Illustration of the background subtraction step in our pipeline for our observation of 2MJ0219 b. Top row: Calibrated datacube, represented both in its unfolded state (left) and as wavelength-averaged intensity image (right). Middle row: Background model as obtained using the algorithm described in Sect. D.3, i.e. using a sum of a Gaussian filter and a B-spline for the spectral, respectively spatial, dimensions. Bottom row: Data after subtraction of the background model. Most of the structures visible in the background of the calibrated datacube are successfully removed. The linear colour scale is identical in all six images.