Compressed Sensing 3D Fluorescence Microscopy Using Optimized Phase Mask
Kyrollos YannyNick AntipaWilliam A. LibertiSam DehaeckKristina MonakhovaFanglin Linda LiuKonlin ShenRen NgLaura Waller
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Abstract:
We demonstrate a single-shot miniature 3D computational microscope with an optimized phase encoder. Our method uses sparsity-based reconstruction to achieve a 2.76-m lateral and 15،nm axial resolution across most of the 900 x 700 x 390،nm 3 volume.Keywords:
Single shot
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling matrices such as Gaussian and Bernoulli matrices. In common physically feasible signal acquisition and reconstruction scenarios such as super-resolution of images, the sensing matrix has a non-random structure with highly correlated columns. Here we present a compressive sensing recovery algorithm that exploits this correlation structure. We provide algorithmic justification as well as empirical comparisons.
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Nyquist–Shannon sampling theorem
Nyquist rate
Matrix (chemical analysis)
Signal reconstruction
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Compressed Sensing is a new sampling theorem,it points out that if a signal can be compressed under some conditions,that a very accurate reconstruction can be obtained from a relatively small number of non-traditional samples.On the basis of compressed sensing,the paper presents multiscale compressed sensing.The numerical experiments demonstrate that multiscale compressed sensing can give better quality reconstruction than a literal deployment of the compressed sensing methodology.
Signal reconstruction
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We present a single-pixel microscope with optical sectioning by combining two structured illumination methods: structured illumination microscopy (SIM) and single-pixel imaging (SPI). Experimental results are shown for the application in 3D fluorescence microscopy by scanning different axial planes.
Optical sectioning
Photoactivated localization microscopy
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Compressive sensing provides a new way for increasing the ability of information acquisition. Compressive sensing asserts that it is possible to accurately reconstruct signals from sub-Nyquist sampling,provided some additional assumptions( sparse or compressible) are made about the signal in question. The compressive imaging technology,which is based on the compressive sensing theory,integrates the processes of sensing,compression and processing perfectly,avoiding the resource waste caused by a traditional sample-then-compressframework. With a review of some of the recent progress in compressive sensing theory from the following three aspects: sparsity,the design of measuring matrix and recovery conditions,the reconstruction algorithms,several optical compressive imaging systems are introduced,and some key challenges in this area have been discussed in the end.
Nyquist rate
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Fluorescence microscopy is a useful tool to image defect nanostructures in the bulk of dielectric materials. The application of microscopy with laser-induced fluorescence on optics to detect the damage of optical films was explored. A fluorescence image system was built that incorporated in-situ damage testing capabilities. The experimental results was checked under an ex-situ Nomarski microscope.
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Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling matrices such as Gaussian and Bernoulli matrices. In common physically feasible signal acquisition and reconstruction scenarios such as super-resolution of images, the sensing matrix has a non-random structure with highly correlated columns. Here we present a compressive sensing recovery algorithm that exploits this correlation structure. We provide algorithmic justification as well as empirical comparisons.
SIGNAL (programming language)
Nyquist–Shannon sampling theorem
Nyquist rate
Matrix (chemical analysis)
Signal reconstruction
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It will be useful in biological applications if two or more physical parameters are simultaneously measured in a digital holographic microscope. In this paper, we present a hybrid digital holographic microscope that can measure simultaneously three-dimensional (3D) phase and 3D fluorescence distributions. This property has big advantage compared with conventional optical microscopes such as phase contrast microscope and fluorescence microscope. We present an optical setup for measuring both phase and fluorescence images. In the experiments, two objects that are fluorescence beads and egera densa are used. The separation method of phase and fluorescence images is presented.
Digital Holographic Microscopy
Digital holography
Digital microscope
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This paper presents a novel approach, compressive mobile sensing, to use mobile sensors to sample and reconstruct sensing fields based on compressive sensing. Compressive sensing is an emerging research field based on the fact that a small number of linear measurements can recover a sparse signal without losing any useful information. Using compressive sensing, the signal can be recovered by a sampling rate that is much lower than the requirements from the well-known Shannon sampling theory. The proposed compressive mobile sensing approach has not only the merits of compressive sensing, but also the flexibility of different sampling densities for areas of different interests. A special measurement process makes it different from normal compressive sensing. Adopting importance sampling, compressive mobile sensing enables mobile sensors to move adaptively and acquire more samples from more important areas. A motion planning algorithm is designed based on the result of sparsity analysis to locate areas of more interests. At last, experimental results of 2-D mapping are presented as an implementation compressive mobile sensing.
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Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes sure that an original sparse signal can be reconstructed from few measurements. The construction of compressed sensing matrices is a central problem in compressed sensing theory. In this paper, the deterministic compressed sensing matrices with characters of finite fields are constructed and the coherence of the matrices are computed. Furthermore, the maximum sparsity of recovering the original sparse signals by using our compressed sensing matrices is obtained. Meanwhile, a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. In the numerical simulations, our compressed sensing matrix outperforms DeVore’s matrix in the process of recovering original sparse signals.
Mutual coherence
Matrix (chemical analysis)
SIGNAL (programming language)
Restricted isometry property
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