SymKL: A Unified Representation-Space Measure of Signal Degradation

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.