Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

/pdf/distributed-optimization-and-statistical-learning-via-the-8s9gtddw0d.pdf

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Summary Background Since December, 2019, Wuhan, China, has experienced an outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epidemiological and clinical characteristics of patients with COVID-19 have been reported but risk factors for mortality and a detailed clinical course of illness, including viral shedding, have not been well described. Methods In this retrospective, multicentre cohort study, we included all adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Jinyintan Hospital and Wuhan Pulmonary Hospital (Wuhan, China) who had been discharged or had died by Jan 31, 2020. Demographic, clinical, treatment, and laboratory data, including serial samples for viral RNA detection, were extracted from electronic medical records and compared between survivors and non-survivors. We used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death. Findings 191 patients (135 from Jinyintan Hospital and 56 from Wuhan Pulmonary Hospital) were included in this study, of whom 137 were discharged and 54 died in hospital. 91 (48%) patients had a comorbidity, with hypertension being the most common (58 [30%] patients), followed by diabetes (36 [19%] patients) and coronary heart disease (15 [8%] patients). Multivariable regression showed increasing odds of in-hospital death associated with older age (odds ratio 1·10, 95% CI 1·03–1·17, per year increase; p=0·0043), higher Sequential Organ Failure Assessment (SOFA) score (5·65, 2·61–12·23; p Interpretation The potential risk factors of older age, high SOFA score, and d-dimer greater than 1 μg/mL could help clinicians to identify patients with poor prognosis at an early stage. Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future. Funding Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences; National Science Grant for Distinguished Young Scholars; National Key Research and Development Program of China; The Beijing Science and Technology Project; and Major Projects of National Science and Technology on New Drug Creation and Development.

Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study

In this paper, we are interested in the recovery of an unknown signal corrupted by a linear operator, a nonlinear function, and an additive Gaussian noise. In addition, some of the observations contain outliers. Many robust data fit functions which alleviate sensitivity to outliers can be expressed as piecewise rational functions. Based on this fact, we reformulate the robust inverse problem as a rational optimization problem. The considered framework allows us to incorporate nonconvex constraints such as unions of subsets. The rational problem is then solved using recent optimization techniques which offer guarantees for global optimality. Finally, experimental results illustrate the validity of the recovered global solutions and the good quality of the reconstructed signals despite the presence of outliers.

/pdf/robust-reconstruction-with-nonconvex-subset-constraints-a-41akf17cn5.pdf

Robust Reconstruction with Nonconvex Subset Constraints: A Polynomial Optimization Approach

Un petit tutoriel sur les méthodes primales-duales pour l'optimisation convexe

The point spread function (PSF) of imaging systems plays an essential role in image reconstruction. In the context of confocal microscopy, optical performance degrades towards the edge of the field of view. In confocal macroscopy, the related artifacts are even stronger, as the field of view is much larger. Because the related PSFs are strongly spatially variant, it is essential to be able to model them with few parameters. The field aberrations in fluorescence macroscopy were observed to be symmetrical and to increase with the distance from the center of the field of view. In this paper we propose an experiment and an optimization method for assessing the center of the field of view. The obtained results constitute an important step towards reducing the number of parameters in macroscopy PSF models.

Spatially variant PSF modeling in confocal macroscopy

In this paper, we are interested in designing lossless coders for a class of multispectral images. More precisely, we consider quincunx sampled images such as those encountered in new generation satellite imaging systems. Our approach exploits both the spatial and the spectral correlations existing in these images by applying block-adaptive predictors. A clustering algorithm is applied to the spectral bands of the original image in order to compute optimal predictors within each group of blocks. Simulation tests carried out on natural multicomponent images show that the proposed adaptive interband differential prediction outperforms state-of-art lossless coders.

A block-based predictive lossless cod for quincunx multispectral images

We introduce a neural network architecture to solve inverse problems linked to a onedimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function which consists of the sum of a data-fidelity function and a Tikhonov-type regularization function. The robustness of this inversion method with respect to a perturbation of the input is theoretically analyzed. Ensuring robustness is consistent with inverse problem theory since it guarantees both the continuity of the inversion method and its insensitivity to small noise. The latter is a critical property as deep neural networks have been shown to be vulnerable to adversarial perturbations. One of the main novelties of our work is to show that the proposed network is also robust to perturbations of its bias. In our architecture, the bias accounts for the observed data in the inverse problem. We apply our method to the inversion of Abel integral operators, which define a fractional integration involved in wide range of physical processes. The neural network is numerically implemented and tested to illustrate the efficiency of the method. Lipschitz constants after training are computed to measure the robustness of the neural networks.

Jean-Christophe Pesquet

Papers

Robust Reconstruction with Nonconvex Subset Constraints: A Polynomial Optimization Approach

Un petit tutoriel sur les méthodes primales-duales pour l'optimisation convexe

Spatially variant PSF modeling in confocal macroscopy

A block-based predictive lossless cod for quincunx multispectral images

Inversion of Integral Models: a Neural Network Approach