Primary and secondary superresolution by data inversion

Matson, Charles L.; Tyler, David W.

doi:10.1364/opex.14.000456

Cited by 11 publications

(7 citation statements)

References 16 publications

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“…We may also treat the problem of point-source location from the perspective of the space-bandwidth product (SBP) [28][29][30][31]. One may regard the ability to localize a point source, for which the SBP is essentially 0, to sub-critical-pixel accuracy as being equivalent to a somewhat meaningless extension of SBP by an infinitesimal amount.…”

Section: Mmse For Super-resolving the Source Locationmentioning

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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Section: Mmse For Super-resolving the Source Locationmentioning

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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“…With the elements of the data-mean matrices given by Eqs. (16), let us now expand each term in the numerator Q of the MPE expression, defined by relation (11), in a power series in K, interchange the order of the resulting infinite sum and the pixel sum, and then perform the pixel sum by means of its continuous version. We arrive in this way at the following expression for Q:…”

Section: Bayesian Mpe Analysis For the Point-source-pair Superresolutmentioning

confidence: 99%

“…At the risk of over-simplification, we sharpen this debate with the mention of two specific OSR problems here. For one, the prohibitively difficult prospects of bandwidth extension beyond the diffraction limited cut-off by means of data inversion performed by imposing physical constraints [14,12,13,15,16,17] constitute a very different problem from that of superresolving point sources. The degree of bandwidth extension is typically logarithmic in the signal-to-noise ratio (SNR), a fact that is also well understood from Shannon's channel capacity theorem [14].…”

Section: Introductionmentioning

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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“…The PCID algorithm can be run to global convergence in this scenario, but image restorations using penalty-function-based regularization include restored Fourier data at all spatial frequencies. When there are zeros in the system OTF, the restored Fourier data at these locations are superresolved and thus are biased [53], and these biases do not have closed-form expressions in general. A third scenario is regularized blind deconvolution, single-or multi-frame, since there is no closed-form solution to the blind deconvolution problem in general.…”

Section: φ φ B I ∇ +mentioning

confidence: 99%

Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects

et al. 2008

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We report a multiframe blind deconvolution algorithm that we have developed for imaging through the atmosphere. The algorithm has been parallelized to a significant degree for execution on high-performance computers, with an emphasis on distributed-memory systems so that it can be hosted on commodity clusters. As a result, image restorations can be obtained in seconds to minutes. We have compared and quantified the quality of its image restorations relative to the associated Cramér-Rao lower bounds (when they can be calculated). We describe the algorithm and its parallelization in detail, demonstrate the scalability of its parallelization across distributed-memory computer nodes, discuss the results of comparing sample variances of its output to the associated Cramér-Rao lower bounds, and present image restorations obtained by using data collected with ground-based telescopes.

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Primary and secondary superresolution by data inversion

Cited by 11 publications

References 16 publications

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

Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects

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