An Integrated Variational Decomposition Models for Overlapped Nonstationary Multicomponent Signal Isolation with Incomplete Data

Signal analysis is often challenging due to the complexity of signals, which comprise multiple components that can overlap in frequency and be affected by noise and interference. In many cases, only partial information about these components is available, making signal analysis even more difficult. This paper presents a method to decompose such complex signals using Integrated Variational Decomposition Models. The procedure begins with generating a partially completed multicomponent signal based on radar equations. Then, the signal is transformed into a time-frequency representation using the Short-time Fourier Transform (STFT). Then, a technique called compressive sensing, specifically Rapid Iterative Shrinkage Thresholding Network (RISTN), is utilized to restructure the time-frequency representation by solving a sparse regularization problem. The Instantaneous Frequencies (IF) are subsequently estimated using the Simplified Variational Mode Decomposition (SVMD) algorithm. Finally, the individual components of the overlapped nonstationary multicomponent signal are isolated using an algorithm called Extended Variational Chirp Component Decomposition (EVCCD). The proposed method outperforms existing methods in terms of Root Mean Square Error (RMsE), Mean Squared Error (MSE), Root Mean Absolute Error (RMAE), and computational time, achieving better values such as -15.829 dB, -31.062 dB, 0.034 dB, and 0.90282 respectively.