  In the present work, we propose a new method aiming at extracting the kinetic
Sunyaev-Zel'dovich (KSZ) temperature fluctuations embedded in the primary
anisotropies of the cosmic microwave background (CMB). We base our study on
simulated maps without noise and we consider very simple and minimal
assumptions. Our method essentially takes benefit from the spatial correlation
between KSZ and the Compton parameter distribution associated with the thermal
Sunyaev-Zel'dovich (TSZ) effect of the galaxy clusters, the later can be
obtained by means of multi-frequency based component separation techniques. We
reconstruct the KSZ signal by interpolating the CMB fluctuations without making
any hypothesis besides the CMB fluctuations are Gaussian distributed. We
present two ways of estimating the KSZ fluctuations, after the interpolation
step. In the first way we use a blind technique based on canonical Principal
Component Analysis, while the second uses a minimisation criterion based on the
fact that KSZ dominates a small angular scales and that it follows a
non-Gaussian distribution. We show using the correlation between the input and
reconstructed KSZ map that the latter can be reconstructed in a very
satisfactory manner (average correlation coefficient between 0.62 and 0.90),
furthermore both the retrieved KSZ power spectrum and temperature fluctuation
distribution are in quite good agreement with the original signal. The ratio
between the input and reconstructed power spectrum is indeed very close to one
up to a multipole $\ell\sim 200$ in the best case. The method presented here
can be considered as a promising starting point to identify in CMB observations
the temperature fluctuation associated with the KSZ effect.
