A Fully Interpretable Takagi-Sugeno-Kang Fuzzy Image Compression Method Based on Gaussian Mixture Model

Although rate–distortion (RD) performance has traditionally driven image compression research, practical applications increasingly require model-based and interpretable methods. Inspired by the recently proven theoretical equivalence between Gaussian Mixture Models (GMMs) and first-order Takagi–Sugeno–Kang (TSK) fuzzy systems, this study proposes FI-GTFIC, a fully interpretable grayscale image compression method. FI-GTFIC replaces conventional GMM-based statistical modeling with an equivalent first-order TSK fuzzy representation, allowing explicit rule-based fuzzy reasoning to explain pixel-wise encoding and reconstruction. Its fuzzy-rule antecedents are obtained through Fuzzy C-Means (FCM) clustering, while consequents are directly calculated without training. By treating rule weights as fuzzy rule priors, all rules become fully interpretable. Thus, FI-GTFIC combines GMMs’ local adaptability with TSK systems’ global approximation and uncertainty-handling abilities. Since only a few statistical parameters are encoded into the bitstream, it adds no bit overhead and achieves competitive reconstruction performance with full interpretability on grayscale images.