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

The paper deals with blind source separation by contrast function maximization. A general class of separation criteria valid for both i.i.d. and non i.i.d. sources is exhibited; it is based on third or higher order cross-cumulants between the separator outputs and fixed signals, called references. We show that this approach is applicable not only in a semi-blind context, but also in a completely blind scenario. The most interesting feature concerning our criteria is their quadratic form. It follows a highly simplified optimization procedure which we describe. Simulation results illustrate the validity of our approach, and the appeal of this new class of contrast functions.

Source separation by quadratic contrast functions: a blind approach based on any higher-order statistics

The objective of this paper is the design of adaptive quincunx lifting schemes for lossless compression of multiband images. More precisely, the operators of the lifting scheme are modified according to the local activity of the multivariate input signal. To this respect, a block-based adaptive strategy is adopted: the image is partitioned into a quadtree structure and a couple of optimal operators is assigned to each resulting volumetric segmented block. Our main contribution consists of a suitable quadtree partitioning rule that takes into account simultaneously the spatial and spectral redundancies. Simulations performed on real satellite images show that the proposed adaptive method outperforms the conventional non-adaptive lifting schemes.

Adaptive lifting for multicomponent image coding through quadtree partitioning

Wavelet/wavelet packet decomposition has become a very useful tool in describing nonstationary processes. Important examples of nonstationary processes encountered in practice are cyclostationary processes or almost-cyclostationary processes. In this paper, we study the statistical properties of the wavelet packet decomposition of a large class of nonstationary processes, including in particular cyclostationary and almost-cyclostationary processes. We first investigate in a general framework, the existence and some properties of the cumulants of wavelet packet coefficients. We then study more precisely the almost-cyclostationary case, and determine the asymptotic distributions of wavelet packet coefficients. Finally, we particularize some of our results in the cyclostationary case before providing some illustrative simulations.

/pdf/some-results-on-the-wavelet-packet-decomposition-of-2883098e1m.pdf

Some results on the wavelet packet decomposition of nonstationary processes

Projection-based rank reduction algorithms for multichannel modelling and image compression

Quantization, defined as the act of attributing a finite number of levels to an image, is an essential task in image acquisition and coding. It is also intricately linked to image analysis tasks, such as denoising and segmentation. In this paper, we investigate vector 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 levels, our approach can yield better quality images in terms of SNR, with lower entropy, than conventional optimal quantization methods.

/pdf/a-spatial-regularization-approach-for-vector-quantization-xyokyrjhky.pdf

Jean-Christophe Pesquet

Papers

Source separation by quadratic contrast functions: a blind approach based on any higher-order statistics

Adaptive lifting for multicomponent image coding through quadtree partitioning

Some results on the wavelet packet decomposition of nonstationary processes

Projection-based rank reduction algorithms for multichannel modelling and image compression

A Spatial Regularization Approach for Vector Quantization