  High-precision radial velocity (RV) measurements are crucial for exoplanet
detection and characterisation. Efforts to achieve ~10 cm/s precision have been
made over the recent decades, with significant advancements in instrumentation,
data reduction techniques, and statistical inference methods. However, despite
these efforts, RV precision is currently limited to ~50 cm/s. This value
exceeds state-of-the-art spectrographs' expected instrumental noise floor and
is mainly attributed to RV signals induced by stellar variability. In this
work, we propose a factorisation method to overcome this limitation. The
factorisation is particularly suitable for controlling the effect of localised
changes in the stellar emission profile, assuming some smooth function of a few
astrophysical parameters governs them. We use short-time Fourier transforms
(STFT) to infer the RV in a procedure equivalent to least-squares minimisation
in the wavelength domain and demonstrate the effectiveness of our method in
treating arbitrary temperature fluctuations on the star's surface. The proposed
prescription can be naturally generalised to account for other effects, either
intrinsic to the star, such as magnetic fields, or extrinsic to it, such as
telluric contamination. As a proof-of-concept, we empirically derive a set of
factorisation terms describing the Solar centre-to-limb variation and apply
them to a set of realistic SOAP-GPU spectral simulations. We discuss the
method's capability to mitigate variability-induced RV signals and its
potential extensions to serve as a tomographic tool.
