Hessian-based regularization for 3-D microscopy image restoration

Lefkimmiatis, Stamatios; Bourquard, Aurélien; Unser, Michaël

doi:10.1109/isbi.2012.6235914

Cited by 9 publications

(8 citation statements)

References 11 publications

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“…This is due to the fact that minimizing first derivatives does not give sufficient freedom for natural intensity variations of fluorescence images. Although this problem can be alleviated by using second-order derivatives, there are no practical numerical methods for handling the resulting complexity although there has been a recent attempt (11).…”

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

View full text Add to dashboard Cite

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“…where D is the raw data collected by the camera, H is the optimized data, m is the relative weight between the first term and the Hessian penalty, and R Hessian is the Hessian penalty (Lefkimmiatis et al, 2012), which is expressed by formula (5) where r is the position of each pixel, Ω represents the integral area that contains all pixels within the image H, and H xy is the second-order partial derivative of H versus xy, σ is a parameter that was introduced to enforce the continuity of structures along the time axis.…”

Section: Hessian Algorithm Removes Variance Noise In Single-molecule mentioning

confidence: 99%

Hessian single molecule localization microscopy using sCMOS camera

Xue

et al. 2018

Preprint

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Single-molecule localization microscopy (SMLM) has the highest spatial resolution among the existing super-resolution (SR) imaging techniques, but its temporal resolution needs further improvement. An sCMOS camera can effectively increase the imaging rate due to its large field of view and fast imaging speed. Using an sCMOS camera for SMLM imaging can significantly improve the imaging time resolution, but the unique single pixel-dependent readout noise of sCMOS cameras severely limits their application in SMLM imaging. This paper develops a Hessian-based SMLM (Hessian-SMLM) method that can correct the variance, gain and offset of a single pixel of a camera and effectively eliminate the pixel-dependent readout noise of sCMOS cameras, especially when the signal-to-noise ratio is low. Using Hessian SMLM to image mEos3.2-labeled actin was able to significantly reduce the artifacts due to camera noise.

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“…Several alternative penalty terms with higher-order derivatives have been proposed in other fields, such as image restoration [27] and microscopy imaging deconvolution [28]. These penalty terms do not directly penalize the intensity difference between neighboring pixels.…”

Section: Introductionmentioning

confidence: 99%

Low-Dose CBCT Reconstruction Using Hessian Schatten Penalties

Liu

Xiang

et al. 2017

IEEE Trans. Med. Imaging

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Cone-beam computed tomography (CBCT) has been widely used in radiation therapy. For accurate patient setup and treatment target localization, it is important to obtain high-quality reconstruction images. The total variation (TV) penalty has shown state-of-the-art performance in suppressing noise and preserving edges for statistical iterative image reconstruction, but it sometimes leads to the so-called staircase effect. In this study, we proposed to use a new family of penalties — the Hessian Schatten (HS) penalties — for CBCT reconstruction. Consisting of the second-order derivatives, the HS penalties are able to reflect the smooth intensity transitions of the underlying image without introducing the staircase effect. We discussed and compared the behaviors of several convex HS penalties with orders 1, 2, and +∞ for CBCT reconstruction. We used the majorization-minimization approach with a primal-dual formulation for the corresponding optimization problem. Experiments on two digital phantoms and two physical phantoms demonstrated the proposed penalty family’s outstanding performance over TV in suppressing the staircase effect, and the HS penalty with order 1 had the best performance among the HS penalties tested.

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Hessian-based regularization for 3-D microscopy image restoration

Cited by 9 publications

References 11 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

Hessian single molecule localization microscopy using sCMOS camera

Low-Dose CBCT Reconstruction Using Hessian Schatten Penalties

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