Statistical and numerical optimization for speckle blind structured illumination microscopy

Abstract : Conventional structured illumination microscopy (SIM) can surpass the resolution limit inoptical microscopy caused by the diffraction effect, through illuminating the object with a set of perfectly known harmonic patterns. However, controlling the illumination patterns is a difficult task. Even worse, strongdistortions of the light grid can be induced by the sample within the investigated volume, which may give rise to strong artifacts in SIM reconstructed images. Recently, blind-SIM strategies were proposed, whereimages are acquired through unknown, non-harmonic,speckle illumination patterns, which are much easier to generate in practice. The super-resolution capacity of such approaches was observed, although it was not well understood theoretically. This thesis presents two new reconstruction methods in SIM using unknown speckle patterns (blind-speckle-SIM): one joint reconstruction approach and one marginal reconstruction approach. In the joint reconstruction approach, we estimate the object and the speckle patterns together by considering a basis pursuit denoising (BPDN) model with lp,q-norm regularization, with p=>1 and 0<q<=1. The lp,q-norm is introduced based on the sparsity assumption of the object. In the marginal approach, we only reconstruct the object, while the unknown speckle patterns are considered as nuisance parameters. Our contribution is two fold. First, a theoretical analysis demonstrates that using the second order statistics of the data, blind-speckle-SIM yields a super-resolution factor of two, provided that the support of the speckle spectral density equals the frequency support of the microscope point spread function. Then, numerical implementation is addressed. In order to reduce the computational burden and the memory requirement of the marginal approach, a patch-based marginal estimator is proposed. The key idea behind the patch-based estimator consists of neglecting the correlation information between pixels from different patches. Simulation results and experiments with real data demonstrate the super-resolution capacity of our methods. Moreover, our proposed methods can not only be applied in 2D super-resolution problems with thin samples, but are also compatible with 3D imaging problems of thick samples.
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Penghuan Liu. Statistical and numerical optimization for speckle blind structured illumination microscopy. Optics / Photonic. École centrale de Nantes, 2018. English. ⟨NNT : 2018ECDN0008⟩. ⟨tel-01973622⟩

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