Sparsity Based Super Resolution Fluorescence Microscopy using Dictiona

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Single-shot Sparsity-based Sub-wavelength Fluorescence Imaging Using Dictionary Learning:

Single-shot Sparsity-based Sub-wavelength Fluorescence Imaging Using Dictionary Learning Maor Mutzafi 1 , Yoav Shechtman 1,2 , Yonina C. Eldar 3 , Mordechai Segev 1 1 Physics department, Technion, Israel 2 Chemistry department, Stanford , CA, USA 3 Electrical Engineering, Technion , Israel

Diffraction limit:

Diffraction limit Ernst Abbe Ernst Abbe

Diffraction limit:

- propagating waves - evanescent waves   Diffraction limit Fluorescence microscopy Light Illumination Abbe diffraction limit       Point Spread Function is a low pass filter   Can we go beyond the diffraction limit?

Slide4:

Image from D. J. Müller et al., Pharmacol. Rev. 60 ,43 (2008). E. H. Synge, Phil. Mag. 6 , 356 (1928). E. A. Ash et al., Nature 237 , 510 (1972). A. Lewis et al., Ultramicroscopy 13 , 227 (1984). E. Betzig et al., Science 251 , 1468 (1991). Scanning near-field optical microscopy

Slide5:

S. Hell et al., Opt. Lett. 19 , 780 (1994). Image from: http://www.physorg.com/news64239200.html ST imulated E mission D epletion microscopy Fluorescence microscopy

Slide6:

STORM and PALM The imaging procedure require blinking molecules

Slide7:

Every frame only a small fraction of the molecules shine When different molecules overlap, the STORM method cannot localize them and it throws these measurements away Super-localization on the center of each spot STORM and PALM Every fluorescence molecule become a spot

Slide8:

When different molecules overlap, the STORM method cannot localize them and it throws these measurements away STORM and PALM There is a minimal number of photons per pixel requirement to distinguish between the signal and noise The blinking, and the number of photons requirement, pose numerous limitations, such as acquisition time and the number of exposures required. To satisfy the minimal number of photons per pixel every frame takes ~second The total number of frames is 10,000-100,000 Acquisition time takes minutes All of these methods require multiple shots experiments STORM require 10 4 -10 5 frames Can we do sub-wavelength imaging in a SINGLE SHOT??

Sparsity as prior knowledge:

Sparsity as prior knowledge Every image, that has structure, can be represented compactly, using a small number of degrees of freedom, in some basis. We call this feature Sparsity Using the Sparsity prior knowledge we can recover the high resolution image in a single shot

Sparsity Based Super-Resolution & Phase Retrieval:

Sparsity Based Super-Resolution & Phase Retrieval Sparsity-based recovery of planar (2D) sub-wavelength structures from their far field intensity measurement SEM image   Szameit , A., et al.   Nature materials  11.5 (2012 ).   Sparse recovery Synthetic Fourier Intensity Fourier image Blurred image Measurements 90% is lost Evanescent How do we find a basis of an arbitrary image??

What is a suitable basis for compact representation?:

What is a suitable basis for compact representation? D   d The basis Sparse representation Barbara The Dictionary Dictionary: every image is a sparse superposition of the elements of the dictionary

Slide12:

What is a suitable basis for compact representation? DCT basis is used in JPEG compression method Barbara Barbara under DCT Using only 4.7% degrees of freedom Barbara is well represented We get PSNR=27.35dB DCT = Discrete Cosine Transform

Can we do better?:

Can we do better? KSVD in a learning algorithm for Dictionaries Michael Elad . , “Sparse and redundant representations” Springer publications. , 2010. KSVD algorithm D

Dictionary allows sparse representation:

Dictionary allows sparse representation Barbara Barbara under the dictionary Barbara under DCT With the same number of coefficients we get PSNR=31.62dB compared to PSNR=27.35dB under the DCT basis

Goals:

Create a high resolution Dictionary , for a specific structure (using KSVD) , from STORM experimental data Use this Dictionary for super resolution imaging from a single exposure experiment Goals

Learning the Dictionary:

Experiment #1 Learning the Dictionary Recovery of high resolution image of the Tubulin protein using STORM Downloaded from "http://bigwww.epfl.ch/ smlm /index.html".

Learning the Dictionary:

Learning the Dictionary D The Dictionary Dictionary for Tubulin proteins KSVD algorithm Set of high resolution images

Single exposure experiment:

Single exposure experiment Experiment #2 L : low-pass L d   How can we reconstruct the lost information using our dictionary?

Sparse vector recovery:

Sparse vector recovery   L d  

Sparse vector recovery:

D Sparse vector recovery   d

Sparsity-based high resolution from a single exposure – preliminary results:

Sparsity-based high resolution from a single exposure – preliminary results Low resolution single exposure

Sparsity-based high resolution from a single exposure – preliminary results:

Sparsity-based high resolution from a single exposure – preliminary results Low resolution single exposure Sparsity-based single exposure

Sparsity-based high resolution from a single exposure – preliminary results:

Sparsity-based high resolution from a single exposure – preliminary results Low resolution single exposure Sparsity-based single exposure High resolution 15,000 exposures

Sparsity-based high resolution from a single exposure – preliminary results:

Smoothed High resolution 15,000 exposures Sparsity-based high resolution from a single exposure – preliminary results Low resolution single exposure Sparsity-based single exposure

Sparsity-based high resolution from a single exposure – preliminary results:

Smoothed High resolution 15,000 exposures Sparsity-based high resolution from a single exposure – preliminary results Low resolution single exposure Sparsity-based single exposure

Reconstruction of features that disappear in STORM:

Smoothed High resolution 15,000 exposures Reconstruction of features that disappear in STORM Low resolution single exposure Sparsity-based single exposure

Summary:

Summary We showed a new technique that uses concepts from information science and enables super resolution imaging in a single-shot We can use it for STORM and use single shot instead of using 10 4 -10 5 shots Our method enables super resolution imaging of living organisms in real time and not offline as the current methods are capable Importantly, our methodology can be applied to any kind of images , provided a database of high-resolution images of the same kind is available for the dictionary learning step

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