  We present a self-consistent framework to perform the wavelet analysis of
two-dimensional statistical distributions. The analysis targets the 2D
probability density function (p.d.f.) of an input sample, in which each object
is characterized by two peer parameters. The method performs a probabilistic
detection of various `patterns', or `structures' related to the behaviour of
the p.d.f. Laplacian. These patterns may include regions of local convexity or
local concavity of the p.d.f., in particular peaks (groups of objects) or gaps.
In the end, the p.d.f. itself is reconstructed based on the least noisy (most
economic) superposition of such patterns. Among other things, our method also
involves optimal minimum-noise wavelets and minimum-noise reconstruction of the
distribution density function. The new 2D algorithm is now implemented and
released along with an improved and optimized 1D version. The code relies on
the C++11 language standard, and is fully parallelized. The algorithm has a
rich range of applications in astronomy: Milky Way stellar population analysis,
investigations of the exoplanets diversity, Solar System minor bodies
statistics, etc.
