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Desorption electrospray ionisation-mass spectrometry imaging (DESI-MSI) is a powerful imaging technique for the analysis of complex surfaces. However, the often highly complex nature of biological samples is particularly challenging for MSI approaches, as options to appropriately address molecular complexity are limited. Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) offers superior mass accuracy and mass resolving power, but its moderate throughput inhibits broader application. Here we demonstrate the dramatic gains in mass resolution and/or throughput of DESI-MSI on an FT-ICR MS by developing and implementing a sophisticated data acquisition and data processing pipeline. The presented pipeline integrates, for the first time, parallel ion accumulation and detection, post-processing absorption mode Fourier transform and pixel-by-pixel internal re-calibration. To achieve that, first, we developed and coupled an external high-performance data acquisition system to an FT-ICR MS instrument to record the time-domain signals (transients) in parallel with the instrument's built-in electronics. The recorded transients were then processed by the in-house developed computationally-efficient data processing and data analysis software. Importantly, the described pipeline is shown to be applicable even to extremely large, up to 1 TB, imaging datasets. Overall, this approach provides improved analytical figures of merits such as: (i) enhanced mass resolution at no cost in experimental time; and (ii) up to 4-fold higher throughput while maintaining a constant mass resolution. Using this approach, we not only demonstrate the record 1 million mass resolution for lipid imaging from brain tissue, but explicitly show such mass resolution is required to resolve the complexity of the lipidome.