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Imaging beyond the diffraction limit barrier has attracted wide attention due to the ability to resolve previously hidden image features. Of the various super-resolution microscopy techniques available, a particularly simple method called saturated excitation microscopy (SAX) requires only simple modification of a laser scanning microscope: The illumination beam power is sinusoidally modulated and driven into saturation. SAX images are extracted from the harmonics of the modulation frequency and exhibit improved spatial resolution. Unfortunately, this elegant strategy is hindered by the incursion of shot noise that prevents high-resolution imaging in many realistic scenarios. Here, we demonstrate a technique for super-resolution imaging that we call computational saturated absorption (CSA) in which a joint deconvolution is applied to a set of images with diversity in spatial frequency support among the point spread functions (PSFs) used in the image formation with saturated laser scanning fluorescence microscopy. CSA microscopy allows access to the high spatial frequency diversity in a set of saturated effective PSFs, while avoiding image degradation from shot noise.
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Stable super-resolution of images: theoretical study
Abstract We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex feasibility program, which simply finds a non-negative Borel measure that agrees with the observations collected by the imaging device. In the absence of imaging noise, we show that solving this convex program uniquely retrieves the point sources, provided that the imaging device collects enough observations. This result holds true if the point spread function of the imaging device can be decomposed into horizontal and vertical components and if the translations of these components form a Chebyshev system, i.e., a system of continuous functions that loosely behave like algebraic polynomials. Building upon the recent results for one-dimensional signals, we prove that this super-resolution algorithm is stable, in the generalized Wasserstein metric, to model mismatch (i.e., when the image is not sparse) and to additive imaging noise. In particular, the recovery error depends on the noise level and how well the image can be approximated with well-separated point sources. As an example, we verify these claims for the important case of a Gaussian point spread function. The proofs rely on the construction of novel interpolating polynomials—which are the main technical contribution of this paper—and partially resolve the question raised in Schiebinger et al. (2017, Inf. Inference, 7, 1–30) about the extension of the standard machinery to higher dimensions.
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- Award ID(s):
- 1704204
- PAR ID:
- 10253370
- Date Published:
- Journal Name:
- Information and Inference: A Journal of the IMA
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2049-8772
- Page Range / eLocation ID:
- 161 to 193
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/imaiai/iaaa029
