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

/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

Complex-valued data are encountered in many application areas of signal and image processing. In the context of optimization of functions of real variables, subspace algorithms have recently attracted much interest, due to their efficiency in solving large-size problems while simultaneously offering theoretical convergence guarantees. The goal of this paper is to show how some of these methods can be successfully extended to the complex case. More precisely, we investigate the properties of the proposed complex-valued Majorize-Minimize Memory Gradient (3MG) algorithm. An important practical application of these results arises for image reconstruction in Parallel Magnetic Resonance Imaging (PMRI). Comparisons with existing optimization methods confirm the good performance of our approach for PMRI reconstruction.

A complex-valued Majorize-Minimize Memory Gradient method with application to parallel MRI

A parallel proximal splitting method for disparity estimation under illumination variation

In this paper, we develop a novel second-order method for training feed-forward neural nets. At each iteration, we construct a quadratic approximation to the cost function in a low-dimensional subspace. We minimize this approximation inside a trust region through a two-stage procedure: first inside the embedded positive curvature subspace, followed by a gradient descent step. This approach leads to a fast objective function decay, prevents convergence to saddle points, and alleviates the need for manually tuning parameters. We show the good performance of the proposed algorithm on benchmark datasets.

A Two-Stage Subspace Trust Region Approach for Deep Neural Network Training

Three-dimensional (3D), in vivo and in live imaging of living samples with a sub-micrometer resolution is a current necessity for biomedical researches which corresponds to a hot topic for microscopy engineers. It is likely that the role of computational approaches is yet underestimated and underused in 3D-microscopy. This paper is an illustration of the fundamental role that could be played by such strategies. Usual imaging depths in biomedical microscopy reach few hundreds of micrometers in optimal conditions when multiphoton approaches are favored. However, light scattering and absorption still damage image quality, especially as imaging depth increases. Our approach rests on the multi-parametric 3D-PSF estimation of the true 3DGaussian model of the PSF along multi-millimeter depth. Image acquisition in MPM generates stacks of 2D images constituting an overall 3D-image. 3D-volumes of images containing a single object are selected and isolated all along the depth using automatic morphological tools. Finally, our computational 3DGaussian shape-fitting algorithm named FIGARO is applied on each individual PSF and quantify PSF full-width at half maximum (FWHM) in the 3 dimensions simultaneously with PSF tilt angles. FWHM evolution in the 3 dimensions along the 2 mm depth highlights a highly significant effect of spherical aberrations. Starting from standard values of PSF measured at sample top compared to what expected in MPM, we show an increase with a factor three of the PSF FWHM in axial plane when the sample bottom is reached, and no modification of PSF dimensions in lateral plane all along the depth. The main direction of the PSF shows a convergence toward a focal point that will be discussed

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Multi-parametric 3D-point-spread function estimation in deep multiphoton microscopy with an original computational strategy dedicated to the reconstruction of muscle images

Point spread function (PSF) plays an essential role in image reconstruction. In the context of confocal microscopy, optical performance degrades towards the edge of the field of view as astigmatism, coma and vignetting. Thus, one should expect the related artifacts to be even stronger in macroscopy, where the field of view is much larger. The field aberrations in macroscopy fluorescence imaging system was 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 a step towards reducing the number of parameters in macroscopy PSF model.

Jean-Christophe Pesquet

Papers

A complex-valued Majorize-Minimize Memory Gradient method with application to parallel MRI

A parallel proximal splitting method for disparity estimation under illumination variation

A Two-Stage Subspace Trust Region Approach for Deep Neural Network Training

Multi-parametric 3D-point-spread function estimation in deep multiphoton microscopy with an original computational strategy dedicated to the reconstruction of muscle images

Spatially variant PSF modeling in confocal macroscopy