A number of recent works have emphasized the prominent role played by the Kurdyka-Łojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of two terms: (i) a differentiable, but not necessarily convex, function and (ii) a function that is not necessarily convex, nor necessarily differentiable. The latter function is expressed as a separable sum of functions of blocks of variables. Such an optimization problem can be addressed with the Forward–Backward algorithm which can be accelerated thanks to the use of variable metrics derived from the Majorize–Minimize principle. We propose to combine the latter acceleration technique with an alternating minimization strategy which relies upon a flexible update rule. We give conditions under which the sequence generated by the resulting Block Coordinate Variable Metric Forward–Backward algorithm converges to a critical point of the objective function. An application example to a nonconvex phase retrieval problem encountered in signal/image processing shows the efficiency of the proposed optimization method.

The SARS-COV-2 pandemic has put pressure on intensive care units, so that identifying predictors of disease severity is a priority. We collect 58 clinical and biological variables, and chest CT scan data, from 1003 coronavirus-infected patients from two French hospitals. We train a deep learning model based on CT scans to predict severity. We then construct the multimodal AI-severity score that includes 5 clinical and biological variables (age, sex, oxygenation, urea, platelet) in addition to the deep learning model. We show that neural network analysis of CT-scans brings unique prognosis information, although it is correlated with other markers of severity (oxygenation, LDH, and CRP) explaining the measurable but limited 0.03 increase of AUC obtained when adding CT-scan information to clinical variables. Here, we show that when comparing AI-severity with 11 existing severity scores, we find significantly improved prognosis performance; AI-severity can therefore rapidly become a reference scoring approach.

Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters, which can be estimated through computationally expensive and time-consuming methods. In contrast, deep learning offers very generic and efficient architectures, at the expense of explainability, since it is often used as a black-box, without any fine control over its output. Deep unfolding provides a convenient approach to combine variational-based and deep learning approaches. Starting from a variational formulation for image restoration, we develop iRestNet, a neural network architecture obtained by unfolding a proximal interior point algorithm. Hard constraints, encoding desirable properties for the restored image, are incorporated into the network thanks to a logarithmic barrier, while the barrier parameter, the stepsize, and the penalization weight are learned by the network. We derive explicit expressions for the gradient of the proximity operator for various choices of constraints, which allows training iRestNet with gradient descent and backpropagation. In addition, we provide theoretical results regarding the stability of the network for a common inverse problem example. Numerical experiments on image deblurring problems show that the proposed approach compares favorably with both state-of-the-art variational and machine learning methods in terms of image quality.

In brain MRI radiomics studies, the non-biological variations introduced by different image acquisition settings, namely scanner effects, affect the reliability and reproducibility of the radiomics results. This paper assesses how the preprocessing methods (including N4 bias field correction and image resampling) and the harmonization methods (either the six intensity normalization methods working on brain MRI images or the ComBat method working on radiomic features) help to remove the scanner effects and improve the radiomic feature reproducibility in brain MRI radiomics. The analyses were based on in vitro datasets (homogeneous and heterogeneous phantom data) and in vivo datasets (brain MRI images collected from healthy volunteers and clinical patients with brain tumors). The results show that the ComBat method is essential and vital to remove scanner effects in brain MRI radiomic studies. Moreover, the intensity normalization methods, while not able to remove scanner effects at the radiomic feature level, still yield more comparable MRI images and improve the robustness of the harmonized features to the choice among ComBat implementations.

In this work we address the problem of short-term load forecasting. We propose a generalization of the linear state-space model where the evolution of the state and the observation matrices is unknown. The proposed blind Kalman filter algorithm proceeds via alternating the estimation of these unknown matrices and the inference of the state, within the framework of expectation-maximization. A mini-batch processing strategy is introduced to allow on-the-fly forecasting. The experimental results show that the proposed method outperforms the state-of-the-art techniques by a considerable margin, both on load profile estimation and peak load forecast problems.