federal de Pernambuco (UFPE)（巴伊亚联邦大学（UFPE））；Departamento de Estatística and LACESM, Universidade Federal de Santa Maria（统计系和LACESM，圣玛丽亚联邦大学）；Industrial Signal Processing Laboratory, Departamento de Tecnologia, UFPE（工业信号处理实验室，技术系，UFPE）
Research Center for Logic, Optimization and Security (LOS)（逻辑、优化与安全研究中心（LOS））；Faculty of Mathematics and Computer Science, University of Bucharest（布加勒斯特大学数学与计算机科学学院）
