# Local SVD-Entropy Maps as a Complementary Structural Representation for Full-Reference and No-Reference Image Quality Assessment

arXiv: https://arxiv.org/abs/2609.27959 · HTML: https://mlsanity.com/paper/2609.27959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 23 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [KonIQ-10k: An ecologically valid database for deep learning of blind image quality assessment](https://mlsanity.com/paper/1910.06180/) (2019)
- [Blind Image Quality Assessment Using A Deep Bilinear Convolutional Neural Network](https://mlsanity.com/paper/1907.02665/) (2019)
- [PIPAL: a Large-Scale Image Quality Assessment Dataset for Perceptual Image Restoration](https://mlsanity.com/paper/2007.12142/) (2020)
- [Mean Deviation Similarity Index: Efficient and Reliable Full-Reference Image Quality Evaluator](https://mlsanity.com/paper/1608.07433/) (2016)
- [A Hitchhiker's Guide to Structural Similarity](https://mlsanity.com/paper/2101.06354/) (2021)
- [Exploring Rich Subjective Quality Information for Image Quality Assessment in the Wild](https://mlsanity.com/paper/2409.05540/) (2024)
- [Opinion-Unaware Blind Image Quality Assessment using Multi-Scale Deep Feature Statistics](https://mlsanity.com/paper/2405.18790/) (2024)
- [Subjective Image Quality Assessment with Boosted Triplet Comparisons](https://mlsanity.com/paper/2108.00201/) (2021)
- [No-Reference Color Image Quality Assessment: From Entropy to Perceptual Quality](https://mlsanity.com/paper/1812.10695/) (2018)
- [Deep Shape-Texture Statistics for Completely Blind Image Quality Evaluation](https://mlsanity.com/paper/2401.08107/) (2024)
- [Entropy Approximation by Machine Learning Regression: Application for Irregularity Evaluation of Images in Remote Sensing](https://mlsanity.com/paper/2210.06901/) (2022)
- [Intensity-Sensitive Similarity Indexes for Image Quality Assessment](https://mlsanity.com/paper/2206.11207/) (2022)

## Abstract (arXiv)

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 3×3-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 90circ 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.