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

Nous considerons le probleme de filtrage adaptatif de donnees sismiques composees : de signaux d'interets ("primaires"), de perturbations structurees correspondant a des propagations d'ondes presentant des reflexions multiples ("multiples") et de bruit aleatoire. Ces signaux parasites, tres energetiques, peuvent dissimuler les reflexions primaires interessantes, correspondant aux interfaces entre couches du sous-sol. Elles peuvent etre filtrees a partir de modeles approches qu'il faut adapter en delai, amplitude et frequence. Ce travail permet de contraindre cette adaptation, sous forme de combinaisons de filtres glissants a reponses impulsionnelles finies, a varier lentement en fonction de la profondeur, respectant les variations geologiques attendues. Les approches anterieures pour ce probleme, tres important en sismique reflexion, ne semblent pas prendre en compte de contraintes sur l'adaptation, et peuvent produire des filtres tres mal conditionnes, du fait notamment du caractere passe-bande des donnees sismiques. Cette formulation du probleme permet par ailleurs d'introduire, et de resoudre par optimisation convexe, des a priori de parcimonie des signaux dans des trames d'ondelettes ainsi que de prendre en compte un bruit additif gaussien. Les multiples sont tres bien estimes. La restauration des primaires realisee permet au geophysicien de voir emerger des residus de signal utile, meme en presence de bruit fort.

https://hal.archives-ouvertes.fr/hal-00914637/document

Filtrage de multiples sismiques par ondelettes et optimisation convexe

Proximal methods have been extensively used to find maximum a posteriori (MAP) estimates of unknown images from degraded measurement. Recently, they have been mixed with neural networks (NN) to further improve the reconstruction quality. Two approaches can be distinguished: unfolded NNs, implementing a given iteration number of an optimisation algorithm, and plug-and-play (PnP) algorithms, incorporating NNs in existing optimisation algorithms. Unfolded NNs usually incorporate the measurement operator in the learning process, which can be prohibitive for applications with non-fixed measurement operators. PnP do not have this drawback, but involved NNs still depend on the underlying statistical models (e.g., higher noise level on the measurements requires stronger denoisers). In this work, we propose a PnP algorithm based on forward-backward (FB) iterations, where the learned denoiser is an unfolded NN based on dual-FB iterations. This NN is built to mimic a Gaussian denoiser from a MAP viewpoint. This allows us to introduce a regularisation parameter in the model to tune the regularization strength, similarly to standard variational approaches. This has the advantage of making the learned NN more adaptive to a variety of inverse problem statistical models, without requiring to train the NN for different noise levels.

Dual Forward-Backward Unfolded Network for Flexible Plug-and-Play

We investigate a M-band wavelet decomposition of second order random processes. In particular, we propose an extension of results which are known for the dyadic wavelet transform. The statistical properties of the M-band wavelet coefficients are listed and recursive relations are derived and used to compute their multiscale characteristics. Special attention is also paid to the multiscale analysis of linear parametric models.

M-band wavelet decomposition of second order random processes

Quantization, defined as the act of attributing a finite number of grey-levels to an image, is an essential task in image acquisition and coding. It is also intricately linked to various image analysis tasks, such as denoising and segmentation. In this paper, we investigate quantization combined with regularity constraints, a little-studied area which is of interest, in particular, when quantizing in the presence of noise or other acquisition artifacts. We present an optimization approach to the problem involving a novel two-step, iterative, flexible, joint quantizing-regularization method featuring both convex and combinatorial optimization techniques. We show that when using a small number of grey-levels, our approach can yield better quality images in terms of SNR, with lower entropy, than conventional optimal quantization methods.

/pdf/image-quantization-under-spatial-smoothness-constraints-2pkeaopy4f.pdf

Image quantization under spatial smoothness constraints

Positron emission tomography (PET) is a quantitative imaging modality widely used in oncology, neurology, and pharmacology. The data acquired by a PET scanner correspond to projections of the concentration activity, assumed to follow a Poisson distribution. The reconstruction of images from tomographic projections corrupted by Poisson noise is a challenging ill-posed large-scale inverse problem. Several available solvers use the majorization-minimization (MM) principle, though relying on various construction strategies with a lack of unifying framework. This work fills the gap by introducing the concept of Bregman majorization. This leads to a unified view of MM-based methods for image reconstruction in the presence of Poisson noise. From this general approach, we exhibit three algorithmic solutions and compare their computational efficiency on a problem of dynamic PET image reconstruction, either using GPU or CPU processing.

Jean-Christophe Pesquet

Papers

Filtrage de multiples sismiques par ondelettes et optimisation convexe

Dual Forward-Backward Unfolded Network for Flexible Plug-and-Play

M-band wavelet decomposition of second order random processes

Image quantization under spatial smoothness constraints

A Bregman Majorization-Minimization Framework for Pet Image Reconstruction