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

Convex Analysisの二,三の進展について

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD).We present two distribution free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.

/pdf/a-kernel-two-sample-test-2mr8hwo4ml.pdf

A kernel two-sample test

On robust estimation of the location parameter

1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

Introduction to Wavelets and Wavelet Transforms: A Primer

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Aiming at overcoming the shortcomings of existing wavelet denoising methods, we propose an image denoising algorithm based on wavelets on invariant sets. These wavelets, in comparison with classical wavelets, have the following features: they have vanishing moments of a high order and at the same time a short filter length. Moreover, boundary extension normally required for classical wavelets in wavelet transformations is not needed for wavelets on invariant sets. We identify a class of discrete orthogonal transforms, such as the discrete cosine transform of the second type, the Hadamard transform, the Slant transform and the Hartley transform with the filters of wavelets on invariant sets. This viewpoint gives us an insightful understanding of these transforms in the framework of the multiscale analysis. In turn, it leads to more efficient algorithms to image denoising. We demonstrate the performance of our algorithm on images with varying noise levels. The numerical results show that our proposed algori...

Filters of wavelets on invariant sets for image denoising

Biorthogonal multivariate filter banks from centrally symmetric matrices

Dual Cones, Constrained n-Convex Lp-Approximation, and Perfect Splines

The purpose of this paper is to investigate the ability of the infimal convolution regularization in curing the staircasing artifacts of the TV model in the SPECT reconstruction. We formulate the problem of SPECT reconstruction with the infimal convolution regularization as a convex three-block optimization problem and characterize its solution by a system of fixed-point equations in terms of the proximity operator of the functions involved in its objective function. We then develop a novel fixed-point proximity algorithm based on the fixed-point equations. Moreover, we introduce a preconditioning matrix motivated by the classical MLEM (maximum-likelihood expectation maximization) algorithm. We prove convergence of the proposed algorithm. The numerical results are included to show that the infimal convolution regularization is capable of effectively reducing the staircasing artifacts, while maintaining comparable image quality in terms of the signal-to-noise ratio and coefficient recovery contrast. Mathematics subject classification: 68U10, 49Q20.

http://www.global-sci.org/jcm/volumes/v34n6/pdf/346-626.pdf

Reducing Staircasing Artifacts in SPECT Reconstruction by an Infimal Convolution Regularization

/pdf/asymptotic-error-analysis-of-a-quadrature-method-for-2748d3elpc.pdf

Yuesheng Xu

Papers

Filters of wavelets on invariant sets for image denoising

Biorthogonal multivariate filter banks from centrally symmetric matrices

Dual Cones, Constrained n-Convex Lp-Approximation, and Perfect Splines

Reducing Staircasing Artifacts in SPECT Reconstruction by an Infimal Convolution Regularization

Asymptotic Error Analysis of a Quadrature Method for Integral Equations with Green's Function Kernels