Pixon sub-diffraction space imaging

Puetter, R. C.; Hier, R. G.

doi:10.1117/12.794055

Cited by 2 publications

(5 citation statements)

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“…In the present problem, there is considerable prior knowledge in the sense that the source is known to be a single point and located at one of at most M possible regularly spaced positions. Nevertheless, the qualitatively different and rather modest threshold behavior suggested by my analysis seems to be upheld by at least some practical OSR algorithms discussed over the last decade or so, which exploit prior knowledge in an essential way [13,14].…”

Section: Mmse For Super-resolving the Source Locationmentioning

confidence: 70%

“…A comparison of this threshold to that obtained by Lucy [10] for the related but more involved problem of photon-limited optical superresolution (OSR) of two closely spaced, equally bright point sources, and to those in more recent papers [9,11] for a wider class of problems, will show that the latter thresholds are overly pessimistic. In fact, large OSR can be achieved even at modest SNRs if high-quality prior information is available, as has been demonstrated more recently [12][13][14].…”

Section: Introductionmentioning

confidence: 87%

“…Since both χn; X and H n HjX decrease monotonically with n, Eq. (14) is upper bounded by Eχ1; XH 1 HjX R ∞ 1 n −2 dn, or by the equivocation itself, EH 1 HjX, since χ1; X 1. This typically rather loose bound was first obtained by Rényi [5].…”

Section: Lower and Upper Bounds On The Mpe In Hypothesis Testingmentioning

confidence: 99%

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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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Section: Mmse For Super-resolving the Source Locationmentioning

confidence: 70%

Section: Introductionmentioning

confidence: 87%

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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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“…But the knowledge that all sources in a scene are point-like, rather than being extended with arbitrary variations of brightness across them, is sufficiently information-bearing that superresolving them to well within the diffraction limit requires, as we hope to prove, rather more modest source-signal strengths. Independent confirmations of this claim are provided by a number of studies involving actual computational algorithms, including those presented in [18,19,20,21,22]. These algorithms make use, in essential ways, of the point-like extension of sources being reconstructed from noisy, filtered image data.…”

Section: Introductionmentioning

confidence: 92%

“…From expressions (22) and (23), the large-u approximations for q 1 (u) and q 2 (u) follow quite simply, since for u >> 1 any positive power of u dominates any constants or logarithms of u or negative powers of u,…”

Section: A Certain Gaussian Integralsmentioning

confidence: 99%

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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Pixon sub-diffraction space imaging

Cited by 2 publications

References 1 publication

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

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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