Related papers: Slepian Scale-Discretised Wavelets on Manifolds
Wavelets have been shown to be effective bases for many classes of natural signals and images. Standard wavelet bases have the entire vector space $\mathbb R^n$ as their natural domain. It is fairly straightforward to adapt these to…
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…
This paper introduces the unsupervised assignment flow that couples the assignment flow for supervised image labeling with Riemannian gradient flows for label evolution on feature manifolds. The latter component of the approach encompasses…
We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly…
Recovering frequency-localized functions from pointwise data is a fundamental task in signal processing. We examine this problem from an approximation-theoretic perspective, focusing on least squares and deep learning-based methods. First,…
It is known that the continuous wavelet transform of a function $f$ decays very rapidly near the points where $f$ is smooth, while it decays slowly near the irregular points. This property allows one to precisely identify the singular…
Self-supervised learning (SSL) has emerged as a powerful strategy for representation learning under limited annotation regimes, yet its effectiveness remains highly sensitive to many factors, especially the nature of the target task. In…
Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…
In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
The construction of B-spline wavelet bases on nonequispaced knots is extended to wavelets that are piecewise segments from any combination of smooth functions. The extended wavelet family thus provides multiresolution basis functions with…
Spectral subspaces of a linear dynamical system identify a large class of invariant structures that highlight/isolate the dynamics associated to select subsets of the spectrum. The corresponding notion for nonlinear systems is that of…
Despite the remarkable progress, weakly supervised segmentation approaches are still inferior to their fully supervised counterparts. We obverse the performance gap mainly comes from their limitation on learning to produce high-quality…
This paper develops a discrete theory of real Riemann surfaces based on quadrilateral cellular decompositions (quad-graphs) and a linear discretization of the Cauchy-Riemann equations. We construct a discrete analogue of an antiholomorphic…
This paper investigates a variational model for splines in the image metamorphosis model for the smooth interpolation of key frames in the space of images. The Riemannian manifold of images based on the metamorphosis model defines shortest…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…