791 research outputs found
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
A Recursive Algorithm for Computing Cramer-Rao-Type Bouads on Estimator Covariance
We give a recursive algorithm to calculate submatrices of the Cramer-Rao (CR) matrix bound on the covariance of any unbiased estimator of a vector parameter ?_. Our algorithm computes a sequence of lower bounds that converges monotonically to the CR bound with exponential speed of convergence. The recursive algorithm uses an invertible “splitting matrix” to successively approximate the inverse Fisher information matrix. We present a statistical approach to selecting the splitting matrix based on a “complete-data-incomplete-data” formulation similar to that of the well-known EM parameter estimation algorithm. As a concrete illustration we consider image reconstruction from projections for emission computed tomography.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85950/1/Fessler104.pd
All degree six local unitary invariants of k qudits
We give explicit index-free formulae for all the degree six (and also degree
four and two) algebraically independent local unitary invariant polynomials for
finite dimensional k-partite pure and mixed quantum states. We carry out this
by the use of graph-technical methods, which provides illustrations for this
abstract topic.Comment: 18 pages, 6 figures, extended version. Comments are welcom
Space-Alternating Generalized Expectation-Maximization Algorithm
The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional log-likelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all parameters simultaneously, which has two drawbacks: 1) slow convergence, and 2) difficult maximization steps due to coupling when smoothness penalties are used. The paper describes the space-alternating generalized EM (SAGE) method, which updates the parameters sequentially by alternating between several small hidden-data spaces defined by the algorithm designer. The authors prove that the sequence of estimates monotonically increases the penalized-likelihood objective, derive asymptotic convergence rates, and provide sufficient conditions for monotone convergence in norm. Two signal processing applications illustrate the method: estimation of superimposed signals in Gaussian noise, and image reconstruction from Poisson measurements. In both applications, the SAGE algorithms easily accommodate smoothness penalties and converge faster than the EM algorithms.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85886/1/Fessler103.pd
Penalized Maximum-Likelihood Image Reconstruction Using Space-Alternating Generalized EM Algorithms
Most expectation-maximization (EM) type algorithms for penalized maximum-likelihood image reconstruction converge slowly, particularly when one incorporates additive background effects such as scatter, random coincidences, dark current, or cosmic radiation. In addition, regularizing smoothness penalties (or priors) introduce parameter coupling, rendering intractable the M-steps of most EM-type algorithms. This paper presents space-alternating generalized EM (SAGE) algorithms for image reconstruction, which update the parameters sequentially using a sequence of small “hidden” data spaces, rather than simultaneously using one large complete-data space. The sequential update decouples the M-step, so the maximization can typically be performed analytically. We introduce new hidden-data spaces that are less informative than the conventional complete-data space for Poisson data and that yield significant improvements in convergence rate. This acceleration is due to statistical considerations, not numerical overrelaxation methods, so monotonic increases in the objective function are guaranteed. We provide a general global convergence proof for SAGE methods with nonnegativity constraints.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85850/1/Fessler102.pd
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