相关论文: Optimal whitening and decorrelation

We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are…

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding…

We address the problem of soft color segmentation, defined as decomposing a given image into several RGBA layers, each containing only homogeneous color regions. The resulting layers from decomposition pave the way for applications that…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of…

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson…

We address the problem of decomposing a single image into reflectance and shading. The difficulty comes from the fact that the components of image---the surface albedo, the direct illumination, and the ambient illumination---are coupled…

Linear principal component analysis (PCA) learns (semi-)orthogonal transformations by orienting the axes to maximize variance. Consequently, it can only identify orthogonal axes whose variances are clearly distinct, but it cannot identify…

In functional linear regression, the slope ``parameter'' is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of…

We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…

Real-space refinement of atomic models in macromolecular crystallography or in cryo electron microscopy fits a model to a map obtained experimentally. This requires generating model maps of a limited resolution which moreover may vary from…

Deconvolution, imaging and calibration of data from radio interferometers is a challenging computational (inverse) problem. The upcoming generation of radio telescopes poses significant challenges to existing, and well proven data reduction…

In a fully-Bayesian Functional Principal Components Analysis (FPCA) the principal components are treated as unknown infinite-dimensional parameters. By projecting the functional principal components on a rich orthonormal spline basis, we…

This paper introduces an adaptive filtering process based on shrinking wavelet coefficients from the corresponding signal wavelet representation. The filtering procedure considers a threshold method determined by an iterative algorithm…

Image demosaicking and denoising are the first two key steps of the color image production pipeline. The classical processing sequence has for a long time consisted of applying denoising first, and then demosaicking. Applying the operations…

Colorization is a computer-aided process, which aims to give color to a gray image or video. It can be used to enhance black-and-white images, including black-and-white photos, old-fashioned films, and scientific imaging results. On the…

We propose an algorithmic framework for computing sparse components from rotated principal components. This methodology, called SIMPCA, is useful to replace the unreliable practice of ignoring small coefficients of rotated components when…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

In this paper we describe a self-contained method for performing the spectral-imaging deconvolution of X-ray data on clusters of galaxies observed by the ASCA satellite. Spatially-resolved spectral studies of data from this satellite…