Astrophysical images issued from different instruments and/or spectral bands often require to be processed together, either for fitting or comparison purposes. However each image is affected by an instrumental response, also known as PSF, that depends on the characteristics of the instrument as well as the wavelength and the observing strategy. Given the knowledge of the PSF in each band, a straightforward way of processing images is to homogenise them all to a target PSF using convolution

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... ls, so that they appear as if they had been acquired by the same instrument. We propose an algorithm that generates such PSF-matching kernels, based on Wiener filtering with a tunable regularisation parameter. This method ensures all anisotropic features in the PSFs to be taken into account. We compare our method to existing procedures using measured Herschel/PACS and SPIRE PSFs and simulated JWST/MIRI PSFs. Significant gains up to two orders of magnitude are obtained with respect to the use of kernels computed assuming Gaussian or circularised PSFs.