Combining deep learning with SUPPOSe and compressed sensing for SNR-enhanced localization of overlapping emitters

Abstract

We present gSUPPOSe, a novel, to the best of our knowledge, gradient-based implementation of the SUPPOSe algorithm that we have developed for the localization of single emitters. We study the performance of gSUPPOSe and compressed sensing STORM (CS-STORM) on simulations of single-molecule localization microscopy (SMLM) images at different fluorophore densities and in a wide range of signal-to-noise ratio conditions. We also study the combination of these methods with prior image denoising by means of a deep convolutional network. Our results show that gSUPPOSe can address the localization of multiple overlapping emitters even at a low number of acquired photons, outperforming CS-STORM in our quantitative analysis and having better computational times. We also demonstrate that image denoising greatly improves CS-STORM, showing the potential of deep learning enhanced localization on existing SMLM algorithms. The software developed in this work is available as open source Python libraries.

Improving STED microscopy with SUPPOSe: enhancing resolution from a single-image

“…BA averages these two effects, indicating a slightly better performance for a larger PSF than the exact one (note that the optimum value is at size +10 %), which may be due to the pixel size and low SNR of the images. These behaviours corresponds to the ones observed in [13], where a thorough analysis of the capabilities of SUP-POSe to localize single emitters within the PSF is presented.…”

“…There are some basic recommendations when applying SUPPOSe to experimental images. Despite being very robust against high-frequency noise, SUP-POSe solutions may be affected by low-frequency noise that introduces artifacts from overfitting [13]. In a previous work it was shown that it is possible to detect these artifacts by acquiring at least three images of the same region under working conditions, and then process them separately to compare the reconstructions [12].…”

“…On the other hand, a narrow PSF introduces false positives by making the clusters disaggregate into smaller ones, which is consistent with underestimating the true PSF size because a single cluster of virtual sources will not be enough to cover the whole spot of a sub-resolution emitter. Noise artifacts also depend on the ratio between PSF size and pixel size because SUPPOSe is only sensitive to noise at frequency components near and below the PSF cutoff [13]. As the PSF size becomes similar to the pixel size, the algorithm struggles to differentiate the noise fluctuations from the emitters' signal, and the spurious local minima in the fitness function introduces a number of low-intensity clusters that becomes significant at the smallest PSF sizes.…”

“…In this sense, the SUPPOSe method is a convolution-based algorithm for improving microscopy images that relies on representing any object under test as a superposition of virtual point sources, all with the same intensity [8][9][10][11]. By knowing the image formation process, SUPPOSe solves an optimization problem that retrieves the optimum set of positions of the virtual sources and their intensity from a single image, resulting in a description of the object with a resolution that is more than three times better the instrument resolution under normal measurement conditions [12,13]. Thus, SUP-POSe enhances the image resolution by combining information about the instrument response, a simple and intuitive representation of the sample, and a mathematical model based on general principles of optical microscopy.…”

Improving the resolution of STED microscopy using the SUPPOSe algorithm

“…In fluorescence microscopy, each acquired sample is the result of a noise process acting on the convolution between an underlying object -an arrangement of fluorescent proteins tied to the things we want to see-with the microscope response function -known as Point Spread Function or PSF. SUPPOSe is a convolution-based algorithm for improving microscopy images that relies on representing the object under microscope as a SUPperposition of POint SourcEs with the same intensity [1][2][3][4][5][6][7][8]. By knowing the instrument Point-Spread Function (PSF) and the image formation model, the optimum position of these sources can be retrieved by iteratively solving an optimization problem that results in a description of the object with better resolution than the image itself.…”