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.

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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

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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

Wavelet decompositions based on lifting schemes have been widely used in image coding. Generally, the efficiency of such compression methods strongly depends on the design of the lifting operators, namely the prediction and update filters. To improve their performance, we propose in this paper to optimize these filters by resorting to two learning strategies. In the first one, classical Fully Connected Networks (FCNs) are exploited to perform the prediction and update. In the second approach, we develop an adaptive learning method that takes into account the input image, yielding a dynamical model of FCN. Experimental results, carried out on the standard Challenge Learned Image Compression (CLIC) dataset, show the benefits that can be drawn from the proposed approaches compared to conventional ones.

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Optimized Lifting Scheme Based on A Dynamical Fully Connected Network for Image Coding

Soft thresholding plays a central role in the various signal processing problems in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties. We then propose a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems, and establish the strong convergence of a proximal thresholding algorithm to solve it. Numerical applications to signal recovery are demonstrated.

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Sparse signal recovery by iterative proximal thresholding

PMRI is a fast imaging technique that allows reconstruction of full FoV images based on undersampled k-space data acquired using multiple reciever coils with complementary sensitivity profiles. It enables the acquisition of highly resolved images either in space or in time, which is of particular interest in applications like neuroimaging. These improvements are counterbalanced by a degraded SNR and the presence of artifacts that depend on the reconstruction algorithm. To improve the performance of the widely used SENSE algorithm, regularization in the wavelet domain has been efficiently investigated. In this paper, we illustrate the gain induced by such a regularization in terms of statistical impact on fMRI data analysis using a fast-event related protocol. Our results show that the reconstruction algorithm has a dramatic impact on the statistical sensitivity in fMRI and that the proposed method outperforms classical SENSE reconstruction at the subject-level using different acquisition setups.

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Impact of the parallel imaging reconstruction algorithm on brain activity detection in fMRI

Total variation has been used exclusively as an objective in the formulation of image deconvolution problems. In this paper, we propose an alternative framework in which total variation is used as a constraint. In contrast with the standard approach, this framework requires an a priori bound on the total variation of the original image, while no a priori information on the noise is necessary. Furthermore, it places no limitation on the incorporation of additional constraints in the recovery process and can be solved efficiently via powerful block-iterative methods.

Image deconvolution with total variation bounds

Algorithms based on the minimization of the Total Variation are prevalent in computer vision. They are used in a variety of applications such as image denoising, compressive sensing and inverse problems in general. In this work, we extend the TV dual framework that includes Chambolle's and Gilboa-Osher's projection algorithms for TV minimization in a flexible graph data representation by generalizing the constraint on the projection variable. We show how this new formulation of the TV problem may be solved by means of a fast parallel proximal algorithm, which performs better than the classical TV approach for denoising, and is also applicable to inverse problems such as image deblurring.

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Jean-Christophe Pesquet

Papers

Optimized Lifting Scheme Based on A Dynamical Fully Connected Network for Image Coding

Sparse signal recovery by iterative proximal thresholding

Impact of the parallel imaging reconstruction algorithm on brain activity detection in fMRI

Image deconvolution with total variation bounds

Dual constrained TV-based regularization