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Aim: To evaluate potential scan time reduction in (23)Na-Magnetic Resonance Imaging with the chemical shift imaging sequence (CSI) using undersampled data of high-quality datasets, reconstructed with an iterative constrained reconstruction, compared to reduced resolution or reduced signal-to-noise ratio., Materials and Methods: CSI (23)Na-images were retrospectively undersampled and reconstructed with a constrained reconstruction scheme. The results were compared to conventional methods of scan time reduction. The constrained reconstruction scheme used a phase constraint and a finite object support, which was extracted from a spatially registered (1)H-image acquired with a double-tuned coil. The methods were evaluated using numerical simulations, phantom images and in-vivo images of a healthy volunteer and a patient who suffered from cerebral ischemic stroke., Results: The constrained reconstruction scheme showed improved image quality compared to a decreased number of averages, images with decreased resolution or circular undersampling with weighted averaging for any undersampling factor. Brain images of a stroke patient, which were reconstructed from three-fold undersampled k-space data, resulted in only minor differences from the original image (normalized root means square error < 12%) and an almost identical delineation of the stroke region (mismatch < 6%)., Conclusion: The acquisition of undersampled (23)Na-CSI images enables up to three-fold scan time reduction with improved image quality compared to conventional methods of scan time saving., (Copyright © 2014. Published by Elsevier GmbH.)