SymKL: A Unified Representation-Space Measure of Signal Degradation

Dhananjaya Jayasundara; Sudarshan Rajagopalan; Vishal M. Patel

cs.CVOct 29, 2026

SymKL: A Unified Representation-Space Measure of Signal Degradation

Authors: Dhananjaya Jayasundara, Sudarshan Rajagopalan, Vishal M. Patel

Organizations: Johns Hopkins University.

Abstract

Quantifying degradation between a pristine signal and its degraded observation is fundamental to signal processing, yet existing full-reference measures are inherently modality-specific. We introduce SymKL, a unified full-reference degradation measure based on implicit neural representations (INRs). An INR is fitted once to the pristine reference and characterized by its diagonal Fisher information, which captures the local information geometry of the learned representation. Evaluating the Fisher information with the pristine reference and a degraded observation yields two parameter-sensitivity profiles whose symmetric KL divergence defines the degradation score. The proposed formulation requires only the reference and degraded observation, without knowledge of the corruption process or degradation severity, making it applicable across images, audio, and 3D data. We further derive an exact closed-form expression for the diagonal Fisher of SIREN, enabling efficient computation. Experiments on image, speech, and volumetric 3D benchmarks demonstrate that SymKL accurately tracks degradation severity, remains monotonic where conventional metrics saturate or fail, and provides a unified modality-agnostic measure of signal degradation. Code will be made publicly available after the review process.

Figures & tables

Figure 1: Conceptual comparison between existing degradation measures and the proposed SymKL . Existing approaches rely on modality-specific measures, requiring separate metrics for images, audio, and 3D data. In contrast, SymKL represents signals using an INR and characterizes degradation through Fisher information geometry, yielding a unified degradation measure across modalities.

Figure 2: Overview of SymKL . Given a reference signal, SymKL first fits an INR to the reference and subsequently freezes its parameters. The frozen reference INR is then evaluated on both the reference and degraded signals to obtain their Fisher information representations. The symmetric KL divergence between these Fisher representations yields a universal degradation score that consistently quantifies degradation across diverse signal modalities

	Image-domain baselines						Weight-space baselines
Distortion	PSNR	SSIM	MS-SSIM	LPIPS	CLIP	DSim	F-Cos	F- $\ell_{2}$	G-Cos	G- $\ell_{2}$	Adam-Cos	SymKL
Motion blur	1.678	1.659	2.678	1.187	2.399	2.860	0.391	2.749	0.345	1.137	0.132	3.479
JPEG2000	1.418	0.843	1.154	1.363	1.506	1.558	1.963	1.962	0.649	0.790	0.179	2.921
White noise	0.963	0.364	0.634	0.552	0.339	0.557	0.504	0.974	0.396	0.512	0.120	1.169
Impulse noise	1.004	0.799	0.827	0.515	0.334	0.702	0.461	1.004	0.452	0.580	0.118	1.345
Mean shift	3.059	2.382	3.222	3.172	2.787	3.338	0.402	2.990	0.052	1.068	0.034	3.462

Table 1: Mean relative sensitivity on KADID-10k distortions image-domain and weight-space baselines. Best results are shown in bold and second-best results are underlined. Higher is better.

Figure 3: Responses of different image-quality metrics to progressively increasing degradation severity. Top: increasing color blocks (2–10). Bottom: decreasing quantization levels (Q20–Q7). Existing metrics exhibit inconsistent or non-monotonic responses, whereas SymKL increases smoothly and monotonically with degradation severity.

Figure 4: Normalized sensitivity profiles across degradation types. Each axis is normalized by the highest sensitivity attained for the corresponding degradation. Across both occupancy-field (left) and audio (right) degradations, SymKL consistently exhibits the strongest relative sensitivity, demonstrating a more responsive characterization of degradation than conventional modality-specific measures.

	Color Blocks (CB)				Quantization (Q)
Metric	CB2	CB6	CB8	CB10	Q20	Q16	Q10	Q7
PSNR	25.865	23.131	21.295	21.711	31.529	29.515	25.421	23.884
SSIM	0.989	0.970	0.964	0.958	0.956	0.932	0.856	0.864
MS-SSIM	0.981	0.920	0.874	0.917	0.990	0.983	0.957	0.959
LPIPS	0.045	0.135	0.196	0.166	0.017	0.029	0.078	0.060
CLIP	1.000	0.820	0.835	0.800	0.976	0.982	0.974	0.973

Table 2: Responses of different image-quality metrics to progressively increasing color-block degradation (CB) and progressively decreasing quantization levels (Q), both corresponding to increasing degradation severity. Underlined values indicate points at which a metric violates the expected monotonic response.

Simpler and Stronger Baselines for All-in-One Image Restoration
Dec 11, 2025Hongyu Du, Yuqi Wang, Wenlong Jiao +2All-in-One Image Restoration Image Restoration
Causal Disentanglement-Inspired Degradation Representation Learning for Full-Reference Image Quality Assessment
Apr 23, 2026Zhen Zhang, Jielei Chu, Tian Zhang +5Disentangled Representation Learning Image Quality Assessment
School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu 611756, China · School of Physics, Northeast Normal University, Changchun 130024, China · School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, China +2
SLER-IR: Spherical Layer-wise Expert Routing for All-in-One Image Restoration
Mar 6, 2026Peng Shurui, Xin Lin, Shi Luo +5Image Restoration All-in-One Image Restoration
Sichuan University · University of California San Diego · Insta360 Research

Dec 11, 2025J/K move · Enter open · S save

Simpler and Stronger Baselines for All-in-One Image Restoration

Hongyu Du, Yuqi Wang, Wenlong Jiao, Wenwen Li+1

All-in-One Image Restoration Image Restoration U-Net

Open paper AskPDF arXiv

Current methods for all-in-one image restoration increasingly rely on complex mechanisms, such as Mixture-of-Experts or prompt learning, to handle diverse degradations.In this work, we challenge this trend by showing that structural symmetry provides a strong and effective inductive bias, which is often sufficient to support high-quality restoration in many practical settings. We propose SymUNet, a minimalist baseline that enforces strict encoder-decoder alignment via simple additive fusion, which outperforms complex state-of-the-art models on standard benchmarks while significantly reducing computational costs. Furthermore, to address the negative transfer observed in highly diverse degradation scenarios (e.g., 5-task settings), we introduce SE-SymUNet, which leverages frozen semantic priors (CLIP) to disentangle conflicting restoration tasks. Extensive experiments demonstrate that our approach establishes a simpler, stronger, and more efficient foundation for multi-degradation learning.

Abstract

Explore similar work

Simpler and Stronger Baselines for All-in-One Image Restoration

Causal Disentanglement-Inspired Degradation Representation Learning for Full-Reference Image Quality Assessment

SLER-IR: Spherical Layer-wise Expert Routing for All-in-One Image Restoration