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We propose a low rank structured matrix completion algorithm for image inpainting problems originated from scanning microscopy. The proposed method exploits the annihilation property observed in Gaussian Markov Random Field (GMRF) or partial differential equation (PDE)-based inpainting approaches. By utilizing the commutative property of the convolution, the annihilation property is embodied into...
A variety of far-field super-resolution microscopy techniques have been proposed recently by exploiting nonlinear phenomenon in optics or specialized photo-switchable probes. Here, we present a linear optics based super-resolution microscopy for standard probes and experimental protocols. Rather than exploiting the nonlinearity in optics or photo-switchable probes, we use a nonlinear reconstruction...
Super-resolution localization microscopy relies on sparse activation of photo-switchable probes. Such activation, however, introduces limited temporal resolution. High-density imaging overcomes this limitation by allowing several neighboring probes to be activated simultaneously. In this work, we propose an algorithm that incorporates a continuous-domain sparsity prior into the high-density localization...
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