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 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.

This paper provides original results on the global and local convergence properties of half-quadratic (HQ) algorithms resulting from the Geman and Yang (GY) and Geman and Reynolds (GR) primal-dual constructions. First, we show that the convergence domain of the GY algorithm can be extended with the benefit of an improved convergence rate. Second, we provide a precise comparison of the convergence rates for both algorithms. This analysis shows that the GR form does not benefit from a better convergence rate in general. Moreover, the GY iterates often take advantage of a low cost implementation. In this case, the GY form is usually faster than the GR form from the CPU time viewpoint.

Computed tomography (CT) images exhibit a variable amount of noise and blur, depending on the physical characteristics of the apparatus and the selected reconstruction method. Standard algorithms tend to favor reconstruction speed over resolution, thereby jeopardizing applications where accuracy is critical. In this paper, we propose to enhance CT images by applying half-quadratic edge-preserving image restoration (or deconvolution) to them. This approach may be used with virtually any CT scanner, provided the overall point-spread function can be roughly estimated. In image restoration, Markov random fields (MRFs) have proven to be very flexible a priori models and to yield impressive results with edge-preserving penalization, but their implementation in clinical routine is limited because they are often viewed as complex and time consuming. For these practical reasons, we focused on numerical efficiency and developed a fast implementation based on a simple three-dimensional MRF model with convex edge-preserving potentials. The resulting restoration method provides good recovery of sharp discontinuities while using convex duality principles yields fairly simple implementation of the optimization. Further reduction of the computational load can be achieved if the point-spread function is assumed to be separable. Synthetic and real data experiments indicate that the method provides significant improvements over standard reconstruction techniques and compares well with convex-potential Markov-based reconstruction, while being more flexible and numerically efficient.

This study gives original results on the global and local convergence properties of half-quadratic (HQ) algorithms resulting from the Geman and Yang (GY) and Geman and Reynolds (GR) primal-dual constructions. In particular, we show that the: convergence domain of the GY algorithm can be extended with the benefit of an improved convergence rate.