Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems.

Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond to the likelihood and prior-probability models, respectively. The Bayesian approach gives more flexibility in choosing these terms and, in particular, the prior term via hierarchical models and hidden variables. However, the Bayesian computations can become very heavy computationally. The machine learning (ML) methods such as classification, clustering, segmentation, and regression, based on neural networks (NN) and particularly convolutional NN, deep NN, physics-informed neural networks, etc. can become helpful to obtain approximate practical solutions to inverse problems. In this tutorial article, particular examples of image denoising, image restoration, and computed-tomography (CT) image reconstruction will illustrate this cooperation between ML and inversion.

Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain.

In this paper, a hierarchical prior model based on the Haar transformation and an appropriate Bayesian computational method for X-ray CT reconstruction are presented. Given the piece-wise continuous property of the object, a multilevel Haar transformation is used to associate a sparse representation for the object. The sparse structure is enforced via a generalized Student-t distribution ( S t g ), expressed as the marginal of a normal-inverse Gamma distribution. The proposed model and corresponding algorithm are designed to adapt to specific 3D data sizes and to be used in both medical and industrial Non-Destructive Testing (NDT) applications. In the proposed Bayesian method, a hierarchical structured prior model is proposed, and the parameters are iteratively estimated. The initialization of the iterative algorithm uses the parameters of the prior distributions. A novel strategy for the initialization is presented and proven experimentally. We compare the proposed method with two state-of-the-art approaches, showing that our method has better reconstruction performance when fewer projections are considered and when projections are acquired from limited angles.

Clinical Relevance of the First Domomedicine Platform Securing Multidrug Chronotherapy Delivery in Metastatic Cancer Patients at Home: The inCASA European Project.

BACKGROUND: Telehealth solutions can improve the safety of ambulatory chemotherapy, contributing to the maintenance of patients at their home, hence improving their well-being, all the while reducing health care costs. There is, however, need for a practicable multilevel monitoring solution, encompassing relevant outputs involved in the pathophysiology of chemotherapy-induced toxicity. Domomedicine embraces the delivery of complex care and medical procedures at the patient's home based on modern technologies, and thus it offers an integrated approach for increasing the safety of cancer patients on chemotherapy. OBJECTIVE: The objective was to evaluate patient compliance and clinical relevance of a novel integrated multiparametric telemonitoring domomedicine platform in cancer patients receiving multidrug chemotherapy at home. METHODS: Self-measured body weight, self-rated symptoms using the 19-item MD Anderson Symptom Inventory (MDASI), and circadian rest-activity rhythm recording with a wrist accelerometer (actigraph) were transmitted daily by patients to a server via the Internet, using a dedicated platform installed at home. Daily body weight changes, individual MDASI scores, and relative percentage of activity in-bed versus out-of-bed (I

An interpretable machine learning approach to study the relationship beetwen retrognathia and skull anatomy.

Mandibular retrognathia (C2Rm) is one of the most common oral pathologies. Acquiring a better understanding of the points of impact of C2Rm on the entire skull is of major interest in the diagnosis, treatment, and management of this dysmorphism, but also permits us to contribute to the debate on the changes undergone by the shape of the skull during human evolution. However, conventional methods have some limits in meeting these challenges, insofar as they require defining in advance the structures to be studied, and identifying them using landmarks. In this context, our work aims to answer these questions using AI tools and, in particular, machine learning, with the objective of relaying these treatments automatically. We propose an innovative methodology coupling convolutional neural networks (CNNs) and interpretability algorithms. Applied to a set of radiographs classified into physiological versus pathological categories, our methodology made it possible to: discuss the structures impacted by retrognathia and already identified in literature; identify new structures of potential interest in medical terms; highlight the dynamic evolution of impacted structures according to the level of gravity of C2Rm; provide for insights into the evolution of human anatomy. Results were discussed in terms of the major interest of this approach in the field of orthodontics and, more generally, in the field of automated processing of medical images.

Bayesian approach with hidden Markov modeling and mean field approximation for hyperspectral data analysis.

The main problems in hyperspectral image analysis are spectral classification, segmentation, and data reduction. In this paper, we propose a Bayesian estimation approach which gives a joint solution for these problems. The problem is modeled as a blind sources separation (BSS). The data are M hyperspectral images and the sources are K < M images which are composed of compact homogeneous regions and have mutually disjoint supports. The set of all these regions cover the total surface of the observed scene. To insure these properties, we propose a hierarchical Markov model for the sources with a common hidden classification field which is modeled via a Potts-Markov field. The joint Bayesian estimation of the hidden variable, sources, and the mixing matrix of the BSS gives a solution for all three problems: spectra classification, segmentation, and data reduction of hyperspectral images. The mean field approximation (MFA) algorithm for the posterior laws is proposed for the effective Bayesian computation. Finally, some results of the application of the proposed methods on simulated and real data are given to illustrate the performance of the proposed method compared to other classical methods, such as PCA and ICA.

Hidden Markov models for wavelet-based blind source separation.

In this paper, we consider the problem of blind source separation in the wavelet domain. We propose a Bayesian estimation framework for the problem where different models of the wavelet coefficients are considered: the independent Gaussian mixture model, the hidden Markov tree model, and the contextual hidden Markov field model. For each of the three models, we give expressions of the posterior laws and propose appropriate Markov chain Monte Carlo algorithms in order to perform unsupervised joint blind separation of the sources and estimation of the mixing matrix and hyper parameters of the problem. Indeed, in order to achieve an efficient joint separation and denoising procedures in the case of high noise level in the data, a slight modification of the exposed models is presented: the Bernoulli-Gaussian mixture model, which is equivalent to a hard thresholding rule in denoising problems. A number of simulations are presented in order to highlight the performances of the aforementioned approach: 1) in both high and low signal-to-noise ratios and 2) comparing the results with respect to the choice of the wavelet basis decomposition.

Precise periodic components estimation for chronobiological signals through Bayesian Inference with sparsity enforcing prior.

The toxicity and efficacy of more than 30 anticancer agents present very high variations, depending on the dosing time. Therefore, the biologists studying the circadian rhythm require a very precise method for estimating the periodic component (PC) vector of chronobiological signals. Moreover, in recent developments, not only the dominant period or the PC vector present a crucial interest but also their stability or variability. In cancer treatment experiments, the recorded signals corresponding to different phases of treatment are short, from 7 days for the synchronization segment to 2 or 3 days for the after-treatment segment. When studying the stability of the dominant period, we have to consider very short length signals relative to the prior knowledge of the dominant period, placed in the circadian domain. The classical approaches, based on Fourier transform (FT) methods are inefficient (i.e., lack of precision) considering the particularities of the data (i.e., the short length). Another particularity of the signals considered in such experiments is the level of noise: such signals are very noisy and establishing the periodic components that are associated with the biological phenomena and distinguishing them from the ones associated with the noise are difficult tasks. In this paper, we propose a new method for the estimation of the PC vector of biomedical signals, using the biological prior informations and considering a model that accounts for the noise. The experiments developed in cancer treatment context are recording signals expressing a limited number of periods. This is a prior information that can be translated as the sparsity of the PC vector. The proposed method considers the PC vector estimation as an Inverse Problem (IP) using the general Bayesian inference in order to infer the unknown of our model, i.e. the PC vector but also the hyperparameters (i.e the variances). The sparsity prior information is modeled using a sparsity enforcing prior law. In this paper, we propose a Student's t distribution, viewed as the marginal distribution of a bivariate normal-inverse gamma distribution. We build a general infinite Gaussian scale mixture (IGSM) hierarchical model where we assign prior distributions also for the hyperparameters. The expression of the joint posterior law of the unknown PC vector and hyperparameters is obtained via Bayes rule, and then, the unknowns are estimated via joint maximum a posteriori (JMAP) or posterior mean (PM). For the PM estimator, the expression of the posterior distribution is approximated by a separable one, via variational Bayesian approximation (VBA), using the Kullback-Leibler (KL) divergence. For the PM estimation, two possibilities are considered: an approximation with a partially separable distribution and an approximation with a fully separable one. Both resulting algorithms corresponding to the PM estimation and the one corresponding to the JMAP estimation are iterative algorithms. The algorithms are presented in detail and are compared with the ones corresponding to the Gaussian model. We examine the convergency of the algorithms and give simulation results to compare their performances. Finally, we show simulation results on synthetic and real data in cancer treatment applications. The real data considered in this paper examines the rest-activity patterns of KI/KI Per2::luc mouse, aged 10 weeks, singly housed in RealTime Biolumicorder (RT-BIO).

Polygonal and polyhedral contour reconstruction in computed tomography.

This paper is about three-dimensional (3-D) reconstruction of a binary image from its X-ray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonlinear inverse problem using the Bayesian framework. Vertice estimation is done without using a voxel approximation of the 3-D image. It is based on the construction and optimization of a regularized criterion that accounts for surface smoothness. We investigate original deterministic local algorithms, based on the exact computation of the line projections, their update, and their derivatives with respect to the vertice coordinates. Results are first derived in the two-dimensional (2-D) case, which consists of reconstructing a 2-D object of deformable polygonal contour from its tomographic data. Then, we investigate the 3-D extension that requires technical adaptations. Simulation results illustrate the performance of polygonal and polyhedral reconstruction algorithms in terms of quality and computation time.

A circadian clock transcription model for the personalization of cancer chronotherapy.

Circadian timing of anticancer medications has improved treatment tolerability and efficacy several fold, yet with intersubject variability. Using three C57BL/6-based mouse strains of both sexes, we identified three chronotoxicity classes with distinct circadian toxicity patterns of irinotecan, a topoisomerase I inhibitor active against colorectal cancer. Liver and colon circadian 24-hour expression patterns of clock genes Rev-erbα and Bmal1 best discriminated these chronotoxicity classes, among 27 transcriptional 24-hour time series, according to sparse linear discriminant analysis. An 8-hour phase advance was found both for Rev-erbα and Bmal1 mRNA expressions and for irinotecan chronotoxicity in clock-altered Per2(m/m) mice. The application of a maximum-a-posteriori Bayesian inference method identified a linear model based on Rev-erbα and Bmal1 circadian expressions that accurately predicted for optimal irinotecan timing. The assessment of the Rev-erbα and Bmal1 regulatory transcription loop in the molecular clock could critically improve the tolerability of chemotherapy through a mathematical model-based determination of host-specific optimal timing.

Joint NDT image restoration and segmentation using Gauss-Markov-Potts prior models and variational Bayesian computation.

In this paper, we propose a method to simultaneously restore and to segment piecewise homogeneous images degraded by a known point spread function (PSF) and additive noise. For this purpose, we propose a family of nonhomogeneous Gauss-Markov fields with Potts region labels model for images to be used in a Bayesian estimation framework. The joint posterior law of all the unknowns (the unknown image, its segmentation (hidden variable) and all the hyperparameters) is approximated by a separable probability law via the variational Bayes technique. This approximation gives the possibility to obtain practically implemented joint restoration and segmentation algorithm. We will present some preliminary results and comparison with a MCMC Gibbs sampling based algorithm. We may note that the prior models proposed in this work are particularly appropriate for the images of the scenes or objects that are composed of a finite set of homogeneous materials. This is the case of many images obtained in nondestructive testing (NDT) applications.