Related papers: Compactly Supported Shearlets
We give two low-complexity algorithms, one for dimensionality reduction and one for dimensionality increase, which are applicable to any dataset, regardless of whether the set has an intrinsic dimension or not. The corresponding methods…
We provide a statistical analysis of the ability of digitized continuous shearlet systems to detect objects embedded in white noise. We analyze the possibility to subsample the shearlet transform and obtain a subset of significantly reduced…
A study of correlations in tractable multiparticle cascade models in terms of wavelets reveals many promising features. The selfsimilar construction of the wavelet basis functions and their multiscale localization properties provide a new…
This paper introduces a novel framework for single-pixel imaging via compressive sensing (CS) in shift-invariant (SI) spaces by exploiting the sparsity property of a wavelet representation. We reinterpret the acquisition procedure of a…
An effective way to model the complex real world is to view the world as a composition of basic components of objects and transformations. Although humans through development understand the compositionality of the real world, it is…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
Significant progress has been made in training large generative models for natural language and images. Yet, the advancement of 3D generative models is hindered by their substantial resource demands for training, along with inefficient,…
A recent cutting-edge topic in multimodal modeling is to unify visual comprehension and generation within a single model. However, the two tasks demand mismatched decoding regimes and visual representations, making it non-trivial to jointly…
The generation of chiral laser emission offers promising opportunities for modern photonic applications and the study of chiral light-mater interactions. Despite the great process made in recent years, the direct generation of chiral lasers…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
Implicit Neural Representations (INRs) have emerged in the last few years as a powerful tool to encode continuously a variety of different signals like images, videos, audio and 3D shapes. When applied to 3D shapes, INRs allow to overcome…
Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
We present the source separation framework SCARLET for multi-band images, which is based on a generalization of the Non-negative Matrix Factorization to alternative and several simultaneous constraints. Our approach describes the observed…
A new representation of splines that targets efficiency in the analysis of functional data is implemented. The efficiency is achieved through two novel features: using the recently introduced orthonormal spline bases, the so-called {\it…
Recently, various convolutions based on continuous or discrete kernels for point cloud processing have been widely studied, and achieve impressive performance in many applications, such as shape classification, scene segmentation and so on.…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
Multimodal learning is an essential paradigm for addressing complex real-world problems, where individual data modalities are typically insufficient to accurately solve a given modelling task. While various deep learning approaches have…