Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration

Kempen, Geert M. P. van; Voort, H. T. M. van der; Bauman, Jakub; Strasters, K. C.

doi:10.1109/51.482846

Cited by 39 publications

(44 citation statements)

References 19 publications

(14 reference statements)

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“…The earliest work that used derivatives constructed the smoothness functional as the sum of squares of the image gradients (7). The main advantage in minimizing the sum of squares is that the cost can be expressed in Fourier space and the solution can be obtained in a single step.…”

Section: Resultsmentioning

confidence: 99%

High-resolution restoration of 3D structures from widefield images with extreme low signal-to-noise-ratio

Arigovindan

Fung

Elnatan³

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

109

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Four-dimensional fluorescence microscopy-which records 3D image information as a function of time-provides an unbiased way of tracking dynamic behavior of subcellular components in living samples and capturing key events in complex macromolecular processes. Unfortunately, the combination of phototoxicity and photobleaching can severely limit the density or duration of sampling, thereby limiting the biological information that can be obtained. Although widefield microscopy provides a very light-efficient way of imaging, obtaining high-quality reconstructions requires deconvolution to remove optical aberrations. Unfortunately, most deconvolution methods perform very poorly at low signal-to-noise ratios, thereby requiring moderate photon doses to obtain acceptable resolution. We present a unique deconvolution method that combines an entropy-based regularization function with kernels that can exploit general spatial characteristics of the fluorescence image to push the required dose to extreme low levels, resulting in an enabling technology for high-resolution in vivo biological imaging.4D microscopy | low dose microscopy | noise-suppressing regularization T he study of dynamic processes is an important facet of cell biology research. Fluorescently tagged proteins combined with four-dimensional fluorescence microscopy, which records 3D image information as a function of time, provide a powerful framework for studying the dynamics of molecular processes in vivo. One of the most crucial challenges in 4D fluorescence microscopy is to ensure that normal biological function is not significantly perturbed as a result of the high doses of illumination (phototoxicity) incurred during 4D imaging. Recent work indicates that the maximal photon dose that avoids biological perturbation is 100-to 1,000-fold lower than that typically used for in vivo imaging (1). Dose limitations are even more challenging, given the desire to densely sample in time or to record over extended periods, especially in the context of analyzing multiple subcellular components via multiwavelength imaging.Under normal imaging conditions, widefield microscopy combined with image restoration using deconvolution methods provides an excellent modality for multiwavelength 4D imaging as it makes very efficient use of the illuminating photons. However, its effectiveness, in particular its ability to resolve subcellular detail sufficiently in the presence of noise, is limited by the performance of the deconvolution method. Such limitations can seriously degrade image quality at the low signal levels required for unperturbed in vivo imaging. The noise behavior of the deconvolution algorithm is determined by the efficiency of the noise stabilization term, known as the regularization functional. In particular, the functional's ability to discriminate the noise-related high frequencies from weak high frequencies in the signal ultimately determines the final resolution of the deconvolution. Currently used noise-stabilization techniques are largely based on ad hoc form...

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Section: Resultsmentioning

confidence: 99%

High-resolution restoration of 3D structures from widefield images with extreme low signal-to-noise-ratio

Arigovindan

Fung

Elnatan³

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

109

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“…From previous experiments (van Kempen et al, 1996), we observed that the Richardson-Lucy algorithm is very sensitive to noise. We use a method that reduces this noise sensitivity by suppressing those parts of the image spectrum that do not contain any signal information (or where the noise contribution is far larger than the signal contribution).…”

Section: Restoration Methodsmentioning

confidence: 82%

“…In previous work (van Kempen et al, 1996) we have used the mean-square-error (MSE) and the I-divergence as performance measures. The MSE is given as…”

Section: Performance Measuresmentioning

confidence: 99%

“…In previous work (van Kempen et al, 1996) the performance of the iterative constrained Tikhonov-Miller (ICTM) algorithm to restore diffraction-induced distortions was compared with the Richardson-Lucy algorithm. Quantitative texture measurements, based on the greyvalue distance transform, showed that the results improved when applied to images after restoration.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, we have tested different methods for determining the regularization parameter of both the ICTM and the Carrington algorithm. Previous work (van Kempen et al, 1996) showed that a regularization parameter inversely proportional to the signal-to-noise ratio causes too much smoothing. Furthermore, we examine a method to reduce the noise sensitivity that is frequently observed with the Richardson-Lucy algorithm (Snyder & Miller, 1991).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A quantitative comparison of image restoration methods for confocal microscopy

Kempen

Vliet

Verveer

et al. 1997

Journal of Microscopy

148

111

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SummaryIn this paper, we compare the performance of three iterative methods for image restoration: the Richardson-Lucy algorithm, the iterative constrained Tikhonov-Miller algorithm (ICTM) and the Carrington algorithm. Both the ICTM and the Carrington algorithm are based on an additive Gaussian noise model, but differ in the way they incorporate the non-negativity constraint. Under low light-level conditions, this additive (Gaussian) noise model is a poor description of the actual photon-limited image recording, compared with that of a Poisson process. The RichardsonLucy algorithm is a maximum likelihood estimator for the intensity of a Poisson process. We have studied various methods for determining the regularization parameter of the ICTM and the Carrington algorithm and propose a (Gaussian) prefiltering to reduce the noise sensitivity of the Richardson-Lucy algorithm. The results of these algorithms are compared on spheres convolved with a point spread function and distorted by Poisson noise. Our simulations show that the Richardson-Lucy algorithm, with Gaussian prefiltering, produces the best result in most of the tests. Finally, we show an example of how restoration methods can improve quantitative analysis: the total amount of fluorescence inside a closed object is measured in the vicinity of another object before and after restoration.

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Calibration: Sampling Density and Spatial Resolution

Young

1998

CP Cytometry

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Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration

Cited by 39 publications

References 19 publications

High-resolution restoration of 3D structures from widefield images with extreme low signal-to-noise-ratio

High-resolution restoration of 3D structures from widefield images with extreme low signal-to-noise-ratio

A quantitative comparison of image restoration methods for confocal microscopy

Calibration: Sampling Density and Spatial Resolution

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