Detection and Resolution of Incoherent Objects by a Background-Limited Optical System*

Helstrom, Carl W.

doi:10.1364/josa.59.000164

Cited by 48 publications

(17 citation statements)

References 17 publications

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“…This framework extends previous work applying Fisher information to individual imaging techniques (e.g., Helstrom, 1969;Winick, 1986;Ober et al, 2004;Aguet et al, 2005;Shahram, 2005;Shahram and Milanfar, 2006;Marengo et al, 2009;Sanches et al, 2010;Mukamel and Schnitzer, 2012;Quirin et al, 2012;Shechtman et al, 2014). For example, many studies have used Fisher information to examine the theoretical optimal resolution of specific optical imaging techniques (Helstrom, 1969;Winick, 1986;Ober et al, 2004;Aguet et al, 2005;Shahram, 2005;Shahram and Milanfar, 2006;Marengo et al, 2009;Mukamel and Schnitzer, 2012;Quirin et al, 2012;Shechtman et al, 2014). However, using Fisher information to optimize other neural recording technologies, while occasionally done (e.g., MRI in Sanches et al, 2010), is not as common.…”

Section: Framework Discussionsupporting

confidence: 63%

Spatial Information in Large-Scale Neural Recordings

Cybulski¹,

Glaser²,

Marblestone

et al. 2014

Preprint

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To record from a given neuron, a recording technology must be able to separate the activity of that neuron from the activity of its neighbors. Here, we develop a Fisher information based framework to determine the conditions under which this is feasible for a given technology. This framework combines measurable point spread functions with measurable noise distributions to produce theoretical bounds on the precision with which a recording technology can localize neural activities. If there is sufficient information to uniquely localize neural activities, then a technology will, from an information theoretic perspective, be able to record from these neurons. We (1) describe this framework, and (2) demonstrate its application in model experiments. This method generalizes to many recording devices that resolve objects in space and should be useful in the design of next-generation scalable neural recording systems.

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Section: Framework Discussionsupporting

confidence: 63%

Spatial Information in Large-Scale Neural Recordings

Cybulski¹,

Glaser²,

Marblestone

et al. 2014

Preprint

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“…A related problem of determining the signal-to-noise ratio (SNR) required for beating the Rayleigh diffraction limit on resolving two closely located point sources has been well studied from a binary-hypothesis-testing viewpoint over the last four decades, beginning with Helstrom's early work [8]. A more recent analysis [9] of the same problem has asked, like Helstrom's, the question of deciding between two alternatives: whether a double source or a single source of the same integrated flux is present, based on the available signal in a noisy environment.…”

Section: Introductionmentioning

confidence: 99%

New error bounds for M-testing and estimation of source location with subdiffractive error

Prasad

2012

J. Opt. Soc. Am. A

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I present new lower and upper bounds on the minimum probability of error (MPE) in Bayesian multihypothesis testing that follow from an exact integral of a version of the statistical entropy of the posterior distribution, or equivocation. I also show that these bounds are exponentially tight and thus achievable in the asymptotic limit of many conditionally independent and identically distributed measurements. I then relate the minimum mean-squared error (MMSE) and the MPE by means of certain elementary error probability integrals. In the second half of the paper, I compare the MPE and MMSE for the problem of locating a single point source with subdiffractive uncertainty. The source-strength threshold needed to achieve a desired degree of source localization seems to be far more modest than the well established threshold for the different optical super-resolution problem of disambiguating two point sources with subdiffractive separation.

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“…Similar questions of source-pair OSR in the framework of Bayesian inference have been asked previously by others [6,7,8,9]. These analyses are more limited, however, because they either employ simpifying assumptions such as one-dimensional PDFs or do not account for non-Gaussian sources of noise and consider the full range of noise sources from additive sensor noise to signal and background-based shot noise comprehensively.…”

Section: Introductionmentioning

confidence: 85%

Asymptotics of Bayesian error probability and 2D pair superresolution

Prasad¹

2014

Opt. Express

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This paper employs a recently developed asymptotic Bayesian multi-hypothesis testing (MHT) error analysis [1] to treat the problem of superresolution imaging of a pair of closely spaced, equally bright point sources. The analysis exploits the notion of the minimum probability of error (MPE) in discriminating between two competing equi-probable hypotheses, a single point source of a certain brightness at the origin vs. a pair of point sources, each of half the brightness of the single source and located symmetrically about the origin, as the distance between the source pair is changed. For a Gaussian point-spread function (PSF), the analysis makes predictions on the scaling of the minimum source strength, expressed in units of photon number, required to disambiguate the pair as a function of their separation, in both the signal-dominated and background-dominated regimes. Certain logarithmic corrections to the quartic scaling of the minimum source strength with respect to the degree of superresolution characterize the signal-dominated regime, while the scaling is purely quadratic in the background-dominated regime. For the Gaussian PSF, general results for arbitrary strengths of the signal, background, and sensor noise levels are also presented.

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Detection and Resolution of Incoherent Objects by a Background-Limited Optical System*

Cited by 48 publications

References 17 publications

Spatial Information in Large-Scale Neural Recordings

Spatial Information in Large-Scale Neural Recordings

New error bounds for M-testing and estimation of source location with subdiffractive error

Asymptotics of Bayesian error probability and 2D pair superresolution

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