  The synchrosqueezing method aims at decomposing 1D functions as
superpositions of a small number of "Intrinsic Modes", supposed to be well
separated both in time and frequency. Based on the unidimensional wavelet
transform and its reconstruction properties, the synchrosqueezing transform
provides a powerful representation of multicomponent signals in the
time-frequency plane, together with a reconstruction of each mode.
  In this paper, a bidimensional version of the synchrosqueezing transform is
defined, by considering a well-adapted extension of the concept of analytic
signal to images: the monogenic signal. The natural bidimensional counterpart
of the notion of Intrinsic Mode is then the concept of "Intrinsic Monogenic
Mode" that we define. Thereafter, we investigate the properties of its
associated Monogenic Wavelet Decomposition. This leads to a natural bivariate
extension of the Synchrosqueezed Wavelet Transform, for decomposing and
processing multicomponent images. Numerical tests validate the effectiveness of
the method for different examples.
