Image reconstruction from incomplete and noisy data

Gull, S. F.; Daniell, G.J.

doi:10.1038/272686a0

Cited by 949 publications

(534 citation statements)

References 12 publications

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“…At this point, it is interesting to consider the connection between compressed sensing and existing techniques in NMR, such as maximum entropy [15][16] and minimum area [17] reconstruction, used for the related problem of computation of spectra from short, noisy data records. Recently, Stern et al showed that a specific form of iterative thresholding, a technique similar to maximum entropy and minimum area reconstruction, is equivalent to the minimum ℓ 1 norm reconstruction in compressed sensing [18].…”

Section: Key Results From Compressed Sensing Literaturementioning

confidence: 99%

Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI

Lustig

Chen

et al. 2008

Journal of Magnetic Resonance

173

203

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High polarization of nuclear spins in liquid state through dynamic nuclear polarization has enabled the direct monitoring of 13 C metabolites in vivo at very high signal to noise, allowing for rapid assessment of tissue metabolism. The abundant SNR afforded by this hyperpolarization technique makes high resolution 13 C 3D-MRSI feasible. However, the number of phase encodes that can be fit into the short acquisition time for hyperpolarized imaging limits spatial coverage and resolution. To take advantage of the high SNR available from hyperpolarization, we have applied compressed sensing to achieve a factor of 2 enhancement in spatial resolution without increasing acquisition time or decreasing coverage. In this paper, the design and testing of compressed sensing suited for a flyback 13 C 3D-MRSI sequence are presented. The key to this design was the undersampling of spectral k-space using a novel blipped scheme, thus taking advantage of the considerable sparsity in typical hyperpolarized 13 C spectra. Phantom tests validated the accuracy of the compressed sensing approach and initial mouse experiments demonstrated in vivo feasibility.

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Section: Key Results From Compressed Sensing Literaturementioning

confidence: 99%

Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI

Lustig

Chen

et al. 2008

Journal of Magnetic Resonance

173

203

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“…While a natural choice for S would appear to be the expected value of chi-squared, there is considerable debate on the matter. Gull [1989] suggested setting the parameter according to the number of significant singular values in the forward model. The efficacy of this strategy is unclear, however, and the problem remains unresolved.…”

Section: Discussionmentioning

confidence: 99%

“…A natural choice for the ''default'' profile in the occultation case is a Chapman profile or a profile from an empirical or physics-based model. One can also construct prior probability expressions that favor models with statistical correlations between spatially neighboring regions [e.g., Molina et al, 2001;Gull, 1989].…”

Section: Discussionmentioning

confidence: 99%

Inverting ionospheric radio occultation measurements using maximum entropy

Hysell

2007

Radio Science

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[1] Practical aspects of the inversion of ionospheric radio occultation data using the Abel transform and its inverse are discussed. The linear inverse transform exhibits poor error propagation characteristics, producing significant artifacts preferentially at low altitudes where they might easily be mistaken for intermediate or sporadic layers in the ionosphere. Tikhonov regularization, which can be viewed as fixed linear filtering, reduces the artifacts at the expense of discarding fine structure in the profiles. Improved results are obtained using maximum entropy and Bayesian statistics. The maximum entropy algorithm can be viewed as a nonlinear adaptive filter which suppresses artifacts while preserving fine structure to the degree the data can support. Other advantages of and avenues for improving the basic maximum entropy algorithm are discussed.

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“…The method employed here in the retrieval of the object function is that of maximum entropy (Gull & Daniell, 1978;Gull & Skilling, 1984). This technique is based on Bayesian probability theory and centres on the selection of a 'most likely' object function (given a particular point spread function) by choosing that with the highest entropy which is consistent with the evidence of the available data.…”

Section: Introductionmentioning

confidence: 99%

Crystal structure retrieval by maximum entropy analysis of atomic resolution incoherent images

McGibbon

Pennycook

Jesson

1999

Journal of Microscopy

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SummaryIn this paper, we discuss the application of the maximum entropy method to atomic resolution Z-contrast images acquired in a scanning transmission electron microscope. Zcontrast is an incoherent imaging technique, and can be described as a convolution between an object function (the real-space map of the columnar scattering cross-section to high angles) and a point spread function (the effective electron probe). As such, we show that the technique is ideally suited to maximum entropy analysis which can, given an electron probe distribution, retrieve the 'most likely' Z-contrast object function. Using both simulated and experimentally acquired data, we explore the capabilities of maximum entropy analysis when applied to atomic resolution Z-contrast images, drawing conclusions on both the range of applicability of the technique and the nature of the retrieved crystal structures. Ultimately, we show the way in which the combination of Z-contrast imaging with maximum entropy analysis can be used to yield important information on unexpected atomic structures.

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Image reconstruction from incomplete and noisy data

Cited by 949 publications

References 12 publications

Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI

Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI

Inverting ionospheric radio occultation measurements using maximum entropy

Crystal structure retrieval by maximum entropy analysis of atomic resolution incoherent images

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