Mass spectrometry imaging (MSI) allows for untargeted mapping of the chemical composition of tissues with attomole detection limits. MSI using Fourier transform (FT)-based mass spectrometers, such as FT-ion cyclotron resonance (FT-ICR), grants the ability to examine the chemical space with unmatched mass resolution and mass accuracy. However, direct imaging of large tissue samples using FT-ICR is slow. In this work, we present an approach that combines the subspace modeling of ICR temporal signals with compressed sensing to accelerate high-resolution FT-ICR MSI. A joint subspace and spatial sparsity constrained model computationally reconstructs high-resolution MSI data from the sparsely sampled transients with reduced duration, allowing a significant reduction in imaging time. Simulation studies and experimental implementation of the proposed method in investigation of brain tissues demonstrate a 10-fold enhancement in throughput of FT-ICR MSI, without the need for instrumental or hardware modifications.