Attenuation Compensation in Lossy Media via the Wave Operator Model

The wave operator model provides a framework for modeling wave propagation by encoding material parameter distributions into matrix-form operators. This paper extends this framework from lossless to lossy media. We present a derivation of the wave operator solution for the electric field in dissipative environments, which can be decomposed into a closed-form propagation term and a non-closed-form dissipation term. Based on an analysis of the dominant exponential decay within the propagation term, an attenuation compensation strategy is proposed to restore the attenuated data to an approximate lossless state. The performance of this compensation strategy is analyzed and validated through numerical experiments, establishing the theoretical foundation for reduced order model (ROM)-based techniques in lossy media.