Sparsity-based super-resolution microscopy from correlation information

Abstract

For more than a century, the wavelength of light was considered to be a fundamental limit on the spatial resolution of optical imaging. Particularly in light microscopy, this limit, known as Abbe's diffraction limit, places a fundamental constraint on the ability to image sub-cellular organelles with high resolution. However, modern microscopy techniques such as STED, PALM, and STORM, manage to recover sub-wavelength information, by relying on fluorescence imaging. Specifically, PALM/STORM acquire large sequences of fluorescence images from molecules attached to the organelles within the imaged specimen, such that in each frame only a small set of fluorophores are active. The position of each fluorophore can be found accurately in each frame, and the image is recovered by superimposing the points from all frames. The resulting grainy image is subsequently smoothed to produce the final super-resolved image with a resolution of tens of nano-meters. However, because PALM/STORM rely on many (>10,000) exposures, they suffer from poor temporal resolution. To address that, super-resolution optical fluctuation imaging (SOFI) was shown to produce sub-diffraction images with increased temporal resolution, by allowing for higher fluorophore density and exploiting the temporal statistics of the emissions. However, the improved temporal resolution of SOFI comes at the expense of its spatial resolution, which is not as high as that of PALM/STORM. Here, we present a new method called SPARCOM: sparsity-based super-resolution correlation microscopy, which combines a shorter integration time than previously reported with spatial resolution comparable to PALM and STORM. SPARCOM relies on sparsity in the correlation domain, exploiting the sparse distribution of fluorescent molecules and the lack of correlation between different emitters. We demonstrate our technique in simulations and in experiments and provide comparisons to state-of-the-art high density methods.

Learned SPARCOM: Unfolded Deep Super-Resolution Microscopy

“…To circumvent the long acquisition periods required for SMLM methods, a variety of techniques have emerged, which enable the use of a smaller number of frames for reconstructing the 2-D super-resolved image [3][4][5][6][7][8][9]. These techniques take advantage of prior information regarding either the optical setup, the geometry of the sample, or the statistics of the emitters.…”

3D super-resolution imaging using a generalized and scalable progressive refinement method on sparse recovery (PRIS)

“…For the same reason, we have access to the much higher density conditions in our characterization. PRIS also exhibit comparable performance as compared to 2D approaches [3,4,20], regardless of the fact that the 3D PSFs used in our characterizations are imposing an intrinsically more challenging recovery task as compared to the 2D approaches where the regular PSFs are much more compact. When the PSF expands a larger area (SPINDLE), we expect an increase of the overlapping region, and the total budget of photons would also spread over a larger area, resulting in a lower SNR.…”

“…where x is a vector (we dub as the target vector) accounting for all possible signal sources, y is the observation vector corresponding to the observed image, A is the sensing matrix (observation matrix) describing the linear mapping from the signal source to the observation, and  represents an additive noise component. The effect of omitting the Poisson noise is negligible as demonstrated by the existing compressive sensing applications for SR microscopy [3,4,20,21]. The following L1-norm regularized sparse recovery solves for x when A and y are known and with the prior knowledge that x is sparse (possesses a small portion of non-zero entries):…”

“…For all the correct localizations, the fitting error is defined as the displacement of the localization result from the ground truth, and the fitting precision is calculated as the standard deviation of the fitting errors. Figure 5(b) shows the comparison of PRIS with the 2D methods [3,4,20] by comparing the standard deviation of fitting errors in the XY-plane (dubbed as xy). We can see that PRIS demonstrate comparable or better performance in the lateral precision at high-density conditions (> 2.5 m -2 ).…”

“…Higher time resolution requires a faster accumulation of localized fluorophores, which can be achieved with localizations at higher emitter densities that require less frames of camera acquisitions. Such methods include fittings of multiple emitters that are demonstrated to work with moderate to high densities [18,19], and compressive sensing methods such as CSSTORM [3], L1-homotopy [4] and SOFI inspired sparse recovery [20,21].…”