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

Andrei Velichko; Petr Boriskov

eess.IVAug 23, 2026

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

Authors: Andrei Velichko, Petr Boriskov

Organizations: Institute of Physics and Technology, Petrozavodsk State University, 185910 Petrozavodsk, Russia

Abstract

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.

Figures & tables

Approach	Representation or cues	Main idea	Relation to the present work
SSIM / MS-SSIM [ 41 , 43 ]	Local luminance, contrast, structure; multiple scales	Direct structural comparison in the image domain	Baseline structural similarity used throughout the FR experiments
Complementary FR-IQA [ 47 , 25 , 8 ]	Gradient, phase, color, structure, texture, learned features	Combine complementary perceptual cues	Establishes complementarity as a valid alternative to “replacement” claims
Pairwise / restoration quality [ 21 , 11 ]	Relative human judgments; restoration-specific artifacts	Resolve small quality differences and complex restoration degradations	Motivates separate analysis of absolute quality and state-to-state sensitivity
Entropy-based IQA [ 17 , 6 ]	Spatial, spectral, and local entropy	Describe irregularity and local complexity rather than only pixel fidelity	Motivates entropy as an IQA-relevant representation
Earlier 2-D entropy maps [ 37 ]	Circular 2-D kernel $\rightarrow$ ordered 1-D sequence $\rightarrow$ entropy	Build spatial irregularity maps with rotation-stable traversal	Direct methodological precursor; the present method removes traversal and embedding
SVD-based IQA / patch analysis [ 19 , 28 , 39 ]	Singular-value and patch-structure descriptors	Use local or global matrix structure for distortion analysis	Supports singular values as structural features but not the same local HSVD-map construction

Table 1: Representative literature lines motivating the present work and their relation to the proposed HSVD representation.

Figure 1: Direct visualization of the HSVD representation for the clean Lena image and the first nested-noise level ( $5\%$ ). The two HSVD maps are shown on the same fixed $[0,1]$ scale and were not independently rescaled for display. The $5\%$ level is used because it is the first level in the experimental sequence.

Panel of Figure 2 — Figure 2: Representative stages of the nested salt-and-pepper-noise experiment. Every higher noise level contains all corrupted pixels from the preceding level plus newly corrupted pixels.

Figure 3: Similarity to the clean Lena reference as nested salt-and-pepper density increases. Conventional image-domain SSIM decreases more gradually, whereas HSVD-SSIM reacts more strongly to early local corruption.

Figure 4: SSIM between consecutive nested-noise states. Image-domain SSIM approaches saturation near one in the high-noise regime, while HSVD-SSIM retains a substantially larger response to each additional $5\%$ corruption step.

Noise (%)	SSIM-clean	HSVD-clean	SSIM-neighbor	HSVD-neighbor
5	0.3341	0.1372	0.3341	0.1372
20	0.0945	0.0323	0.8532	0.7570
50	0.0312	0.0134	0.9439	0.8172
80	0.0112	0.0070	0.9637	0.8726
100	0.0037	0.0044	0.9700	0.9019

Table 2: Selected values from the Lena experiment. “Clean” denotes similarity to the original image; “neighbor” denotes similarity to the immediately preceding noise level.

Metric	SRCC	PLCC	Kendall
Image-domain SSIM	0.6189	0.5759	0.4470
HSVD-SSIM	0.4504	0.4377	0.3153

Table 3: Standalone full-reference correlation with KADID-10k subjective quality.

Metric change	SRCC	PLCC	Kendall
Image-domain $1-SSIM$	0.1115	-0.0041	0.0720
HSVD-domain $1-SSIM$	0.1338	0.0683	0.0866

Table 4: KADID neighboring-level correlation with the magnitude of subjective change

|\Delta DMOS|

. Metric change is

1-SSIM

between adjacent distorted states.

Panel of Figure 5 — Figure 5: Illustrative KADID-10k examples with nearly matched conventional SSIM but substantially different subjective quality. Top row: $SSIM_{A}=0.934090$ , $SSIM_{B}=0.934098$ , while $HSVD_{A}=0.6695$ and $HSVD_{B}=0.9036$ . Bottom row: $SSIM_{A}=0.933774$ , $SSIM_{B}=0.933802$ , while $HSVD_{A}=0.5785$ and $HSVD_{B}=0.8411$ . These examples illustrate complementarity and were selected post hoc; statistical conclusions are based on the full benchmark.

Model	SRCC	PLCC	Kendall	RMSE	MAE	$R^{2}$
SSIM only	0.6175	0.5752	0.4455	0.8856	0.7601	0.3308
HSVD only	0.4492	0.4369	0.3142	0.9738	0.8394	0.1909
SSIM + HSVD	0.6590	0.5796	0.4744	0.8823	0.7582	0.3359

Table 5: Full-reference DMOS prediction under 10

\times

5-fold grouped cross-validation by reference image.

Figure 6: Repeated grouped cross-validation for full-reference DMOS prediction. Adding HSVD-SSIM to conventional SSIM consistently improves rank correlation on held-out reference images.

Regressor	Features	SRCC	PLCC	Kendall	RMSE	MAE	$R^{2}$
HGB	Image	0.5277	0.5643	0.3727	0.9182	0.7483	0.2807
HGB	HSVD	0.5157	0.5593	0.3627	0.9019	0.7397	0.3059
HGB	Combined	0.5748	0.6067	0.4109	0.8826	0.7075	0.3353
Ridge	Image	0.4157	0.4220	0.2858	0.9859	0.8368	0.1708
Ridge	HSVD	0.4116	0.4554	0.2856	0.9640	0.8180	0.2071
Ridge	Combined	0.4884	0.5181	0.3409	0.9301	0.7748	0.2619

Table 6: No-reference absolute DMOS prediction under 5

\times

5-fold grouped cross-validation by reference image. No pristine image, distortion identity, distortion type, or level is used as a predictive feature.

Panel of Figure 7 — Figure 7: No-reference performance. Left: absolute-quality rank correlation for Image-only, HSVD-only, and Combined feature sets. Right: accuracy of the quality ordering between adjacent states derived from independently predicted out-of-fold DMOS values.

Figure 8: True versus out-of-fold predicted DMOS for the HGB Combined no-reference model. Predictions exhibit noticeable regression toward the center of the quality range, highlighting the remaining difficulty of absolute no-reference quality estimation.

Observation	Supported interpretation	Does not imply
HSVD falls faster than SSIM relative to clean Lena	Strong response to widespread local structural perturbation	Better absolute perceptual-quality prediction
HSVD retains larger response between heavily degraded neighbors	Greater incremental structural sensitivity in that regime	Accurate prediction of $\|\Delta DMOS\|$ by similarity alone
Standalone HSVD $<$ standalone SSIM on KADID	Local spectral complexity is insufficient as a universal FR quality variable	HSVD contains no useful quality information
SSIM+HSVD $>$ SSIM in grouped CV	HSVD contains residual information complementary to SSIM	The two scores are statistically independent quality axes
Image+HSVD $>$ Image-only in NR prediction	HSVD contains reference-free quality-related information	State-of-the-art blind IQA performance

Table 7: Interpretation of the main empirical observations. The third column states conclusions that should not be inferred from the corresponding result.

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