On the Fuzzy Convolution Operator in Image Processing in the Context of Studying Spectral Properties for Fuzzy Bounded Operators

This work introduces a fuzzy version of the convolution operator and explores how its spectral properties extend classical results into the setting of fuzzy normed spaces. By adopting a fuzzy norm that satisfies a Hadz̆ić type condition, the study builds a bridge between traditional operator theory and fuzzy analysis. The paper not only generalizes known spectral results in a setup composed of just metrizable spaces but also illustrates how these concepts can be applied in real-world problems. In particular, a practical algorithm based on the fuzzy bounded convolution operator is developed for image enhancement in Contrast-Enhanced Ultrasonography (CEUS), showing how fuzzy mathematical tools can contribute to improving medical imaging and interpretation.