In some research papers in the nuclear magnetic resonance field Ref:, Logan's theorem is used to provide a justification for randomized sampling of free induction decay curves which are converted to NMR spectrum. The same technology is now used in imaging the human body by magnetic resonance imaging (MRI). The cited reference is Logan's PhD thesis from Columbia University, 1965.
"Logan’s Theorem states that perfect recovery of the spectrum is possible even from incomplete and noisy measurements by minimizing the $l_1$ norm of the spectrum while ensuring consistency with the measured data, provided that certain conditions on sparsity and noise level are met, and the spectrum is band-limited." B. F. Logan. Properties of high-pass signals. (Ph.D. thesis, Department of Electrical Engineering, Columbia University, 1965).
I got hold of the thesis copy from Columbia University by interlibrary loan (don't have it anymore) but could not find any explicit statement like this anywhere. The question is
(i) Has anyone else encountered this Logan's theorem in some other form but relevant to compressive sensing or is it eponymous association?
Note: It is not related to Logan's 1977, Information in the Zero Crossings of Bandpass-Signals as far as I could tell. The thesis is not available online anywhere until and unless some reader has access to Columbia University library.
