Superresolved labeling nanoscopy based on temporally flickering nanoparticles and the Kfactor image deshadowing Tali Ilovitsh,1,* Yossef Danan,1 Asaf Ilovitsh,1 Amihai Meiri,2 Rinat Meir,1 and Zeev Zalevsky1 2
1 Faculty of Engineering, Bar Ilan University, Ramat-Gan 5290002, Israel Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, Utah, USA *
[email protected]
Abstract: Localization microscopy provides valuable insights into cellular structures and is a rapidly developing field. The precision is mainly limited by additive noise and the requirement for single molecule imaging that dictates a low density of activated emitters in the field of view. In this paper we present a technique aimed for noise reduction and improved localization accuracy. The method has two steps; the first is the imaging of gold nanoparticles that labels targets of interest inside biological cells using a lock-in technique that enables the separation of the signal from the wide spread spectral noise. The second step is the application of the K-factor nonlinear image decomposition algorithm on the obtained image, which improves the localization accuracy that can reach 5nm and enables the localization of overlapping particles at minimal distances that are closer by 65% than conventional methods. © 2015 Optical Society of America OCIS codes: (170.0180) Microscopy; (100.0100) Image processing; (100.3010) Image reconstruction techniques; (100.6640) Superresolution; (170.4090) Modulation techniques.
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1. Introduction The spatial resolution of an optical system is limited by the phenomenon of diffraction to approximately half the wavelength of the light [1–3]. In visible light microscope the diffraction limit is about 200–300 nm in the lateral direction. When imaging subcellular structures at smaller sizes, they will appear as a diffraction-limited spots in the shape of a point spread function (PSF) given by an Airy function. Localization microscopy is one category of Super resolution (SR) techniques that enable to achieve sub diffraction limit accuracy [4]. These methods, like photoactivated localization microscopy (PALM) [5] and stochastic optical reconstruction microscopy (STORM) [6], use optical control to activate a sparse subset of fluorophores labeling a structure, measure their fluorescence and determine the location of each molecule to a much higher accuracy than conventional optical methods [7]. The precision of these techniques is limited by the number of photons collected from each emitter and by assuming that there are no multiple single molecules within a diffractionlimited spot. Low photon count and high density of activated emitters increase the #232861 - $15.00 USD Received 20 Jan 2015; revised 23 Feb 2015; accepted 23 Feb 2015; published 12 Mar 2015 (C) 2015 OSA 1 Apr 2015 | Vol. 6, No. 4 | DOI:10.1364/BOE.6.001262 | BIOMEDICAL OPTICS EXPRESS 1263
localization error. Several methods were presented with the aim of localizing overlapping PSFs. One utilizes a maximum likelihood technique assuming an increased number of point sources within the recorded PSF in the localization algorithm, however it requires the use of a graphics processing unit (GPU) analysis [8–10]. Another paper uses a statistical deconvolution technique that iterates through the observed PSF with a guess-work of overlapping PSFs. This approach is very slow and requires ~10 times more computation time/frame than the other methods of single-emitter fitting [11]. The method proposed in this paper is aimed for noise reduction and enables the detection of overlapping PSFs, which increases the density of activated molecules. Therefore, it will allow faster data acquisition rates and improve localization precision. Our proposed technique is an alternative approach for molecule imaging based on the use of gold nano particles (GNPs) as biomarkers [12–16]. GNPs exhibit the localized surface plasmon resonance (SPR) effect, which is manifested by enhanced absorption and scattering at a specific optical frequency when are under optical illumination that matches this resonant wavelength [17]. However, the GNPs heat during the process and when used as biomarkers, the heat is harmful for most biological samples. This heating restricts the laser intensity and therefore increases the shot noise in the obtained image [18]. In addition, when the particles are to be detected in cells or tissues, they need to be discriminated from high background noise [19]. This dictates working in poor signal-to-noise ratio (SNR) conditions. Various imaging methods measure the scattering from GNPs tagged biological samples. These include dark-field illumination [20], differential interference contrast and video enhancement [21], and total internal reflection [22]. However, none addresses the low SNR restriction and they are all based on the use of a high laser intensity. The proposed method has two steps, first a temporally sequenced labeling (TSL) routine that was described in a previous work [23] is used to image the sample. The TSL technique increases the SNR, enables the extraction of signal even in poor photon count and improves the localization accuracy of a single particle. The reconstructed TSL image undergoes a second step of signal processing using the K-factor algorithm [24]. This algorithm reduces the overlap between closely spaced PSFs, therefore allows their detection and in addition improves the localization precision of each PSF, making this approach applicable for superresolution imaging. 2. Theoretical background The TSL is the process in which the GNPs that label a biological sample are excited using a modulated laser beam with a wavelength that matches the GNPs SPR wavelength. The modulated illumination results in a temporal flickering of the scattered light from the GNPs at a known frequency. The mathematical analysis of the technique is presented in [23]. Briefly, the captured intensity images are a temporal sequence of the light scattered from the sample that contains the GNPs. The intensity of each image is proportional to the sum of a time sample of the modulated signal and the additive noise. The obtained signal is convolved with the modulation signal and after the convolution, the elements that are at the frequency of the modulation signal are recovered (i.e. the image data), whereas components at different frequencies (i.e. the noise), are attenuated significantly. This allows the extraction of the signal from the wide spectrum noise. The next step is to apply the K-factor algorithm on the obtained TSL image. The K-factor is a nonlinear image decomposition that divides the image pattern into a nonlinear set of contrast-ordered pseudo-image factors whose joint product reassembles the original image [25,26]. The uniqueness of the decomposition is that factors that contain noise elements are distinct from those containing the image structure of interest. In this decomposition, the first few components, which have the highest contrast depth, contain mainly the desired image information while the higher orders contain mostly noise components. Therefore, it enables a distinct separation between noise and data elements. The algorithm is an iterative technique, which reduces an image The reconstructed image I(x,y) can be described mathematically as:
#232861 - $15.00 USD Received 20 Jan 2015; revised 23 Feb 2015; accepted 23 Feb 2015; published 12 Mar 2015 (C) 2015 OSA 1 Apr 2015 | Vol. 6, No. 4 | DOI:10.1364/BOE.6.001262 | BIOMEDICAL OPTICS EXPRESS 1264
M
I ( x, y ) = ∏f n ( x, y )
(1)
n =1
where M is the number of factors that reconstruct the image, and fn are the pseudo-image factors that are given by: f
( x, y ) = n
1 + kng
n
( x, y )
1 + kn
(2)
where the parameter k controls the contrast depth at each level with a value is between 0 and 1, and gn is a binary image computed as: 1 g n ( x, y ) = 0
I ( x, y )
∏
f ( x, y )
n −1
j=1 j
≥
1 1+ kn
(3)
O.W
The full reconstruction of the image involves the multiplication of all fn, n = 1…M factors. However, in a previous paper [27] we had shown that the first few factors of the decomposition, marked by fh, where h
