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Abstract In lensless digital holography the resolving power is limited by factors such as the finite size of recorded area, pixel dimensions and sampling rate of digital acquisition system. These factors acts as a filter that discards high-frequency components with useful information about the analyzed object. In the present work, we propose a method to overcome these limitations to proving the resolution recovery in digital in-line holography by utilizing adjustable magnification in a compressive sensing framework. Here, we model the sensed field as low-pass filtered and projected on a Fresnel base with adjustable magnification and use sparse regularization in an inverse problem approach to image reconstruction. Our method enhances image reconstruction resolution from a single recorded hologram with magnification independent of parameters such as propagation distance and wavelength of light, which enables to be used in applications like multi-wavelength digital holography. In addition, this technique offers high noise immunity and eliminates typical problems of holographically reconstructed images such as twin image and speckle. Therefore, we demonstrate by simulations and experimentally results that our approach significantly improves the quality of reconstructed images when compared with conventional techniques. Highlights • An approach for holographic magnification using compressive sensing is proposed. • The technique enables holographic reconstruction even from very noisy holograms. • Improves resolution on magnified image reconstructed from a single hologram. • Reduces typical holography problems such as speckle, twin image and aliasing. [ABSTRACT FROM AUTHOR]