Abstract
Random illumination microscopy (RIM) using uncontrolled speckle patterns has shown the capacity to surpass the Abbe's diffraction barrier, providing the possibility to design inexpensive and versatile structured illumination microscopy (SIM) devices. In this paper, I first present a review of the state-of-the-art joint reconstruction methods in RIM, and then propose a unified joint reconstruction approach in which the performance of various regularization terms can be evaluated under the same model. The model hyperparameter is easily tuned and robust in comparison to the previous methods and ℓ2,1 regularizer is proven to be a reasonable prior in most practical situations. Moreover, the degradation entailed by out-of-focus light in conventional SIM can be easily solved in RIM setup.
Highlights
The results shown in the first column are obtained by only considering p,q norm regularizer while the images shown in the second column are obtained using p,q norm regularizer plus the total variation (TV) regularizer, with the hyperparameters μ = 0
In this paper a unified joint reconstruction approach in blindspeckleSIM based on constrained p,q norm minimization of the data is proposed, other prior information of the object can be incorporated into the model without big changes of the associated optimization algorithm
Mathematical analysis demonstrates that the joint sparsity of matrix Q implies the sparsity assumption of the object
Summary
T HE conventional optical microscopy is a diffraction limited system whose spatial resolution is limited by diffraction effect (often modeled as a low-pass filter in Fourier domain). In reference [13], a marginal approach is reported and the super-resolution capacity of blind-speckleSIM has been demonstrated as good as classic SIM by taking advantage of the second-order statistics of the data in asymptotic condition when the Fourier support of speckle is identified with the OTF of system. Where · F denotes Frobenius norm, Q = [q1, · · · , qM ] = [ρ ◦ I1, · · · , ρ ◦ IM ] and Φ(Q) is the regularizer term that enforces the priori knowledge of Q, such as positivity constraint [1], positivity and sparsity constraint [2], or joint sparsity constraint [11] In this model, the super-resolution is induced by the regularizer term, while the data fidelity term gives no super-resolution information if only the first order statistics of speckle is used [2]
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