提出新型低复杂度16/32/64点DCT近似，性能优于已有方法。
Extensions on Low-complexity DCT Approximations for Larger Blocklengths Based on Minimal Angle Similarity
- 通过最小化精确与近似DCT矩阵行间夹角设计新近似。
- 在16/32/64点下均优于文献已知近似方法。
- 适合需要高效图像编码的场景，尤其关注计算成本。
离散余弦变换（DCT）是图像和视频编码的核心工具，因其与最优的卡尔亨尼-洛夫变换（KLT）相关，可有效保留变换系数并实现数据去相关。本文通过分别最小化精确DCT矩阵与近似变换矩阵行之间的夹角，提出了16、32和64点的低复杂度DCT近似。基于若干经典评价指标，所提变换在性能上超越了文献中已有的各类近似方法。同时，为这些低复杂度变换开发了快速算法，实现了性能与计算开销的良好平衡。实际图像编码应用表明，该方法在16、32和64点块长下的表现优于现有近似方案。
原文摘要 · Abstract (English)
The discrete cosine transform (DCT) is a central tool for image and video coding because it can be related to the Karhunen-Loève transform (KLT), which is the optimal transform in terms of retained transform coefficients and data decorrelation. In this paper, we introduce 16-, 32-, and 64-point low-complexity DCT approximations by minimizing individually the angle between the rows of the exact DCT matrix and the matrix induced by the approximate transforms. According to some classical figures of merit, the proposed transforms outperformed the approximations for the DCT already known in the literature. Fast algorithms were also developed for the low-complexity transforms, asserting a good balance between the performance and its computational cost. Practical applications in image encoding showed the relevance of the transforms in this context. In fact, the experiments showed that the proposed transforms had better results than the known approximations in the literature for the cases of 16, 32, and 64 blocklength.
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