用Weyl-Heisenberg变换替代JPEG的DCT，提升压缩效率。
Weyl-Heisenberg Transform Capabilities in JPEG Compression Standard
- 用二维离散正交Weyl-Heisenberg变换替代DCT，保持块结构。
- 实验表明新算法压缩效率优于传统JPEG标准。
- 适合图像压缩优化研究者参考。
本文致力于开发一种基于Weyl-Heisenberg基（WH-技术）的新压缩技术，用于改进JPEG压缩标准并提升其性能。分析了JPEG算法的主要阶段，指出了限制其效率进一步提升的关键问题。为克服这些局限，提出在变换编码阶段使用实数形式的二维离散正交Weyl-Heisenberg变换（DWHT），替代原有的离散余弦变换（DCT）。与DCT不同，DWHT具有初始块结构，基于最优信号基构建，其函数在时域和频域均正交且局域性好。这一特性使得变换后图像每个块内的元素值能更高效地去相关，从而在后续量化和信息编码阶段更有效地筛选出不显著分量。基于此，提出了新的JPEG压缩算法，并建立了评估压缩效率与质量损失的便捷指标。实验结果证实，所提算法相比传统JPEG标准具有更高的压缩效率。
原文摘要 · Abstract (English)
This paper is devoted to the development and research of a new compression technology based on Weyl-Heisenberg bases (WH-technology) for modifying the JPEG compression standard and improving its characteristics. For this purpose, the paper analyzes the main stages of the JPEG compression algorithm, notes its key features and problems that limit further enhancement of its efficiency. To overcome these limitations, it is proposed to use the real version of the two-dimensional discrete orthogonal Weyl-Heisenberg transform (DWHT) instead of the discrete cosine transform (DCT) at the stage of transformation coding. This transformation, unlike DCT, initially has a block structure and is built on the basis of the Weyl-Heisenberg optimal signal basis, the functions of which are orthogonal and well localized both in the frequency and time domains. This feature of DWHT allows for more efficient decorrelation and compression of element values in each block of the image after transformation coding. As a result, it is possible to obtain more efficient selection and screening of insignificant elements at the subsequent stages of quantization and information coding. Based on DWHT, a new version of the JPEG compression algorithm was developed, and convenient criteria for evaluating the compression efficiency and metrics of quality losses were proposed. The results of an experimental study are presented, confirming the higher compression efficiency of the proposed algorithm in comparison with the JPEG compression standard.
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