This paper addresses the problem of disentangling nonoverlapping multicomponent signals from their observation being possibly contaminated by external additive noise. We aim to extract and to retrieve the elementary components (also called modes) present in an observed nonstationary mixture signal. To this end, we propose a new pseudo-Bayesian algorithm to perform the estimation of the instantaneous frequency of the signal modes from their time-frequency representation. In a second time, a detection algorithm is developed to restrict the time region where each signal component behaves, to enhance quality of the reconstructed signal. We finally deal with the presence of noise in the vicinity of the estimated instantaneous frequency by introducing a new reconstruction approach relying on nonbinary band-pass synthesis filters. We validate our methods by comparing their reconstruction performance to state-of-the-art approaches through several experiments involving both synthetic and real-world data under different experimental conditions.