Project Summary Non-Fourier methods of spectrum analysis have enabled previously intractable multidimensional NMR experiment on biomolecules by providing high resolution spectra from data collected using nonuniform (sparse) sampling. Compared to the Fourier Transform, we know much less about the properties of these methods. In order to fully realize their potential benefits, and to understand their vulnerabilities, it is essential that we investigate their robustness, failure modes, and convergence properties. Further improvements in these methods are essential for meeting the challenges posed by larger, more complex, fleetingly stable, and dynamically disordered systems, but the lack of detailed understanding as well as the absence of robust metrics for spectral quality has hampered systematic approaches, critical comparison of competing approaches, or determination of best practices. The broad aim of this proposal is to develop robust metrics and apply them to improve the methods, and apply them to enable challenging biomolecular applications of multidimensional NMR. A domain of the protein USP7, involved in cancer, will serve as a case study. The potential impact of these developments is substantial because they will improve the power of the installed base of NMR spectrometers for biomolecular applications.