Super-resolution fight club

Holden, Séamus; Sage, Daniel

doi:10.1038/nphoton.2016.22

Cited by 12 publications

(9 citation statements)

References 9 publications

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“…Moving the spikes positions takes advantage of the continuous framework of the problem (the domain X is not discretized) which is the main ingredient that leads to a typical N -step convergence observed empirically. Finally, this approach has later been used in [10] and provides state of the art results in many sparse inverse problems such as matrix completion or Single Molecule Localization Microscopy (SMLM) [50,73].…”

Section: Solving the Blassomentioning

confidence: 99%

The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy

Denoyelle¹,

Duval²,

Peyré³

et al. 2019

Inverse Problems

167

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This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem.The BLASSO is a continuous (i.e. off-the-grid or grid-less) counterpart to the well-known 1 sparse regularisation method (also known as LASSO or Basis Pursuit). Our algorithm is a variation on the classical Frank-Wolfe (also known as conditional gradient) which follows a recent trend of interleaving convex optimization updates (corresponding to adding new spikes) with non-convex optimization steps (corresponding to moving the spikes). Our main theoretical result is that this algorithm terminates in a finite number of steps under a mild non-degeneracy hypothesis. We then target applications of this method to several instances of single molecule fluorescence imaging modalities, among which certain approaches rely heavily on the inversion of a Laplace transform. Our second theoretical contribution is the proof of the exact support recovery property of the BLASSO to invert the 1-D Laplace transform in the case of positive spikes. On the numerical side, we conclude this paper with an extensive study of the practical performance of the Sliding Frank-Wolfe on different instantiations of single molecule fluorescence imaging, including convolutive and non-convolutive (Laplace-like) operators. This shows the versatility and superiority of this method with respect to alternative sparse recovery technics.

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Section: Solving the Blassomentioning

confidence: 99%

The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy

Denoyelle¹,

Duval²,

Peyré³

et al. 2019

Inverse Problems

167

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show abstract

“…In this section we briefly describe existing techniques, almost all of which are based on maximum-likelihood estimation. Maximum-likelihood and regularized maximum-likelihood methods for inverse problems have proven to be effective over a wide variety of applications, and SMLM is no exception: the highest-performing SMLM algorithms are all variations on maximum-likelihood estimation [18,38]. In this section we describe one family of convex approximations to the SMLM maximum-likelihood estimation problem.…”

Section: Maximum-likelihood Methodsmentioning

confidence: 99%

DeepLoco: Fast 3D Localization Microscopy Using Neural Networks

Boyd¹,

Jonas²,

Babcock³

et al. 2018

Preprint

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Single-molecule localization super-resolution microscopy (SMLM) techniques like STORM and PALM have transformed cellular microscopy by substantially increasing spatial resolution. In this paper we introduce a new algorithm for a critical part of the SMLM process: estimating the number and locations of the fluorophores in a single frame. Our algorithm can analyze a 20000-frame experimental 3D SMLM dataset in about one second -substantially faster than real-time and existing algorithms. Our approach is straightforward but very different from existing algorithms: we train a neural network to minimize the Bayes' risk under a generative model for single SMLM frames. The neural network maps a frame directly to a collection of fluorophore locations, which we compare to the ground truth using a novel loss function. While training the neural network takes several hours, it only has to be done once for a given experimental setup. After training, localizing fluorophores in new images is extremely fast -orders of magnitude faster than existing algorithms. Faster recovery opens the door to real-time calibration and accelerated acquisition, and future work could tackle more complicated optical systems and more realistic simulators.

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“…Penalty parameters were chosen by a visual inspection of the results (except for simulations for which some metrics such as the recall rate or the number of false‐positives can be used, see supporting information and Holden and Sage). A future challenge is to find a way to estimate the penalty parameters in an automatic way to avoid manual tuning and visual inspection of the results.…”

Section: Methodsmentioning

confidence: 99%

“…In each frame, ideally, only a sparse subset of fluorophores is active, and for each pixel of the camera, a time trace is observed from the blinking dynamics of the fluorophore(s) whose signal contributed at this position. How to analyze the so obtained data cube is the second most important aspect in superresolution fluorescence microscopy …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved superresolution microscopy imaging by sparse deconvolution with an interframe penalty

Hugelier

Eilers

Devos

et al. 2016

Journal of Chemometrics

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Penalized regression with a combination of sparseness and an interframe penalty is explored for image deconvolution in wide‐field single‐molecule fluorescence microscopy. The aim is to reconstruct superresolution images, which can be achieved by averaging the positions and intensities of individual fluorophores obtained from the analysis of successive frames. Sparsity of the fluorophore distribution in the spatial domain is obtained with an L0‐norm penalty on estimated fluorophore intensities, effectively constraining the number of fluorophores per frame. Simultaneously, continuity of the fluorophore localizations in the time mode is obtained by penalizing the total numbers of pixel status changes between successive frames. We implemented the interframe penalty in a sparse deconvolution algorithm (sparse image deconvolution and reconstruction) for improved imaging of densely labeled biological samples. For simulated and real biological data, we show that more accurate estimates of the final superresolution images of cellular structures can be obtained.

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Super-resolution fight club

Cited by 12 publications

References 9 publications

The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy

The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy

DeepLoco: Fast 3D Localization Microscopy Using Neural Networks

Improved superresolution microscopy imaging by sparse deconvolution with an interframe penalty

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