Magnetic resonance force microscopy (MRFM) enables three-dimensional imaging of nuclear spin densities in nanoscale objects. On the basis of numerical simulations, we evaluate the performance of strained $\mathrm{SiN}$ resonators as force sensors and show that their out-of-plane oscillation direction improves the quality of the reconstructed sample. We further introduce a multislice, compressed-sensing scan protocol that maximizes the information obtained for a given measurement time. Our simulations predict that these scanning protocols and optimized algorithms can shorten the total acquisition time by up to 2 orders of magnitude while maintaining the reconstruction fidelity. Our results demonstrate that combining advanced scanning protocols with state-of-the-art resonators is a promising path toward high-resolution MRFM for volumetric imaging of biological nanostructures.

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• Inverse problems
• Micromechanical & nanomechanical oscillators
• Nanotechnology
• Nitrides
• Imaging & optical processing
• Magnetic force microscopy
• Magnetic resonance imaging
• Scanning probe microscopy