Constrained Plug-and-Play Priors for Image Restoration.

The Plug-and-Play framework has demonstrated that a denoiser can implicitly serve as the image prior for model-based methods for solving various inverse problems such as image restoration tasks. This characteristic enables the integration of the flexibility of model-based methods with the effectiveness of learning-based denoisers. However, the regularization strength induced by denoisers in the traditional Plug-and-Play framework lacks a physical interpretation, necessitating demanding parameter tuning. This paper addresses this issue by introducing the Constrained Plug-and-Play (CPnP) method, which reformulates the traditional PnP as a constrained optimization problem. In this formulation, the regularization parameter directly corresponds to the amount of noise in the measurements. The solution to the constrained problem is obtained through the design of an efficient method based on the Alternating Direction Method of Multipliers (ADMM). Our experiments demonstrate that CPnP outperforms competing methods in terms of stability and robustness while also achieving competitive performance for image quality.

Constrained and unconstrained deep image prior optimization models with automatic regularization.

Deep Image Prior (DIP) is currently among the most efficient unsupervised deep learning based methods for ill-posed inverse problems in imaging. This novel framework relies on the implicit regularization provided by representing images as the output of generative Convolutional Neural Network (CNN) architectures. So far, DIP has been shown to be an effective approach when combined with classical and novel regularizers. Unfortunately, to obtain appropriate solutions, all the models proposed up to now require an accurate estimate of the regularization parameter. To overcome this difficulty, we consider a locally adapted regularized unconstrained model whose local regularization parameters are automatically estimated for additively separable regularizers. Moreover, we propose a novel constrained formulation in analogy to Morozov's discrepancy principle which enables the application of a broader range of regularizers. Both the unconstrained and the constrained models are solved via the proximal gradient descent-ascent method. Numerical results demonstrate the robustness with respect to image content, noise levels and hyperparameters of the proposed models on both denoising and deblurring of simulated as well as real natural and medical images.

DeepCEL0 for 2D single-molecule localization in fluorescence microscopy.

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.

Recursive Deep Prior Video: A super resolution algorithm for time-lapse microscopy of organ-on-chip experiments.

Biological experiments based on organ-on-chips (OOCs) exploit light Time-Lapse Microscopy (TLM) for a direct observation of cell movement that is an observable signature of underlying biological processes. A high spatial resolution is essential to capture cell dynamics and interactions from recorded experiments by TLM. Unfortunately, due to physical and cost limitations, acquiring high resolution videos is not always possible. To overcome the problem, we present here a new deep learning-based algorithm that extends the well-known Deep Image Prior (DIP) to TLM Video Super Resolution without requiring any training. The proposed Recursive Deep Prior Video method introduces some novelties. The weights of the DIP network architecture are initialized for each of the frames according to a new recursive updating rule combined with an efficient early stopping criterion. Moreover, the DIP loss function is penalized by two different Total Variation-based terms. The method has been validated on synthetic, i.e., artificially generated, as well as real videos from OOC experiments related to tumor-immune interaction. The achieved results are compared with several state-of-the-art trained deep learning Super Resolution algorithms showing outstanding performances.