相关论文: Topological IIR Filters over Simplicial Topologies…
Topological filters via sheaves generalize the classical linear translation-invariant filter theory by attaching the filter computation locally to a simplicial topological space. This paper develops topological filters for causal signal…
A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their…
The design of digital filters is a fundamental process in the context of digital signal processing. The purpose of this paper is to study the use of $\lp$ norms (for $2 < p < \infty$) as design criteria for digital filters, and to introduce…
Recursive filters are treated as linear time-invariant (LTI) systems but they are not: uninitialised, they have an infinite number of outputs for any given input, while if initialised, they are not time-invariant. This short tutorial…
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…
This paper introduces a systematic approach to address the topological path identification (TPI) problem in power distribution networks. Our approach starts by listing the DSO's raw information coming from several sources. The raw…
An interval translation map (ITM) is a map $T \colon I \to I$ defined as a piecewise translation on a finite partition of an interval $I$ into $r \ge 2$ subintervals. Unlike classical interval exchange transformations (IETs), the images of…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Topological Insulators (TIs) exhibit exciting optical properties, which opens up a new pathway to generate ultrashort pulses from fiber lasers. Layered TIs display distinct saturable absorption property due to excited state absorption, as…
Interactive Image Retrieval (IIR) aims to retrieve images that are generally similar to the reference image but under the requested text modification. The existing methods usually concatenate or sum the features of image and text simply and…
The main focus of this paper is a nonparametric filtering technique for the estimation of interface geometry in bulk materials obtainable from modern imaging measurements. The filtering methodology relies on an assumed hierarchy of…
In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We…
Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
Porous materials exhibit vast structural diversity and support critical applications in gas storage, separations, and catalysis. However, predictive modeling remains challenging due to the multiscale nature of structure-property…
Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the…