On the noise-resolution duality, Heisenberg uncertainty and Shannon's information

Gureyev, T. E.; Hoog, Frank de; Nesterets, Yakov; Paganin, David M.

doi:10.21914/anziamj.v56i0.9414

Cited by 8 publications

(13 citation statements)

References 18 publications

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“…In the case of Poissonian statistics ( γ = 1), Equation ( 8 ) is close in form to the noise-resolution uncertainty previously demonstrated in the context of X-ray imaging 17 , 21 . It has been shown in ref.…”

Section: Resultssupporting

confidence: 68%

“…Consequently, equations (6)- (7) can be modified in the general d-dimensional case to give the following noise-resolution uncertainty principle: (6) and is valid in all cases, including sub-Poissonian statistics, in particular). In the case of Poissonian statistics (γ = 1), equation (8) is close in form to the noise-resolution uncertainty previously demonstrated in the context of X-ray imaging [17,21]. It has been shown in [21] that the quantity 2…”

Section: Noise-resolution Uncertainty Inequality For Boson Fieldssupporting

confidence: 64%

“…It has been shown in ref. 21 that the quantity has characteristics somewhat similar to “information capacity per single particle”. Equation ( 8 ) is equivalent to the statement that cannot exceed an absolute upper limit: .…”

Section: Resultsmentioning

confidence: 99%

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On noise-resolution uncertainty in quantum field theory

Gureyev

Kozlov

Nesterets

et al. 2017

Sci Rep

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An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck’s constant and a dimensionless functional which reflects the joint signal-to-noise ratio of the position and momentum of vacuum fluctuations in the region of the phase space occupied by the mode. Experimental X-ray synchrotron measurements provide an initial verification of the proposed theory in the case of Poisson statistics.

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Section: Resultssupporting

confidence: 68%

Section: Noise-resolution Uncertainty Inequality For Boson Fieldssupporting

confidence: 64%

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On noise-resolution uncertainty in quantum field theory

Gureyev

Kozlov

Nesterets

et al. 2017

Sci Rep

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“…We have recently introduced a notion of intrinsic imaging quality, which incorporates both the spatial resolution and the noise propagation properties of an imaging system [6][7][8][9][10]. Compared to previous publications on this and related topics, Section 2 of this paper extends the notion of intrinsic imaging quality from "flat-field" (featureless) images to the situation were the signal and noise levels can vary across the images, but the rate of variation is slow compared to that of the point-spread function (PSF) of the imaging system.…”

Section: Introductionmentioning

confidence: 99%

Spatial resolution, signal-to-noise and information capacity of linear imaging systems

Gureyev¹,

Nesterets²,

Hoog³

2016

Opt. Express

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A simple model for image formation in linear shift-invariant systems is considered, in which both the detected signal and the noise variance are varying slowly compared to the point-spread function of the system. It is shown that within the constraints of this model, the square of the signal-to-noise ratio is always proportional to the "volume" of the spatial resolution unit. In the case of Poisson statistics, the ratio of these two quantities divided by the incident density of the imaging particles (e.g. photons) represents a dimensionless invariant of the imaging system, which was previously termed the intrinsic imaging quality. The relationship of this invariant to the notion of information capacity of communication and imaging systems, which was previously considered by Shannon, Gabor and others, is investigated. The results are then applied to a simple generic model of quantitative imaging of weakly scattering objects, leading to an estimate of the upper limit for the amount of information about the sample that can be obtained in such experiments. It is shown that this limit depends only on the total number of imaging particles incident on the sample, the average scattering coefficient, the size of the sample and the number of spatial resolution units.

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“…Such a parameter is the information capacity (IC) [64]. The concept of information capacity has been introduced within the context of Shannon's information theory, in order to assess image information content [65]. However, little work relevant to nuclear medicine imaging has been published up to now [1,3,11,20].…”

Section: Information Capacitymentioning

confidence: 99%

Information Capacity of Positron Emission Tomography Scanners

et al. 2018

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Background: The aim of the present study was to assess the upper information content bound of positron emission tomography (PET) images, by means of the information capacity (IC). Methods: The Geant4 Application for the Tomographic Emission (GATE) Monte Carlo (MC) package was used, and reconstructed images were obtained by using the software for tomographic image reconstruction (STIR). The case study for the assessment of the information content was the General Electric (GE) Discovery-ST PET scanner. A thin-film plane source aluminum (Al) foil, coated with a thin layer of silica and with a 18F-fludeoxyglucose (FDG) bath distribution of 1 MBq was used. The influence of the (a) maximum likelihood estimation-ordered subsets-maximum a posteriori probability-one step late (MLE-OS-MAP-OSL) algorithm, using various subsets (1 to 21) and iterations (1 to 20) and (b) different scintillating crystals on PET scanner’s performance, was examined. The study was focused on the noise equivalent quanta (NEQ) and on the single index IC. Images of configurations by using different crystals were obtained after the commonly used 2-dimensional filtered back projection (FBP2D), 3-dimensional filtered back projection re-projection (FPB3DRP) and the (MLE)-OS-MAP-OSL algorithms. Results: Results shown that the images obtained with one subset and various iterations provided maximum NEQ values, however with a steep drop-off after 0.045 cycles/mm. The single index IC data were maximized for the range of 8–20 iterations and three subsets. The PET scanner configuration incorporating lutetium orthoaluminate perovskite (LuAP) crystals provided the highest NEQ values in 2D FBP for spatial frequencies higher than 0.028 cycles/mm. Bismuth germanium oxide (BGO) shows clear dominance against all other examined crystals across the spatial frequency range, in both 3D FBP and OS-MAP-OSL. The particular PET scanner provided optimum IC values using FBP3DRP and BGO crystals (2.4829 bits/mm2). Conclusions: The upper bound of the image information content of PET scanners can be fully characterized and further improved by investigating the imaging chain components through MC methods.

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On the noise-resolution duality, Heisenberg uncertainty and Shannon's information

Cited by 8 publications

References 18 publications

On noise-resolution uncertainty in quantum field theory

On noise-resolution uncertainty in quantum field theory

Spatial resolution, signal-to-noise and information capacity of linear imaging systems

Information Capacity of Positron Emission Tomography Scanners

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