Many medical (computerized tomography, magnetic resonance imaging) and astronomy imaging problems (Square Kilometre Array), spectroscopy and Fourier optics attempt at reconstructing high quality images in the pixel domain from a limited number of samples in the frequency domain. In this paper, we extend the problem formulation of learnable compressive subsampling that focuses on the learning of the best sampling operator in the Fourier domain adapted to spectral properties of training set of images. We formulate the problem as a reconstruction from a finite number of sparse samples with a prior learned from the external dataset or learned on-fly for the image to be reconstructed. The proposed methods are tested on diverse datasets covering facial images, medical and multi-band astronomical applications using the mean square error and SSIM as a perceptual measure of reconstruction. The obtained results demonstrate some interesting properties of proposed methods that might be of interest for future research and extensions.

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