Signal processing for magnetic resonance force microscopy.

Magnetic resonance force microscopy (MRFM) is an emergent technology that has the potential for three-dimensional, non-destructive, and in-situ imaging of biological molecules with atomic resolution. Experiments at IBM have shown that MRFM is capable of detecting and localizing individual electron spins associated with subsurface atomic defects in silicon dioxide. In principle, detection of single nuclear spins is possible as well. MRFM detects the spins by measuring the small spin-induced forces on a micromachined cantilever. Detection of a single electron spin was studied in additive white Gaussian noise (AWGN). Four models of the single spin-cantilever interaction were proposed. We investigated three of these models. A heuristic argument was used to formulate a detector for the continuous-time classical model. Approximate forms of the optimal likelihood ratio test (LRT) for the discrete-time (DT) random telegraph and DT random walk models were derived which hold under certain conditions. It was shown that, under low signal to noise ratio (SNR), the LRT for a DT finite state Markov process in AWGN reduces to the matched filter statistic with the one-step minimum mean-squared error predictor used in place of the known signal values. The next challenge for MRFM is to demonstrate the technology's applicability as an imaging modality with advantages over those already in existence. We therefore considered the problem of image reconstruction in the MRFM setting, which is reconstructing sparse images from noisy projections. The goal here is to perform sparse reconstruction with the tuning parameters selected in a data-driven fashion. The empirical Bayes framework was investigated, and several sparse image reconstruction methods were proposed that are more scalable and have lower computational complexity than sparse Bayesian learning (SBL). In a simulation study, the proposed methods demonstrate benefits over SBL, Landweber, and the projected Landweber method. Under low SNR, a MAP-based solution produced low l1 and l2 reconstruction error. We found that the maximum penalized likelihood estimator using a l1 norm penalty and with its regularization parameter estimated by minimizing Stein's unbiased risk estimate produced consistently good results across a wide range of SNRs.Ph.D.Applied SciencesElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125905/2/3224766.pd