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Treating the analysis of experimental spectroscopic data as an inverse problem and using regularization techniques to obtain stable pseudoinverse solutions, allows access to previously unavailable level of spectroscopic detail. The data is mapped into an appropriate physically relevant parameter space, leading to better qualitative and quantitative understanding of the underlying physics, and in turn, to better and more detailed models. A brief survey of relevant inverse methods is illustrated by several successful applications to the analysis of nuclear magnetic resonance data, yielding new insight into the structure and dynamics of biomembrane lipids.