The imaging of galaxy clusters through the Sunyaev–Zel’dovich effect is a valuable tool to probe the thermal pressure of the intra-cluster gas, especially in the outermost regions where X-ray observations suffer from photon statistics. For the first time, we produce maps of the Comptonization parameter by applying a locally parametric algorithm for sparse component separation to the latest frequency maps released by Planck. The algorithm takes into account properties of real cluster data through the two-component modelling of the spectral energy density of thermal dust, and the masking of bright point sources. Its robustness has been improved in the low signal-to-noise regime, thanks to the implementation of a deconvolution of Planck beams in the chi-square minimisation of each wavelet coefficient. We applied this procedure to twelve low-redshift galaxy clusters detected by Planck with the highest signal-to-noise ratio, considered in the XMM Cluster Oustkirts Project (X-COP). Our images show the presence of anisotropic features, such as small-scale blobs and filamentary substructures that are located in the outskirts of a number of clusters in the sample. The significance of their detection is established via a bootstrap-based procedure we propose here for the first time. In particular, we present a qualitative comparison with X-ray data for two interesting systems, namely A2029 and RXCJ1825. Our results are in agreement with the features detected in the outskirts of the clusters in the two bands.