Motivation: In fluorescence microscopy, single-molecule localization microscopy (SMLM) techniques aim at localizing with high-precision high-density fluorescent molecules by stochastically activating and imaging small subsets of blinking emitters. Super resolution plays an important role in this field since it allows to go beyond the intrinsic light diffraction limit. Results: In this work, we propose a deep learning-based algorithm for precise molecule localization of high-density frames acquired by SMLM techniques whose ℓ2-based loss function is regularized by non-negative and ℓ0-based constraints. The ℓ0 is relaxed through its continuous exact ℓ0 (CEL0) counterpart. The arising approach, named DeepCEL0, is parameter-free, more flexible, faster and provides more precise molecule localization maps if compared to the other state-of-the-art methods. We validate our approach on both simulated and real fluorescence microscopy data. Availability and implementation: DeepCEL0 code is freely accessible at https://github.com/sedaboni/DeepCEL0.

Deep learning methods have state-of-the-art performances in many image restoration tasks. Their effectiveness is mostly related to the size of the dataset used for the training. Deep image prior (DIP) is an energy-function framework which eliminates the dependency on the training set, by considering the structure of a neural network as an handcrafted prior offering high impedance to noise and low impedance to signal. In this paper, we analyze and compare the use of different optimization schemes inside the DIP framework for the denoising task.

In this paper, we propose a new deep learning approach based on unfolded neural networks for the reconstruction of X-ray computed tomography images from few views. We start from a model-based approach in a compressed sensing framework, described by the minimization of a least squares function plus an edge-preserving prior on the solution. In particular, the proposed network automatically estimates the internal parameters of a proximal interior point method for the solution of the optimization problem. The numerical tests performed on both a synthetic and a real dataset show the effectiveness of the framework in terms of accuracy and robustness with respect to noise on the input sinogram when compared to other different data-driven approaches.