  We present a first application to photometric galaxy clustering and weak
lensing of wavelet based multi-scale higher order summary statistics: starlet
peak counts and starlet $\ell_1$-norm. Peak counts are the local maxima in the
map and the $\ell_1$-norm is computed via the sum of the absolute values of the
starlet (wavelet) decomposition coefficients of a map, providing a fast
multi-scale calculation of the pixel distribution, encoding the information of
all pixels in the map. We employ the cosmo-SLICS simulations sources and lenses
catalogues and we compute wavelet based higher order statistics in the context
of combined probes and their potential when applied to the weak lensing
convergence maps and galaxy maps. We get forecasts on the matter density
parameter $\Omega_{\rm m}$, the reduced Hubble constant $h$, the matter
fluctuation amplitude $\sigma_8$, and the dark energy equation of state
parameter $w_0$. We find that, in our setting for this first application,
considering the two probes as independent, starlet peaks and the $\ell_1$-norm
represent interesting summary statistics that can improve the constraints with
respect to the power spectrum also in the case of photometric galaxy clustering
and when the two probes are combined.
