  We present new clean maps of the CMB temperature anisotropies (as measured by
Planck) constructed with a novel internal linear combination (ILC) algorithm
using directional, scale-discretised wavelets --- Scale-discretised,
directional wavelet ILC or SILC. Directional wavelets, when convolved with
signals on the sphere, can separate the anisotropic filamentary structures
which are characteristic of both the CMB and foregrounds. Extending previous
component separation methods, which use the frequency, spatial and harmonic
signatures of foregrounds to separate them from the cosmological background
signal, SILC can additionally use morphological information in the foregrounds
and CMB to better localise the cleaning algorithm. We test the method on Planck
data and simulations, demonstrating consistency with existing component
separation algorithms, and discuss how to optimise the use of morphological
information by varying the number of directional wavelets as a function of
spatial scale. We find that combining the use of directional and axisymmetric
wavelets depending on scale could yield higher quality CMB temperature maps.
Our results set the stage for the application of SILC to polarisation
anisotropies through an extension to spin wavelets.
