Guided wave (GW) inspection systems offer the capability for online health monitoring of structures and hence the potential for transitioning from schedule-based maintenance to conditioned-based maintenance of nuclear plants. However, a major problem in guided wave NDE is the presence of multiple propagation modes at any actuation frequency that travel with different velocities and interfere with each other which makes interpretation of GW signals complicated. Decomposition of the measured signal into its constituent components is a critical requirement for accurate analysis in terms of detection, location and characterization of structural defects. This paper addresses the above problem using a new two-stage Mode Decomposition (MD) algorithm. The first stage employs fast high-resolution Time-Frequency Representation (TFR) of the signal based on Reassigned Spectrogram with Chirp Transform kernel (RSCT), which is used for preprocessing. The second stage includes efficiently implemented Matching Pursuit with dispersion-based dictionary. The performance of the algorithm is demonstrated on 2-mm thick aluminum plates with surface-bonded piezoelectric wafer sensors. The results show that the algorithm identifies the modes and separates closely spaced or overlapped S0 and A0 wave packets. Automated analysis of the MD output allows for detection of flaw indications corresponding to different modes using standard diagnostic imaging algorithm.