Related papers: Shapelets: I. A Method for Image Analysis
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
The ability to decompose a signal in an orthonormal basis (a set of orthogonal components, each normalized to have unit length) using a fast numerical procedure rests at the heart of many signal processing methods and applications. The…
In this article we give an account of a method of smoothing spatial inhomogeneous data sets by using wavelet reconstruction on a regular grid in an auxilliary space onto which the original data is mapped. In a previous paper by the present…
Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the…
In most practical situations, the compression or transmission of images and videos creates distortions that will eventually be perceived by a human observer. Vice versa, image and video restoration techniques, such as inpainting or…
The precision study of dark matter using weak lensing by large scale structure is strongly constrained by the accuracy with which one can measure galaxy shapes. Several methods have been devised but none have demonstrated the ability to…
Obtaining constraints from the largest scales of a galaxy survey is challenging due to the survey mask allowing only partial measurement of large angular modes. This scatters information from the harmonic-space 2-point function away from…
The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most…
Single-pixel imaging is an indirect imaging technique which utilizes simplified optical hardware and advanced computational methods. It offers novel solutions for hyper-spectral imaging, polarimetric imaging, three-dimensional imaging,…
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
We suggest a set of morphological measures that we believe can help in quantifying the shapes of two-dimensional cosmological images such as galaxies, clusters, and superclusters of galaxies. The method employs non-parametric morphological…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
In medical image analysis, constructing an atlas, i.e. a mean representative of an ensemble of images, is a critical task for practitioners to estimate variability of shapes inside a population, and to characterise and understand how…
We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…
Advances in instrumentation and computation have enabled increasingly sophisticated tomographic reconstruction methods. However, existing evaluation practices -- often based on simple phantoms and global image metrics -- are limited in…
Weak gravitational lensing is a very sensitive way of measuring cosmological parameters, including dark energy, and of testing current theories of gravitation. In practice, this requires exquisite measurement of the shapes of billions of…
A set of orthogonal polynomials on the unit disk $B(0,1)$ known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of…