Entropy-Based Super-Resolution Imaging (ESI): From Disorder to Fine Detail

Abstract

We introduce a novel and universal method for fast optical high -as well as superresolution imaging. Our method is based on reconstructing super-resolved images from conventional image sequences containing rapid random signal fluctuations. Such sequences could be obtained from either wide-field single-molecule blinking experiments or rapid image sequences with fluorophores undergoing random intensity fluctuations. By calculating the local entropy (H) and cross-entropy (xH) values pixel-by-pixel, weighted with higher order-statistics (HOS), a new image with pixel intensities representing the true information content in the time series is obtained. We show that analyzing image sequences by this formalism enables the reconstruction of super-resolved images, where the optical resolution that can be achieved depends only on the number of input frames and the higher order moments used for the calculation. We find that the acquisition of <100 frames per sequence is sufficient to reconstruct super-resolved images of entire cells. We also demonstrate that not only on-off switching of the fluorescent dyes, but also other dynamic events, i.e. photobleaching, can be exploited for

Multiple signal classification algorithm for super-resolution fluorescence microscopy

“…Such techniques include super-resolution optical fluctuations imaging (SOFI [5]), Bayesian analysis of blinking and bleaching (3B [6]), and entropy-based super-resolution imaging (ESI [7]). Although they relax the requirements of SMLM, they do not reach resolution achievable by localization microscopy (approximately 110 nm for SOFI [8], 80 nm for ESI [7], and 50 nm for 3B [6]) and they possess limitations of their own. For example, SOFI uses cumulants of the fluorescence blinking to enhance resolution; since cumulants of orders higher than 6 are prone to shot noise and do not have good approximations, the practically achievable resolution improvement is limited to the factor of √ 6 [5].…”

Nanoscopy on the Chea(i)p

“…1a) enables both the destruction of the static mode field pattern produced by the mode-selective behavior of the WGs [28,34] at frequencies higher than the pixel integration time (e.g. ≥ 500 Hz) or the realization of fluctuating intensity-based super-resolution methods such as SOFI [35], SRRF [18] or ESI [21] at lower-frequencies (e.g. ≤ 10 Hz), where each frame sees a different emitted signal.…”

“…Further, we demonstrate how the immense computational power of the cellphone ensures an improvement in image quality without transferring data to external computers. Similar to the methods SOFI [36,34], SRRF [18] or ESI [21] we want to take advantage of mobile phone optimized image processing libraries like the machine learning framework "Tensorflow Lite [37,38] to calculate instantaneous super-resolution images from intensity fluctuations caused by a variation of the waveguide mode pattern. We aim to preserve the temporal relationship of acquired frames by designing the model using convolutional Long Short Term Memory (cLSTM, [39]) layers.…”

“…Several attempts already showed how to significantly reduce high costs and resulting exclusivity and aimed to provide greater accessibility of SRI [12,13,14]. Substituting expensive electron multiplied charged coupled device (emCCD) cameras by industry-grade [15] or even cellphone cameras [16], as well as relying on entertainment lasers [13] and compensating the lack of imaging quality with tailored image processing [17,18,19,20,21,19,22] contributed greatly to the idea of widely available high-resolution imaging platforms on a budget. Open-source 3D-printed approaches like the Openflexure [23], Attobright [24], Micube [25] or the 3D-printed optical toolbox UC2 [26] can further provide flexible and open hardware solutions in order to support software-based solutions.…”

MusiJ: an ImageJ plugin for video nanoscopy

“…The actual algorithm depends on the statistical approach, thus giving rise to various flavors of this idea. Examples include SOFI (super-resolution optical fluctuation imaging) [17], 3B (Bayesian analysis of blinking and bleaching) [18], ESI (entropy-based super-resolution imaging) [19], and SRRF (super-resolution radial fluctuations) [20]. All of the above mentioned algorithms (except SOFI) have been translated to ImageJ.…”