Abstract:In this communication, a fast reconstruction algorithm is proposed for fluorescence blind structured illumination microscopy (SIM) under the sample positivity constraint. This new algorithm is by far simpler and faster than existing solutions, paving the way to 3D and real-time 2D reconstruction.
“…In comparison, our approach only requires that the illuminations cancel-out the fluorescent object and that their sum is known with sufficient accuracy. Finally, we also note that [20] corresponds to an early version of this work. Compared to [20], several important contributions are presented here, mainly: the super-resolving power of Blind-SIM is now studied in details, and a comprehensive presentation of the proposed PPDS algorithm includes a tuning strategy for the algorithm parameter that allows a substantial reduction of the computation time.…”
Section: Introductionmentioning
confidence: 93%
“…For our specific problem, the implementation of the PPDS iteration requires first the conjugate function (20): with h defined by (14b), the Fenchel conjugate is easily found and reads P σh (ω) = vect (min {ωn, α}) .…”
Section: Resolution Of the Joint Blind-sim Sub-problemmentioning
confidence: 99%
“…According to [20], let us first consider problem (2) without the equality constraint (2b). It is equivalent to M independent quadratic minimization problems:…”
Section: A Reformulation Of the Optimization Problemmentioning
The blind structured illumination microscopy strategy proposed by Mudry et al. is fully re-founded in this paper, unveiling the central role of the sparsity of the illumination patterns in the mechanism that drives super-resolution in the method. A numerical analysis shows that the resolving power of the method can be further enhanced with optimized one-photon or two-photon speckle illuminations. A much improved numerical implementation is provided for the reconstruction problem under the image positivity constraint. This algorithm rests on a new preconditioned proximal iteration faster than existing solutions, paving the way to 3D and real-time 2D reconstruction.
“…In comparison, our approach only requires that the illuminations cancel-out the fluorescent object and that their sum is known with sufficient accuracy. Finally, we also note that [20] corresponds to an early version of this work. Compared to [20], several important contributions are presented here, mainly: the super-resolving power of Blind-SIM is now studied in details, and a comprehensive presentation of the proposed PPDS algorithm includes a tuning strategy for the algorithm parameter that allows a substantial reduction of the computation time.…”
Section: Introductionmentioning
confidence: 93%
“…For our specific problem, the implementation of the PPDS iteration requires first the conjugate function (20): with h defined by (14b), the Fenchel conjugate is easily found and reads P σh (ω) = vect (min {ωn, α}) .…”
Section: Resolution Of the Joint Blind-sim Sub-problemmentioning
confidence: 99%
“…According to [20], let us first consider problem (2) without the equality constraint (2b). It is equivalent to M independent quadratic minimization problems:…”
Section: A Reformulation Of the Optimization Problemmentioning
The blind structured illumination microscopy strategy proposed by Mudry et al. is fully re-founded in this paper, unveiling the central role of the sparsity of the illumination patterns in the mechanism that drives super-resolution in the method. A numerical analysis shows that the resolving power of the method can be further enhanced with optimized one-photon or two-photon speckle illuminations. A much improved numerical implementation is provided for the reconstruction problem under the image positivity constraint. This algorithm rests on a new preconditioned proximal iteration faster than existing solutions, paving the way to 3D and real-time 2D reconstruction.
“…A major alternative to harmonic modulation in classical SIM is the blind-SIM approach [10][11][12][13]. With the blind-SIM approach, a large number of images is generated with different illumination patterns created by speckle.…”
Super-resolution in Structured Illumination Microscopy (SIM) is obtained through de-aliasing of modulated raw images, in which high frequencies are measured indirectly inside the optical transfer function. Usual approaches that use 9 or 15 images are often too slow for dynamic studies. Moreover, as experimental conditions change with time, modulation parameters must be estimated within the images. This paper tackles the problem of image reconstruction for fast super resolution in SIM, where the number of available raw images is reduced to four instead of nine or fifteen. Within an optimization framework, the solution is inferred via a joint myopic criterion for image and modulation (or acquisition) parameters, leading to what is frequently called a myopic or semi-blind inversion problem. The estimate is chosen as the minimizer of the nonlinear criterion, numerically calculated by means of a block coordinate optimization algorithm. The effectiveness of the proposed method is demonstrated for simulated and experimental examples. The results show precise estimation of the modulation parameters jointly with the reconstruction of the super resolution image. The method also shows its effectiveness for thick biological samples.
“…These algorithms are robust and were previously used in LP-SIM since LP patterns are not perfectly sinusoidal [11,12]. The details of these procedures can be looked up elsewhere [1, 7,8,12,14,17,18]. Other experimental imperfections (such as aberrations in the detection PSF) may reduce the SNR but would not render the technique unviable in general.…”
We propose to enhance the performance of localized plasmon structured illumination microscopy (LP-SIM) via intensity correlations. LP-SIM uses sub-wavelength illumination patterns to encode high spatial frequency information. It can enhance the resolution up to threefold before gaps in the OTF support arise. For blinking fluorophores or for quantum antibunching an intensity correlation analysis induces higher harmonics of the illumination pattern and enlarges the effective OTF. This enables ultrahigh resolutions without gaps in the OTF support, and thus a fully deterministic imaging scheme. We present simulations that include shot and external noise and demonstrate the resolution power under realistic photon budgets. The technique has potential in light microscopy where low-intensity illumination is paramount while aiming for high spatial but moderate temporal resolutions.
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