发表机构
Institute of Physics and Technology, Petrozavodsk State University（彼得罗扎沃茨克国立大学物理技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于局部SVD熵的HSVD图作为IQA补充结构表示，与SSIM结合提升全参考（SRCC 0.618→0.659）和无参考（0.528→0.575）性能，且无需原始参考。
AI 中文摘要
我们研究了一种基于直接从二维图像块计算的奇异值香农熵的局部谱复杂度表示，用于感知图像质量评估（IQA）。对于每个$3\times3$像素灰度块，直接应用SVD，归一化奇异值熵定义了一个HSVD图值。该构造既不需要展平也不需要延迟嵌入，不使用边界填充，并且在局部描述符级别对$90^{\circ}$旋转和镜像反射不变。在Lena上进行的分层椒盐噪声实验将绝对相似性与干净参考区分开来，并区分了对额外退化步骤的敏感性。HSVD-SSIM对局部损坏响应更强，并在严重噪声水平下保留更大的相邻状态响应。对所有10,125张失真的KADID-10k图像的验证表明，作为独立的全参考指标，HSVD-SSIM弱于传统SSIM（SRCC $0.450$ vs. $0.619$），但与其结合时具有互补性：分组交叉验证将SRCC从$0.618$提高到$0.659$，增益的bootstrap 95%置信区间为$[0.036,0.046]$。在无参考实验中，添加HSVD派生的单图像描述符将最佳非线性模型从SRCC $0.528$提高到$0.575$（95% CI $[0.033,0.061]$），并改善了相邻失真状态之间质量变化的预测。这些结果支持直接局部SVD熵作为可解释的结构通道，补充了传统的图像域相似性，并在没有原始参考的情况下仍具有信息量。
英文摘要
We investigate a local spectral-complexity representation for perceptual image quality assessment (IQA) based on Shannon entropy of singular values computed directly from two-dimensional image patches. For each $3\times3$-pixel grayscale patch, SVD is applied directly and the normalized singular-value entropy defines one HSVD-map value. The construction requires neither flattening nor delay embedding, uses no boundary padding, and is invariant to $90^{\circ}$ rotations and mirror reflections at the local-descriptor level. A nested salt-and-pepper experiment on Lena separates absolute similarity to a clean reference from sensitivity to an additional degradation step. HSVD-SSIM responds more strongly to local corruption and retains a larger neighboring-state response at severe noise levels. Validation on all 10,125 distorted KADID-10k images shows that HSVD-SSIM is weaker than conventional SSIM as a standalone full-reference metric (SRCC $0.450$ vs. $0.619$), but complementary when combined with it: grouped cross-validation increases SRCC from $0.618$ to $0.659$, with a bootstrap 95\% confidence interval of $[0.036,0.046]$ for the gain. In a no-reference experiment, adding HSVD-derived single-image descriptors improves the best nonlinear model from SRCC $0.528$ to $0.575$ (95\% CI $[0.033,0.061]$) and also improves prediction of quality changes between neighboring distortion states. These results support direct local SVD entropy as an interpretable structural channel that complements conventional image-domain similarity and remains informative without a pristine reference.
Comments24 pages, 8 figures, 7 tables, 48 references
