Inexact Bregman iteration with an application to Poisson data reconstruction

This work deals with the solution of image restoration problems by an iterative regularization method based on the Bregman iteration. Any iteration of this scheme requires to exactly compute the minimizer of a function. However, in some image reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these subproblems. In this paper, we propose an inexact version of the iterative procedure, where the inexactness in the inner subproblem solution is controlled by a criterion that preserves the convergence of the Bregman iteration and its features in image restoration problems. In particular, the method allows to obtain accurate reconstructions also when only an overestimation of the regularization parameter is known. The introduction of the inexactness in the iterative scheme allows to address image reconstruction problems from data corrupted by Poisson noise, exploiting the recent advances about specialized algorithms for the numerical minimization of the generalized Kullback–Leibler divergence combined with a regularization term. The results of several numerical experiments enable to evaluat

Optimization Methods for Image Regularization from Poisson Data

This work regards optimization techniques for image restoration problems in presence of Poisson noise. In several imaging applications (e.g. Astronomy, Microscopy, Medical Imaging) such noise is predominant; hence regularization techniques are needed in order to obtain satisfying restored images. In a variational framework, the image restoration problem consists in finding a minimum of a functional, which is the sum of two terms,: the fit–to–data and the regularization one. The trade–off between these two terms is measured by a regularization parameter. The estimation of such a parameter is very difficult due to the presence of Poisson noise. In this thesis we investigate three models regarding this parameter: a Discrepancy Model, Constrained Model and the Bregman procedure. The former two provide an estimation for the regularization parameter, but in some cases, such as low counts images, they do not allow to obtain satisfactory results. On the other hand, in presence of such images the Bregman procedure provides reliable results and, moreover, it allows to use an overestimation of the regularization parameter, giving satisfying restored images; furthermore, this procedure permits to gain a contrast enhancement on the final result. In the first part of the work, the basics on image restoration problems are recalled, and a survey on the state–of–the–art methods is given, with an original contribution regarding scaling techniques in ε–subgradient methods. Then, the Discrepancy and the Constrained Models are analyzed from both theoretical and practical point of view, developing suitable numerical techniques for their solution; furthermore, an inexact version of the Bregman procedure is introduced: such a version allows to have a minor computational cost and maintains the same theoretical features of the exact version. Finally, in the last part, a wide experimentation shows the computational efficiency of the inexact Bregman procedure; furthermore, the three models are compared, showing that in high counts images they provide similar results, while in case of low counts images the Bregman procedure provides reliable restored images. This last consideration is evident not only on test problems, but also in problems coming from Astronomy imaging, particularly in case of High Dynamic Range images, as shown in the final part of the experimental section

A Learned-SVD approach for Regularization in Diffuse Optical Tomography

Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT reconstruction implies the solution of a severely ill-posed inverse problem, for which regularization techniques are mandatory in order to achieve reasonable results. Traditionally, regularization techniques put a variance prior on the desired solution/gradient via regularization parameters, whose choice requires a fine tuning, specific for each case. In this work we explore deep learning techniques in a fully data-driven approach, able of reconstructing the generating signal (optical absorption coefficient) in an automated way. We base our approach on the so-called Learned Singular Value Decomposition, which has been proposed for general inverse problems, and we tailor it to the DOT application. We perform tests with increasing levels of noise on the measure, and compare it with standard variational approaches

A Proximal Approach for Solving Matrix Optimization Problems Involving a Bregman Divergence

International audienceIn recent years, there has been a growing interest in problems such as shape classification, gene expression inference, inverse covariance estimation. Problems of this kind have a common underlining mathematical model, which involves the minimization in a matrix space of a Bregman divergence function coupled with a linear term and a regularization term. We present an application of the Douglas-Rachford algorithm which allows to easily solve the optimization problem

Majorization-Minimization for sparse SVMs

Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular approaches in the machine learning arena. In this work, we investigate the training of SVMs through a smooth sparse-promoting-regularized squared hinge loss minimization. This choice paves the way to the application of quick training methods built on majorization-minimization approaches, benefiting from the Lipschitz differentiabililty of the loss function. Moreover, the proposed approach allows us to handle sparsity-preserving regularizers promoting the selection of the most significant features, so enhancing the performance. Numerical tests and comparisons conducted on three different datasets demonstrate the good performance of the proposed methodology in terms of qualitative metrics (accuracy, precision, recall, and F 1 score) as well as computational cost

Ecotoxicological effects of atmospheric particulate produced by braking systems on aquatic and edaphic organisms.

Vehicles generate particulate matter (PM) in significant amounts as their brake systems wear. These particles can influence air quality and their transport/deposition may affect the edaphic and aquatic ecosystems. As part of the LOWBRASYS H2020 project, new more eco-friendly brake disc and pad formulations were developed. PMs generated from traditional (FM1-BD1) and innovative (FM4-BD2, FMB-BD7) brake systems in bench tests were studied. The PMs' physical/chemical characteristics were preliminarily investigated. To study the possible environmental impact of the nano-micro particulate, we used a battery of ecotoxicological tests. We employed the microalga Pseudokirchneriella subcapitata, the crustacean Daphnia magna and the bacteria Vibrio fischeri as aquatic bioindicators, while for the edaphic ecosystem we used the seeds of Lepidium sativum and Sorghum saccharatum, the nematode Caenorhabditis elegans, the earthworm Eisenia andrei and the ameba Dictyostelium discoideum. The results showed a higher sensitivity of the freshwater organisms exposed to the soluble PM fraction, with respect to the edaphic ones. FM4-BD2 brake formulation was slightly more toxic for algae (200 mg/L) than FM1-BD1 (500 mg/L). The new system FMB-BD7 particulate was not harmful for crustacean survival, and resulted weakly toxic for algal reproduction only at 500 mg/L. The particulate material per se was found to affect the algal reproduction. No toxic effects were found on nematodes, earthworms and seeds up to 1000 mg/L. However, in D. discoideum the reproduction rate was significantly reduced starting from 100 mg/L; and the lysosomal membrane stability showed a relevant alteration also at minimal concentration (0.1 mg/L). The results demonstrated a minimal risk for biodiversity of the particulates from the different brake systems and highlighted a more eco-friendly performance the new brake-pad FMB-BD7. However, the occurrence of sublethal effects should be considered as a possible contribution of the particle toxicity to the biological effects of the environmental pollution. Keywords: Brake discs and pads, Particulate matter, Bioassays, Sublethal effects, Environmental ris

Validation of a high-density microelectrode array for acute brain slice recordings

Microelectrode arrays (MEAs) are employed to study extracellular electrical activity in neuronal tissues. Nevertheless, commercially available MEAs provide a limited number of recording sites and do not allow a precise identification of the spatio-temporal characterization of the recorded signal. To overcome this limitation, high density MEAs (HDMEA), based on CMOS technology, were recently developed and validated on dissociated preparations. The platform enables extracellular electrophysiological recordings from 4096 electrodes arranged in a squared area of 2.7 mm x 2.7 mm with inter-electrode distance of 21 μm at a sampling rate of 7.7 kHz/electrode. Here, we demonstrate the performances of this HDMEA platform for the acquisition of electrophysiological activity from acute brain slices. The unique recording performances and the large recording area of the chip permit the observation of fast propagating activities involving multiple areas. In our experimental paradigm, epileptic-like discharges were induced by treating hippocampal slices with 4-aminopyridine and/ or bicuculline. The HDMEA allowed us to clearly identify epileptic foci and to describe the involvement of cortical and hippocampal circuitries in the generation of the epileptiform activity. Furthermore, the HDMEA can be coupled with conventional extracellular electrodes for both stimulation and recording, giving the opportunity to perform standard short- and long-term plasticity protocols. We also show that HDMEA can be used in combination with fluorescence live imaging techniques such as Voltage Sensitive Dye recordings. The combination of complementary methodologies supports the HDMEA platform validation and paves the way to detailed electrophysiological studies