Many real signals can be accurately modeled as the superposition of locally band-limited, amplitude and frequency-modulated (AM-FM) components commonly referred to as the modes of f . These multicomponent signals often contain strongly frequency modulated modes, as for instance chirps encoutered in radar, speech processing or gravitational waves detection. These signals can be analyzed using the Short Time Fourier Transform (STFT) which applies a sliding window function (such as a Gaussian) which draws some ridges in the time-frequency (TF) plane.

The reconstruction of the modes, based on the information computed on the ridge, is possible —under certain separation conditions— from reassignment methods or the synchrosqueezing transform (SST). However, when two or more modes are close together or intersect, the mixing of the phases produce constructive or destructive interference resulting in complex patterns that are difficult to analyze. Efficiently separating interference from the rest of the signal in the TF plane is crucial for applying reassignment methods effectively. In image processing, variational approaches involving proximal techniques have been proposed to separate texture from geometry in images, but the results remain incomplete.