Baseband Detection of Bistatic Electron Spin Signals in Magnetic Resonance Force Microscopy (MRFM)

In single spin Magnetic Resonance Force Microscopy (MRFM), the objective is to detect the presence of an electron (or nuclear) spin in a sample volume by measuring spin-induced attonewton forces using a micromachined cantilever. In the OSCAR method of single spin MRFM, the spins are manipulated by an external rf field to produce small periodic deviations in the resonant frequency of the cantilever. These deviations can be detected by frequency demodulation followed by conventional amplitude or energy detection. In this paper, we present an alternative to these detection methods, based on optimal detection theory and Gibbs sampling. On the basis of simulations, we show that our detector outperforms the conventional amplitude and energy detectors for realistic MRFM operating conditions. For example, to achieve a 10% false alarm rate and an 80% correct detection rate our detector has an 8 dB SNR advantage as compared with the conventional amplitude or energy detectors. Furthermore, at these detection rates it comes within 4 dB of the omniscient matched-filter lower bound.Comment: 8 pages, 9 figures, revision of paper contains correction to a typo on the first page (introduction section

Complete-Data Spaces and Generalized EM Algorithms

Expectation-maximization (EM) algorithms have been applied extensively for computing maximum-likelihood and penalized-likelihood parameter estimates in signal processing applications. Intrinsic to each EM algorithm is a complete-data space (CDS)-a hypothetical set of random variables that is related to the parameters more naturally than the measurements are. The authors describe two generalizations of the EM paradigm: (i) allowing the relationship between the CDS and the measured data to be nondeterministic, and (ii) using a sequence of alternating complete-data spaces. These generalizations are motivated in part by the influence of the CDS on the convergence rate, a relationship that is formalized through a data-processing inequality for Fisher information. These concepts are applied to the problem of estimating superimposed signals in Gaussian noise, and it is shown that the new space alternating generalized EM algorithm converges significantly faster than the ordinary EM algorithm.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85977/1/Fessler123.pd

Recursive Algorithms for Computing the Cramer-Rao Bound

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient algorithms. For a large class of inverse problems, we show that nonmonotone Gauss-Seidel and preconditioned conjugate gradient algorithms require significantly fewer flops for convergence than monotone “bound preserving” algorithms.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85866/1/Fessler94.pd

On a problem of estimation for composed and filtered Poisson processes

Compound and filtered Poison processes are useful models for many applications in signal processing, image processing, an d communications . One of the earliest imaging applications of these models was proposed by Bernard Picinbono in a 1955 paper on silver dye photographs . In this paper we treat a generalized model with the primiary objective being to estimate parameter s of the filtered Poisson process in the presence of spatial smoothing and additive Gaussian noise . By imbedding the estimatio n problem into the context of information theory we decompose the model into the cascade of a discrete event Poisson proces s channel and a continuous Gaussian waveform channel . This naturally leads to a expectation-maximization (EM) type estimatio n algorithm and a distortion-rate lower bound on estimation error .Les processus de Poisson composés et filtrés forment une classe de modèles très utile pour certaines applications en traitement du signal, traitement de l'image, et télécommunications. Une des premières applications de ce type de modèle en traitement de l'image a été proposée par Bernard Picinbono en 1955 pour la distribution des grains d'argent dans un film photographique. Ici on introduit un modeèle de Picinbono généralisé dont l'objectif est d'estimer les paramètres du processus de Poisson filtré en présence de lissage spatial et de bruit additif Gaussien. En posant le problème de l'estimation dans le contexte de la théorie de l'information, on est conduit à une représentation du modèle par la composition d'un canal Poissonnien et d'un canal Gaussien. Cette composition mène naturellement à un estimateur paramétrique du type « expectation-maximization (EM) et à une borne du type « distortion-rate » sur l'erreur d'estimation

Bias-Variance Trade-offs Analysis Using Uniform CR Bound for Images

We apply a uniform Cramer-Rao (CR) bound to study the bias-variance trade-offs in parameter estimation. The uniform CR bound is used to specify achievable and unachievable regions in the bias-variance trade-off plane. The applications considered are: (1) two-dimensional single photon emission computed tomography (SPECT) system, and (2) one dimensional edge localization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85969/1/Fessler131.pd

Exploring Estimator Bias-Variance Tradeoffs Using the Uniform CR Bound

We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance, a delta-sigma tradeoff curve is specified that defines an “unachievable region” of the delta-sigma plane for a specified statistical model. In order to place an estimator on this plane for comparison with the delta-sigma tradeoff curve, the estimator variance, bias gradient, and bias gradient norm must be evaluated. We present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log-likelihood. We demonstrate the methods developed in this paper for linear Gaussian and nonlinear Poisson inverse problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86001/1/Fessler98.pd

Uniform CR Bound: Implement ation Issues And Applications

The authors apply a uniform Cramer-Rao (CR) bound (A.O. Hero, 1992) to study the bias-variance trade-offs in single photon emission computed tomography (SPECT) image reconstruction. The uniform CR bound is used to specify achievable and unachievable regions in the bias-variance trade-off plane. The image reconstruction algorithms considered here are: 1) space alternating generalized EM and 2) penalized weighted least-squares.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85905/1/Fessler128.pd